More Simmetries

8/11/2019 More Simmetries

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More simetries4th volumen of simetries in physicsmathematics and chemistry

Well in this case we check more simetries in quantummechanics, electrodynamics, quantum electrodynamics,optics,nuclear physics, particles physics, quantumchromodinamics, and particle physics

Jose luis armenta08/05/2014


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1.-christoffel symbols goes like 312.............................................................................6

2.-diffemorphims if the jacobian exist..........................................................................7

3.-amortguament in legendre functions.......................................................................8

4.-the tensorial product is for each vector of B vector ..............................................9

5.-the valency electrons are in the cliff.........................................................................10

6.-closed cape of neutrons.............................................................................................11

7.-relation between angular and plane momentum......................................................12

8.-for polar coordinates there is a 2 pi ever..................................................................13

9.-pseudo vectors............................................................................................................14

10.-aufbau principle and ferrers diagrams....................................................................15

11.-the forth term ij lagrangian of qcd is gravitational.................................................16

12.-the maxwell boltzmann distribution with n=5 is equal to move the graph in raylegh jeans...........17,18

13.-dual basis as a tensor...............................................................................................17

14.-the gauge bosons goes like 2143 as g f z w............................................................20

15.-lennard jones potential as 3 spheres and sphere and a half.................................21

16.-the chromodynamics going like colors of the rainbow and the clockwise............................22

17.-monotonic barrier and diracs delta.........................................................................23

18.-Gross pietaevskii equation and upper limit null.....................................................24

19.-Bohr magneton and schodinger equation...............................................................25

20.-the pions are only for sincrothrons..........................................................................26

21.-hadamard transformation and rotation matrix........................................................27

22.-spheric simetrie or mirror simetrie...........................................................................28

23.-the graviton as 2 times the dipole electric...............................................................29

24.-the fourier transform and the space of moments and time....................................30

25.-fourier transform and gamma function.....................................................................31

26.-the third term coriolis force is angle by ratio...........................................................32

27.-su(n) has to be greater than 1....................................................................................33


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28.-triangular potential dweell..........................................................................................34

29.-a mesonic simetrie in a hexagonal room..................................................................35

30.-the cape 6 plus 2 is second magic number..............................................................36

31.-spherical coordinates form a matrix 3x3..................................................................37

32.-RLC circuit of diferential equations as a righteous system...................................38

33.-negatives spins and antimatter.................................................................................39

34.-dlembertian matrix form...........................................................................................40

35.-skyrmions as area between a conic..........................................................................41

36.-ricci cuvature have the middle ind ex not repeated. 42

37.-bohr magneton as two mass in a ineslatic colition.................................................43

38.-the baryons positives are upper cero and the others are zero in a potentialdwell.................44

39.-negative and positive as parameter variation...........................................................45

40.-graph of the hermite equation....................................................................................46

41.-graph of the legendre equation..................................................................................47

42.-graph of rodirguez formula.........................................................................................48

43.-grapho of the bessel equation....................................................................................49

44.-multipole variable complex is the perimeter of a circle...........................................50

45.-resistoles theory..........................................................................................................51

46.-a restoring parhabola as paramagnetism.................................................................52

47.-carnot refrigerator and surface tension....................................................................53

48.-free energy of gibbs as 3 molecle energy.................................................................54

49.-free energy of helmotz as 2d energy.. .55

50.-phase portraits of arquimedes spiral........................................................................56

51.-dirac bracket as a force but p or q dot the entire expresion is for alagangrian..................57

52.-poisson structures are empareid...............................................................................58

53.-graph of the jacobi identity........................................................................................59

54.-spherical function of bessel as complex conjugate................................................60


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55.-accelerator gravitational as 1/r2................................................................................61

56.-ovoids as the cartesian plane expantion...................................................................62,63

57.-the magnetic torque pass to be moment...................................................................64

58.-iRLc grapho..................................................................................................................65

59.-hyperbolic sine grapho................................................................................................66

60.-hyperbolic cosine grapho............................................................................................67

61.-there is not negatives logarithms...............................................................................68

