1 Symmetry in Physics Kihyeon Cho March 23, 2010 High Energy Physics.

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Symmetry in Physics

Kihyeon Cho

March 23, 2010High Energy Physics

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Line SymmetryLine SymmetryShape has line symmetry when one half

of it is the mirror image of the other half.

Symmetry exists all around us and many people see it as being a thing of beauty.

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Is a butterfly Is a butterfly symmetrical?symmetrical?

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Line Symmetry exists in Line Symmetry exists in nature but you may not nature but you may not

have noticed.have noticed.

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At the  beach there are a At the  beach there are a variety of shells with line variety of shells with line

symmetry. symmetry.

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Under the sea there are also Under the sea there are also many symmetrical objects many symmetrical objects

such as these crabs such as these crabs

and this starfish. and this starfish.

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Animals that have Line Animals that have Line SymmetrySymmetry

Here are a few more great examples of mirror image in the animal kingdom.

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THESE MASKS HAVE THESE MASKS HAVE SYMMETRYSYMMETRY

These masks have a line of symmetry from the forehead to the

chin.  

The human face also has a line of symmetry in the same place.

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Human SymmetryHuman Symmetry

The 'Proportions of Man' is a famous work of art by

Leonardo da Vinci that shows the symmetry of

the human form.

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REFLECTION IN WATERREFLECTION IN WATER

If an object is reflected in water it is considered to

have line symmetry along the waterline.

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The Taj MahalThe Taj Mahal

Symmetry exists in architecture all around the world.  The best known example of this is the

Taj Mahal.

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This photograph shows 2 lines of symmetry. One vertical, the other along the waterline.

(Notice how the prayer towers, called minarets, are reflected in the water and side to side).

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22D Shapes and SymmetryD Shapes and Symmetry

After investigating the following shapes by cutting and folding, we

found:  

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an equilateral triangle has 3 internal angles and 3 lines of symmetry. 

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    a square has 4 internal angles and 4 lines of

symmetry.   

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   a regular pentagon has 5 internal angles and 5 lines of symmetry.

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a regular hexagon has 6 internal angles and 6 lines of symmetry .

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     a regular octagon has 8 internal angles and

8 lines of symmetry.

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Symmetry in Physics Symmetry is the most crucial

concepts in Physics. Symmetry principles dictate the

basic laws of Physics, and define the fundamental forces of Nature.

Symmetries are closely linked to the particular dynamics of the system:

E.g., strong and EM interactions conserve C, P, and T. But, weak interactions violate all of them.

Different kinds of symmetries: Continuous or Discrete Global or Local Dynamical Internal

Examples of Symmetry Examples of Symmetry OperationsOperations

Translation in SpaceTranslation in TimeRotation in SpaceLorentz TransformationReflection of Space (P)Charge Conjugation (C)Reversal of Time (T)Interchange of IdenticalParticlesChange of Q.M. Phase Gauge TransformationsWe focus on this

카이럴 대칭성카이럴 대칭성

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질량이 없는 광자만 카이럴 대칭성을 가진다 .

=> “카이럴 대칭성” 파괴는 질량을 가진다 .Nanbu 노벨상 2008

카이럴 대칭성 => 입자의 진행 방향에 대하여 스핀이 오른쪽 회전  (+1)

스핀이 왼쪽 회전  (-1)

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Conserved Quantities and SymmetriesConserved Quantities and SymmetriesEvery conservation law corresponds to an invariance of the Hamiltonian (or Lagrangian) of the system under some transformation.We call these invariances symmetries. There are 2 types of transformations: continuous and discontinuousContinuous give additive conservation laws

x x+dx or +d examples of conserved quantities:

electric chargemomentumbaryon #

Discontinuous give multiplicative conservation lawsparity transformation: x, y, z (-x), (-y), (-z)charge conjugation (particleantiparticle): e- e+

examples of conserved quantities: parity (in strong and EM)charge conjugation (in strong and EM)parity and charge conjugation (strong, EM, almost always in weak)

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quark anti quark quark anti quark …… decay

Time

We are all the children of Broken symmetry

Just tiny deviation from perfect symmetry seems to have been enough

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Why matter dominant world?

사하로프의  3 조건• Baryon number violation• CP violation• Start from thermal equilibrium

사하로프의  3 조건

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C, P, T violation?

Since early universe…

“Alice effect”

Intuitively…

Boltzmann and S=kln

• C is violated

• P is violated

• T is violated

‘‘CP’CP’란란  무엇인가무엇인가 ??

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Three Important Discrete Symmetries

• Parity, P– Parity reflects a system through the origin. Converts

right-handed coordinate systems to left-handed ones.– Vectors change sign but axial vectors remain unchanged

• x x L L

• Charge Conjugation, C– Charge conjugation turns a particle into its anti-particle

• e e K K

• Time Reversal, T– Changes the direction of motion of particles in time

• t t

• CPT theorem– One of the most important and generally valid theorems in quantum

field theory.– All interactions are invariant under combined C, P and T

transformations.– Implies particle and anti-particle have equal masses and lifetimes

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Parity Quantum NumberParity Quantum Number

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Charge-conjugation Quantum NumberCharge-conjugation Quantum Number

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Charge conjugate and Parity

CP is the product of two symmetries: C for charge conjugation, which transforms a particle into its antiparticle, and P for parity, which creates the mirror image of a physical system.

C

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C P

CP

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C and P violation!C and P violation!

Experiments show that only circled ones exist in Nature C and P are both maximally violated!

But, CP and T seems to be conserved, or is it?

CP

We can test this in 1st generation meson system: Pions

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Mirror symmetry Parity P

All events should occur in exactly the same way whether they are seen directly or in mirror. There should not be any difference between left and right and nobody should be able to decide whether they are in their own world or in a looking glass world

Charge symmetry Charge C

Particles should behave exactly like their alter egos, antiparticles,

which have exactly the same properties but the opposite charge

Time symmetry Time T

Physical events at the micro level should be equally independent whether they occur forwards or backwards in time.

There are 3 different principles of symmetry in the basic theory

for elementary particles

Three principles of symmetry

Violation in 1956 1957

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Mirror symmetry Parity P

All events should occur in exactly the same way whether they are seen directly or in mirror. There should not be any difference between left and right and nobody should be able to decide whether they are in their own world or in a looking glass world

Charge symmetry Charge C

Particles should behave exactly like their alter egos, antiparticles,

which have exactly the same properties but the opposite charge

Time symmetry Time T

Physical events at the micro level should be equally independent whether they occur forwards or backwards in time.

There are 3 different principles of symmetry in the basic theory

for elementary particles

Three principles of symmetry

Violation in 1964 1980

Violation in 1956 1957

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CP and T violation!CP and T violation!

For 37 years, CP violation involve Kaons only! Is CP violation a general property of the SM or is it

simply an accident to the Kaons only?

CP violationT violation

K0 +-

We can test this in 2nd generation meson system: Kaons

Need 3rd generation system: B-mesons and B-factories

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노벨 물리학상  2008

Citation: 5483

Why CP violation?Why CP violation?

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ReferencesReferences

I.S.Cho’s talk (2008)Class P720.02 by Richard Kass (2003)B.G Cheon’s Summer School (2002)S.H Yang’s Colloquium (2001)Class by Jungil Lee (2004)PDG home page

(http://pdg.lbl.gov)Newton (2009.1)