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Index

Index

Sr,mbols T n)-functions 24, 230 <p(n)-functions 39

A Algebraic - Quantum Theory 22 - SchrMinger Representation 48ff angular momentum density 11 anholonomic coordinates 156 antisymmetric product 56 auxiliary fields 9 Axiomatic Quantum Field Theory 21f

B Bargmann-Wigner equations 106, 138, 154 basis states 252ff -dual 51 - nonorthogonal 51ff, 259 BCS-Hamiltonian 200 - with magnetic fields 216 BCS-model 199ff Bethe-Salpeter equations 106, 129, 175 bipolarons 200 Bochner-Minlos theorem 233 boson transformation 251 bound state equations 107ff, 161, 187 - for Cooper pairs 211 bound states 72ff, 106ff,213ff - Cooper pair 200 - four-fermion 117ff, 161ff - in spinor QED 186 - scalar boson 112ff - vector boson 112ff Brillouin zone 204 BRS-formalism 191

C CAR-algebra 12,25,61 Casimir operators 20 chain rule method 95ff, l3lf, 157, 188f composite particles 72ff, 175, 236ff, 249 connection 155f constraint equation 195f contortion tensor 155 contraction technique 108ff, 162 Cooper pairs 200, 211 correlation functions 237ff coupling

- fermions to gravitation 155ff coupling constant - effective 150f - fermion 140 - for graviton-fermion coupling 174f - for vector bosons 116 coupling theory 130ff - boson-fermion 149ff - graviton-fermion 157ff covariant derivative 155 covariant formalism 21, 45f, 70f, 110ff cyclic vector 55, 223

D decomposition theorem 7 decoupling theorem 90, 135, 158 diquarks 241 Dirac equation - free 124 Dirac spinor 126 direct forces 85ff dressed fermion states 122ff dressed particle - dynamics 102ff - states 73, 99ff, 166ff dual functions 75,101, 138ff, 169f

E effective - boson dynamics 256ff - boson QED 189f - boson theory 77ff, 97ff, 139ff - boson-fermion theory 132ff - Cooper pair dynamics 217 - graviton-fermion theory 157ff - Yang-Mills equations 143f, 150f effective theory - from QCD 237 electric fields - non-abelian 142ff electrical resistance - of superconductors 220ff electromagnetic fields - abelian 177 electron-phonon coupling 220ff energy equation - for BCS-model 202 - for boson fields 80f, 94, 96ff - for Cooper pairs 217

271

272

- for coupling theories 103ff - for graviton-fermion theory 160 - for nonabelian SU(N)-theory 195f - for spinor QED 18lff - for spinorfields - - covariant version 37ff - - one-time version 63ff energy-momentum density 11 equal time limit 70f Euc1iclian space 232 exchange forces 85ff expectation values 145

F fermion determinants 242ff Feynman propator 107 field operator 12 - products 239, 249 field strength 138 Fock space 213, 259 - methods 175 Fock space mappings 251 functional - chain rule 95 - generating 23, 230ff - - for QCD 234 - groundstate 25, 61 - space 23, 25f - - bosonic 77 - - for coupling theories 130, 159, 181 - - one-time version 6lff - states 26, 61, 130, 159, 18lff, 195f functional equation - for BCS-model 202 - for boson fields 80f, 94, 96ff - for coupling theories 103f, 132ff - for graviton-fermion theory 160 - for nonabelian SU(N)-theory 195f - for spinor QED 181ff - for spinorfields - - normaltransformed 40 - - one-time-version 63ff - - time-ordered 36f Functional Quantum Theory 22f Furry picture 190 fusion principle 4, 154

G gauge - Coulomb 175f, 177 - noncovariant 175f -temporal 176, 192f

gauge fields - nonabelian 19lff gauge invariance 204, 218 gauge theories 175ff Gauss law 143f, 192 Gaussian measure 232f General Quantum Field Theory 2lf geometry 153ff Ginzburg-Landau equations 199, 216ff Global Color-Symmetry Model 235 gluon fields 234ff GNS-construction 22f, 54ff - in Liouville space 223 gravitation 153ff graviton 154 - -fermion coupling 171 ff graviton states 117ff Green function 167 - connected gluon 234ff grounds tate - of superconductors 206ff, 214ff