62.-grapho of magnetic suceptibility................................................................................69

63.-grapho of the excentricity goes like zandwich i mean 2 3 2....................................70

64.-poisson distribution and capacitance........................................................................71

65.-cauchy distribution as a circle perimeter..................................................................72

66.-grapho of interaction force particles in a time-line..................................................73

67.-nucleons density and capacitance of a cylinder......................................................74

68.-scattering in a spherical simettrie and the term of y...............................................75

69.-why the planes can fly at inverse..............................................................................76


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Christoffel symbols goes like 312

The Christoffel symbols can be derived from the vanishing of the covariant derivative of the metrictensor :

So the i=1 k=2 and l=3 so the metric tensor is cardinal for 12 for example9


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If exist a Diffemorphism is because exist the jacobian

where the and are arbitrary real numbers, and the omitted terms are of degree at

least two in x and y . We can calculate the Jacobian matrix at 0:

We see that g is a local diffeomorphism at 0 if, and only if,


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Amortiguament term in legendre functions

Associated Legendre functions are solutions of the general Legendre equation

where is a amortiguament factor


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tensorial product is first the package of A by every element of B

By choosing bases of all vector spaces involved, the linear maps S and T can be representedby matrices Then, the matrix describing the tensor product is the

Kronecker product of the two matrices. For example, if V , X , W , and Y are all two-dimensionalabove and bases have been fixed for all of them, and S and T are given by the matrices

and ,

respectively, then the tensor product of these two matrices is


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The valence electron are on the cliff

So the carbon have 8 electrons of valence


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Closed cape of neutrons is the same than a magic number

In nuclear physics, a magic number is a number of nucleons (either protons or neutrons) such thatthey are arranged into complete shells within the atomic nucleus. The seven most widely

recognised magic numbers as of 2007 are 2, 8, 20, 28, 50, 82, and126 (sequence A018226 in OEIS). Recently, another magic number 34 has been predicted andexperimentally confirmed. Atomic nuclei consisting of such a magic number of nucleons have ahigher average binding energy per nucleon than one would expect based upon predictions such asthe semi-empirical mass formula and are hence more stable against nuclear decay.


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Relation between angular momentum and tipical momentum or plane momentum

In physics, angular momentum , moment of momentum , or rotational momentum is the amountof rotation an object has, taking into account its mass and shape It is a vector quantity thatrepresents the product of a body's rotational inertia and rotational velocity about a particular axis.The angular momentum of a system of particles (e.g. a rigid body) is the sum of angular momentaof the individual particles. For a rigid body rotating around an axis od simetry (e.g. the blades of aceiling fan), the angular momentum can be expressed as the product of the body's moment ofinertia I , (i.e., a measure of an object's resistance to changes in its rotation velocity) and its angulavelocity :

In this way, angular momentum is sometimes described as the rotational analog of linearmomentum

For the case of an object that is small compared with the radial distance to its axis of rotation,such as a tin can swinging from a long string or a planet orbiting in an ellipse around the sunthe angular momentum can be expressed as its linear momentum, mv,crossed byits position from the origin, r . Thus, the angular momentum L of a particle with respect to somepoint of origin is

So L=rxp


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For a polar coordinates integral in any theorem in this case divergence goes ever from o to 2 pi

To verify the planar variant of the divergence theorem for a region R , where

and R is the region bounded by the circle

The boundary of R is the unit circle, C , that can be represented parametrically by:

such that where s units is the length arc from the point s = 0 to thepoint P on C . Then a vector equation of C is

At a point P on C :

Therefore,


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Pseudo vector at flux electric or magnetic

In physics and mathematics a pseudovector (or axial vector ) is a quantity that transforms likea vector under a proper rotation, but in three dimensions gains an additional sign flip underan improper rotation such as a reflection Geometrically it is the opposite, of equal magnitude but inthe opposite direction, of its mirror image This is as opposed to a true or polar vector, which onreflection matches its mirror image.

In three dimensions the pseudovector p is associated with the cross product of two polarvectors a and b :

so the pseudo vector is the blue line as a flux electric in case but can be magnetic too.