H Haags theorem 21 Hamilton formalism 47ff, 7Of, IIOff hamiltonian density - for spinorfields 11 Han-Nambu quarks 151 hard core - equation 74 - states 73ff Hausdorff formula 63 Heisenberg equation 61, 63, 180 Heisenberg picture 20, 223 Higgs field 199,219 higher order equations 6ff

I indefinite metric 5, 12, 47ff

Index

inequivalent representations 21, 47, 199f, 229f intermecliate states 242 isospin 5

K Krein space 47ff

L Lagrangian -density 10 - effective Yang-Mills 150f - for nonabelian SU(N)-tbeory 192 - for scalar field theory 230

Index

- of spinor QED 176 lattice calculation 244f Lehmann-Kallen spectral theorem 76 leptons 151 Liouville - -von Neumann operator 222 - equation 222 -space 222 Lorentz group siehe Poincare group LSZ-formalism 21

M magnetic fields - non-abelian 142ff matrix elements 23, 202ff - in spinor QED 179ff - transition 125 matrix mechanics 202ff meson operators 241 metric - background 153, 164 - effective 153 - of dressed fermion states 124ff metrical tensor 57, 164, 169, 213f - for one-fermion states 124ff - for three-fermion states 128 - of Riemann-Cartan space 155 molecular field operator 227

N New Tamm-Dancoff method 23, 48 normalization 58, 62 normalordering 145, 146ff, 186f, 196 - functional 43 - nonperturbative 38ff, 68ff

o one-time formalism siehe Hamilton formalism operator product 129,239,249 - anti symmetric 56, 64ff - time-ordered 23,33, 45f

p path integrals 175, 229ff phase structure - of superconductors 227 physical subspace 50 Poincare group 4, 15ff, 28f - generators 16, 29ff polarization cloud 73ff, 122 probability interpretation 50f propagator 39f, 144, 148

- electron-positron 186 - Feynman 107 - free fermion 42f - - one-time version 69f, 75f, 139 -gluon 235 - selfconsistent 200ff - thermal 226

Q quantization 144ff - of nonabelian SU (N)-theory 195f - of spinor QED 179ff - of spinorfields 12f quantum chromodynamics 175f quantum electrodynamics 175f quark fields 234ff

R

273

reduction technique siehe contraction technique regularization 6, 12 - Pauli-Villars IOf renormalization - of effective theories 190f - of spinor QED 179 -vacuum-58 - vertex 44f, 70, 208 representation -Fock 21 - GNS 22f, 54ff - in Liouville space 225ff - inequivalent 21, 47, 199f, 229f - of operators 53ff, 58ff - of states - - contravariant 53 - - covariant 53 resonating group method 259 restriction of measurement 50 Riemann-Cartan space 155

S scalar boson states 112ff scalar product 28, 51, 53, 169f scattering states 90, 112 Schrooinger equation 252, 256, 258f Schrooinger picture 20 Schwinger-Dyson-Freese equations 21, 37, 230,

237 spinorfield 4f - angular momentum density for 11 - energy-momentum density for 11 -equation 5 - hamiltonian density for 11

274

- Lagrangian density for 10 spinors 156 standard model 130 state - algebraic 22 - bound 72ff, 106ff - dressed fermion 122ff - equilibrium 224ff - graviton 117ff, 16lff -mixed 199 - nonequilibrium 225ff -pure 199 - scalar boson 112ff - scattering 90 - thermo- 221 ff - vacuum 16,22, 206ff - vector boson 112ff, 136ff state space 21, 47ff - indefinite 47ff states - sca~tering 112 statistical mechanics 199, 22lff strong mapping 129f superconductivity 199ff - high temperature 200 superindex 14, 178, 194 superspinor 14 symmetry conditions 15ff

T temporal gauge 138f tensor functions - for graviton states 120ff, 163ff tetrads 156 thermodynamic limit 213, 227f thermofields 199 thermostates 199, 221ff thermostatistics 221 ff time evolution 45f time-ordered product 23, 33, 45f torsion tensor 155

U units 151f Usui transformation 254

v vacuum -Fock 252 - state 16, 22, 206ff vector boson states 112ff - one-time version 136ff

vector potential 138 vertex 5 - renormalization 44f, 70, 208

W wave functions 57 weak mapping 72ff - theorem 80f Weinberg-Witten theorem 107 Wick rule 39 Wightman formalism 21

y Yang-Mills dynamics 130ff, 143f

Index

Bibliography - Springer LINK

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