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ferrers diagrams and aufau principle

the ferrer diagram definition is: The partition 6 + 4 + 3 + 1 of the positive number 14 can berepresented by the following diagram; these diagrams are named in honor of noman macleodferrers

8+4+3+1

And the aufbau principle is:
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The forth term in lagrangian of qcd is gravitational

The dynamics of the quarks and gluons are controlled by the quantum chromodynamicsLagrangian. The gauge invariant QCD lagrangian is


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The Maxwell Boltzmann distribution equal to 5 is the Raleigh jeans if we move F(x-a)

The Maxwell botzmann is the green curve

The original derivation by maxwell assumed all three directions would behave in the same

fashion, but a later derivation by boltzmann dropped this assumption using kinetic theory.

The Maxwell Boltzmann distribution (for energies) can now most readily be derived from

the boltzmann distribution for energies (see also the maxwell boltzmann

statitics of statistical mechanics}


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And here we have the Rayleigh jeans:


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Dual basis as a tensor

In linear algebra, given a vector space V with a basis B of vectors indexed by an indexset I (the cardinality of I is the dimensionality of V ), its dual set is a set B of vectors in the sualspace V with the same index set I such that B and B form a biorthogonal system The dual set isalways linearly indepndent but does not necessarily span V . If it does span V , then B is calledthe dual basis for the basis B.

Denoting the indexed vector sets as and being biorthogonalmeans that the elements pair to 1 if the indexes are equal, and to zero otherwise. Symbolically,evaluating a dual vector in V on a vector in the original space V :


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the gauge bosons goes like 2143 as g f z w

were f=1 g=2 w=3 z=4 like this:


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Lennard jones potential as 3 spheres and sphere and a half

The Lennard-Jones potential (also referred to as the L-J potential , 6-12 potential , or 12-6potential ) is a mathematically simple model that approximates the interaction between a pair ofneutral atoms or molecules. A form of the potential was first proposed in 1924 by John lennard

jones The most common expressions of the L-J potential are

As we see one sphere rea is 4 r 2 and 4x3=12 and 4x1.5 =6


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The rotation accord to the clockwise and the quantum chromodynamics

As we see is going like the clockwise and the colors on the electromagnetic radiation roy g biv were

r is red o is orange y is yellow and g is green b is blue and I indig v is violet as this ordered with the

frequency like the fear factory song tha frequency


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Monotic barriers and dirac deltas

For monotonic function in one variable, the range of values is also easy. If is

monotonically rising or falling in the interval , then for all values in the

interval such that , one of the following inequalities applies:

, or .

The range corresponding to the interval can be calculated by applyingthe function to the endpoints and :

Example:


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Gross pietaevskii equation and upper limit null

The Gross Pitaevskii equation (named after Eugene p gross and lev petrovich pietaevskii)describes the ground state of a quantum system of identical bosons using the hartree fockaproximation and the pseudopotential interaction model.

In the Hartree Fock approximation the total wave function of the system of bosons is takenas a product of single-particle functions ,

where is the coordinate of the -th boson.

The pseudopotential model Hamiltonian of the system is given as

As we see the second sumatory is i


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Bohr magneton and schodinger equation

In atomic physics the Bohr magneton (symbol B) is a physical constant and the natural unit forexpressing an electron magnetic dipole moment The Bohr magneton is defined in si units by

And the schodinger equation is:

So boths are similar nevertheless the e in the numerator and the mass is of the electron


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The pions are only for ciclotrons

In particle physics, a pion (short for pi meson , denoted with ) is any of three subatomicparticles: 0, +, and . Each pion consists of a quark and an antiquark and is therefore a meson .

Pions are the lightest mesons and they play an important role in explaining the low-energyproperties of the strong nuclear force.

Pions are unstable, with the charged pions + and decaying with a mean life time of 26nanoseconds and the neutral pion 0 decaying with an even shorter lifetime. Charged pions tend todecay into muons and muon neutrinos, and neutral pions into gamma rays

Example of a synchrotron
http://en.wikipedia.org/wiki/Mesonhttp://en.wikipedia.org/wiki/Mesonhttp://en.wikipedia.org/wiki/Mesonhttp://en.wikipedia.org/wiki/Meson


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Hadamard transformation as rotation matrix

Recursively, we define the 1 1 Hadamard transform H 0 by the identity H 0 = 1, and thendefine H m for m > 0 by:

a rotation matrix is:

In linear algebra, a rotation matrix is a matrixhat is used to perform a rotation in euclidean space.For example the matrix


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The graviton as 2 times the dipole electric

The electric field of the dipole is the negative gradient of the potential, leading to:

In gravitation is 8

So here we have the simetrie


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The quantum moment and the fourier transform

There are several common conventions or defining the Fourier transform of

an integrable function (kiser 1994, p. 29), (rahaman 2011, p. 11). This article willuse the following definition:

, for any real number .

Were the energy is Et and Px depends the space of moments or of the time space


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Fourier transform and gamma function

The gamma function is defined for all complex numbers except the negative integers and zero. Forcomplex numbers with a positive real part, it is defined via a convergent improper integral:

And the Fourier transform is:

There are several common conventions for defining the Fourier transform of

an integrable function (kiser 1994, p. 29), (rahman 2011, p. 11). This article will usethe following definition:

, for any real number .The exponential appear in boths equations here is the simetrie


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The third term in coriolis force is angle by ratio

The apparent motion of a distant star as seen from Earth is dominated by the Coriolis andcentrifugal forces. Consider such a star (with mass m) located at position r , with declination , so

r = | r |

sin(

), where is the Earth's rotation vector. The star is observed to rotate about theEarth's axis with a period of one sidereal day in the opposite direction to that of the Earth's rotation,making its velocity v = r . The fictitious force, consisting of Coriolis and centrifugal forces, is:
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Su(n) were n has to be more than 1

The special unitary group SU(n ) is a real lie group (though not a complex Lie group). Its dimension

as a real manifold is n 2 1 . Topologically, it is compact and simply connected Algebraically, it is

a simple lie group (meaning its lie algebra is simple; see below). The center of SU(n ) is isomorphic

to the cyclic group Zn . Its oyer automorphism group, for n 3 , is Z2, while the outer automorphism

group of SU(2) is the trivial group .


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Triangler Potential dwell


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Simetrie mesonic in a room acoustic

This is what Sheldon cooper on the big bang theory did

Considering a hexagonal room


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Second magic number as cape 6 plus 2

In atomic physics and quantum chemistry , the electron configuration is the distribution

of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals .

For example, the electron configuration of the neon atom is 1s 2 2s 2 2p 6.

In nuclear physics , a magic number is a number of nucleons (either protons or neutrons ) such

that they are arranged into complete shells within the atomic nucleus The seven most widely

recognised magic numbers as of 2007 are 2, 8, 20, 28, 50, 82, and 126


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The spherical coordinate form a matrix


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Rlc circuit diferential system and a righteous system

For the case where the source is an unchanging voltage, differentiating and dividing by L leadsto the second order differential equation:

R

L

C


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Negatives spins and antimatter

j=n=-1+1/2 fr n=-1 or the first boson of antimatter

j=n=-2+1/2 ,n=- 1+1/2 for the second boson of antimatter and sequently.


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matrix form of the dlembertian

In special relativity, electromagnetism and wave theory, the d'Alembert operator (representedby a box: ), also called the d'Alembertian or the wave operator , is the Laplace

operator of minkowski space The operator is named for French mathematician andphysicist jean le ron dlembert. In Minkowski space in standard coordinates ( t , x , y , z ) it hasthe form:


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Skyrmions as a area between a line

In field theory, skyrmions are homotopically non-trivial classical solutions of a nonlinear sigmamodel with a non-trivial target manifold topology hence, they are topological solitons. Anexample occurs in chiral models of mesons, where the target manifold is a homogeneus

space of the structure group

Were SU(N)L by SU(N)N if are linear indepents are a base so a base by a base is a reameanwhile SU(N)diag is a line diagonal


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Ricci curvature is changing the second index (the between index)

In local coordinates (using the Einstein sumatory convection), one has

where

Were here the seconf indexo or between index is k


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Bohr magneton as two mass in a inelastic condition and quantized electron on

the top of the divide

In atomic physics the Bohr magneton (symbol B) is a physical constant and the natural unitfor expressing an electron magnetic dipole moment. The Bohr magneton is defined in SIunits by

We see on the top of the divie a quantized electron by h bar

And in the bottom 2 mass moving together like this:


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Lambda baryons and the potential dwell

The Lambda baryons are a family of subatomic hadron particles that have the symbols 0, +

c, 0b , and +t

Were lambda cero are in the bottom of the potential dwell

Lambda +

Lambda 0


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negative and positive as parameter variation

by the technique of our choice. Once we've obtained two linearly independent solutions to this

homogeneous differential equation (because this ODE is second-order) call

them u1 and u2 we can proceed with variation of parameters.

Now, we seek the general solution to the differential equation which we assume to be

of the form

So u2 is y and is more minus in this time-line

- O +


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Hermite equation as grapho

This eigenvalue problem is called the Hermite equation , although the term is also used for the

closely related equation

U u

The uhas 2 minus and u has to plus


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Rodriguez formula grapho

These solutions for n = 0, 1, 2, ... (with the normalization P n(1) = 1) form a polynomials

sequence of ortogonal polynomials called the Legendre polynomials . Each Legendre

polynomial P n( x ) is an nth-degree polynomial. It may be expressed using rodriguez formula:


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Bessel function grapho

Bessel functions , first defined by the mathematician Daniel benoulli and generalized

by Friedrich bessel, are the canonical solutions y ( x ) of Bessel's diferenttial equaion

for an arbitrary complex number (the order of the Bessel function). The most important

cases are for an integer or half integer

Complex number axis real number axis


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Multipole complex variable and the perimeter of a circle

Were 2xpixr = pixd using the diameter and ratio of circle perimeter


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A paramagnetism is a restoring parabola

Paramagnetism is a form of magnetism whereby certain materials are attracted by an

externally applied magnetic field In contrast with this behavior, diamagnetic materials are

repelled by magnetic fields. Paramagnetic materials include most chemical elements and some

compounds;they have a relative magnetic permeability greater than or equal to 1 (i.e., a

positive magnetic susceptibility ) and hence are attracted to magnetic fields. The magnetic

moment induced by the applied field is linear in the field strength and rather weak. It typically

requires a sensitive analytical balance to detect the effect and modern measurements on

paramagnetic materials are often conducted with a SQUID magnetometer

as this object that means clueding:


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Surface tension and endurance of a refrigerator

In terms of energy: surface tension of a liquid is the ratio of 1. the change in the energy of

the liquid and 2. the change in the surface area of the liquid (that led to the change in energy).

This can be easily related to the previous definition in terms of force :[5] if is the force

required to stop the side from starting to slide, then this is also the force that would keep the

side in the state of sliding at a constant speed (by Newton's Second Law). But if the side is

moving, then 1. the surface area of the stretched liquid is increasing while 2. the applied force

is doing work on the liquid. This means that increasing the surface area increases the energy

of the film. The work done by the force in moving the side by distance is

; at the same time the total area of the film increases by (the factor of 2 is

here because the liquid has two sides, two surfaces). Thus, multiplying both the numerator and

the denominator of by , we get

.

And the carnot refrigerator is:

Where both use the work W it can be explain like a tension of the coldness
http://en.wikipedia.org/wiki/Surface_tension#cite_note-MIT_Non-Newtonian-5http://en.wikipedia.org/wiki/Surface_tension#cite_note-MIT_Non-Newtonian-5http://en.wikipedia.org/wiki/Surface_tension#cite_note-MIT_Non-Newtonian-5http://en.wikipedia.org/wiki/Surface_tension#cite_note-MIT_Non-Newtonian-5


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Gibbs free energy or energy of 3 molecles

Name Symbol Formula Natural variables

Helmholtz free energy

Gibbs free energy
http://en.wikipedia.org/wiki/Helmholtz_free_energyhttp://en.wikipedia.org/wiki/Gibbs_free_energyhttp://en.wikipedia.org/wiki/Gibbs_free_energyhttp://en.wikipedia.org/wiki/Helmholtz_free_energy


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Free energy of helmoltz of 2d energie

Name Symbol Formula Natural variables

Helmholtz free energy

Gibbs free energy
http://en.wikipedia.org/wiki/Helmholtz_free_energyhttp://en.wikipedia.org/wiki/Gibbs_free_energyhttp://en.wikipedia.org/wiki/Gibbs_free_energyhttp://en.wikipedia.org/wiki/Helmholtz_free_energy


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Phase portrait of arquimedes spiral

Phase portrait of van der Pol's equation


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Dirac bracket as a force

Above is everything needed to find the equations of motion in Dirac's modified Hamiltonianprocedure. Having the equations of motion, however, is not the endpoint for theoretical

considerations. If one wants to canonically quantize a general system, then one needs the

Dirac brackets. Before defining Dirac brackets, first-class and second-class constraints need

to be introduced.

We call a function f(q, p) of coordinates and momenta first class if its Poisson bracket with allof the constraints weakly vanishes, that is,

Were phi is the functional of density or a energy if have f by distance I mean the lagrangian


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Poisson strucutures are empaired

A Poisson bracket (or Poisson structure ) on a smooth manifold is a bilinear map

that satisfies the following three properties:

It is ske symettirc: .

It obeys the jacoby identity: .

It obeys Leibniz's Rule with respect to the first

argument: .


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Jacobi identity graph

In a lie algebra, the objects that obey the Jacobi identity are infinitesimal motions. When acting

on an operator with an infinitesimal motion, the change in the operator is the commutator

The Jacobi Identity

A

B

C


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Spherical function of bessel and complex conjugate

The spherical Bessel functions can also be written as ( Rayleigh's formulas ):[22]

Were x can be square root of x of I were I is the imaginary
http://en.wikipedia.org/wiki/Spherical_Bessel_function#cite_note-22http://en.wikipedia.org/wiki/Spherical_Bessel_function#cite_note-22http://en.wikipedia.org/wiki/Spherical_Bessel_function#cite_note-22http://en.wikipedia.org/wiki/Spherical_Bessel_function#cite_note-22


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Gravitatational accelerators

A particle on the exact design trajectory (or design orbit ) of the accelerator only experiences

dipole field components, while particles with transverse position deviation are re-focused

to the design orbit. For preliminary calculations, neglecting all fields components higher than

quadrupolar, an inhomogenic hill diferential equation

So for be gravitational need to be a forc 1/r 2


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The infinite of the Cartesian as ovoid universe

The Cartesian plane is:

And in infinite they close like a ovoid:


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Were the physicall cosmology is :

Also an ovoid


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Righteous system of iRLC grapho

For the case where the source is an unchanging voltage, differentiating and dividing by L leads

to the second order differential equation:

I R

L C


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Hyperbolc sine as zero in the grapho

Hyperbolic sine:

The grapho will be


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The hyperbolic cosine grapho as 2 positive

Hyperbolic cosine:

The grapho will be:

2e

1e


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There is not negatives logarithms

Because it depends of x and so for x not going to negative


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Magnetic suceptiblity and the non inertial frame or reference

1+ m=

And the grapho will be:

1+ m


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Exentricity of central force goes in sandwich

The formula is: e=

Where the index goes like 2 3 2


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Poisson distribution as capacitance

The poisson distribution goes as:

And if the q equal to numerator and V is numerator we have


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Cauchy distribution a perimeter of a circle

The Cauchy distribution goes as:

And thee perimeter of a circle goes as: D=P


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Grapho of interaction particles in a time line

From gravitational to strong


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Nucleons density and capacitance in a cylinder

The nucleons density is:

And the capacitance is c=

Were natural logarithm is the inverse function of an exponential


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Why the planes can fly at inverse

If two persons blow two lines of paper one in front of the another one stand up and the other in

the ground

The atoms goes down

estability

the atoms goes up

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