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DeWitt B.S. — The global approach to quantum field theory (Vol. 1) |
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Предметный указатель |
, generators of 102 253
-function for model 925
-function for quantum electrodynamics 735
-function for Yang — Mills field 760
977
977
978
978
(n-1)-sphere, volume of 1018
A-numbers 977
Absolute invariants 25
Accelerating detector 622ff
Action function (Hamilton’s principal function) 214
Action functional 13ff
Adjoint of a linear operator 1002
Advanced Green’s function 36
Advanced Green’s function for “in-in” formalism 668
Analytic continuation in dimension 1018ff
Analytic continuation in dimension in presence of Dirac matrices 1035—1037
Analytic continuation in dimension, axioms for 1019
Analytic continuation in dimension, change of integration order 1030
Analytic continuation in dimension, integrals of tensors 1028
Analytic continuation in dimension, integration over Minkowski spacetime 1031ff
Angular momentum tensor 108
Anomalous magnetic moment 747ff
Anti-fields 22
Antisupercommutator 1004
Antisupersymmetric matrix 986
Antisymmetric tensor field (massive) 880ff
Antisymmetric tensor field (massive), action functional for 880
Antisymmetric tensor field (massive), Feynman propagator for 881
Antisymmetric tensor field (massive), field equation for 880
Antisymmetric tensor field (massive), mode functions for 881—882
Antisymmetric tensor field (massive), polarization tensors for 882
Antisymmetric tensor field (massive), space inversion of 714
Antisymmetric tensor field (massive), time reversal of 723
Antisymmetric tensor field (massless) 969ff
Antisymmetric tensor field (massless), equivalence to massless scalar field 974—975
Antisymmetric tensor field (massless), gauge transformations of 969
Antisymmetric tensor field (massless), ghost operators for 970
Antisymmetric tensor field (massless), linear dependence of flow vectors 969
Antisymmetric tensor field (massless), mode functions for 971
Apparatus inertia 118
Arrow of time, decoherence is independent of 202 208—209
Associative law of multiplication, possible failure of in condensed notation 11
Asymptotic fields, classical 73ff
Asymptotic fields, quantum 42Iff
asymptotic freedom 760
Asymptotic invariants 74
Asymptotic invariants, Peierls bracket for 77
Asymptotic states 422ff
Atomic level shifts 752—753
Auxiliary mass 548 555
Axial gauge (deficiencies of) 772
Background field for finite disturbances 64
Background field for reduced effective action 495
Background field, stationary background 292 360—1
Bare vertex functions 27
Batalin — Vilkovisky (BV) equation 23 473
Batalin — Vilkovisky (BV) equation, identities satisfied by the BV bracket 1008
Batalin — Vilkovisky (BV) equation, solubility of 1006ff
Becchi — Rouet — Stora — Tyutin (BRST) transformation 477
Berezin integration 980
Black holes formed by collapse 646ff
Black holes formed by collapse, Bogoliubov coefficients for 651ff
Black holes formed by collapse, decay of 658—659
Black holes formed by collapse, Hawking radiation from 656
Black holes formed by collapse, luminosity of 658
Black holes formed by collapse, pair production by 654—655
Black holes formed by collapse, problem of information loss 659—660
Black holes formed by collapse, temperature and entropy of 657
Black holes formed by collapse, Wightman function for 655—656
Black holes formed by collapse, “in” mode functions for 646ff
Black holes formed by collapse, “out” mode functions for 649ff
Body of a supermanifold 998
Body of a supernumber 976
Bogoliubov coefficients 379
Bogoliubov coefficients between Rindler and Minkowski mode functions 609ff
Bogoliubov relations 380
Bogoliubov, Parasink, Hepp (BPH) method 700ff
Bohr and Rosenfeld 122 125
Bose oscillator 849ff
Bose oscillator, coherent states for 850
Bose oscillator, energy eigenfunctions of 860—861
Bose oscillator, Feynman propagator for 859
Bose oscillator, functional integral for 857—858
Bose oscillator, mode functions for 850
Boulware vacuum 639
Boulware vacuum, reaction of a monopole detector to 646
C-numbers 977
Canonical transformations 707—709
Canonical transformations in the quantum theory 712
Cartan — Killing metric 536
Cartan — Killing metric for the Lorentz group 538
Cartan — Maurer invariant 773
Cartan — Maurer invariant, evaluation of 774ff
Cauchy problem for Jacobi fields 56ff
Caustics 234 280
Changing topology 11
Charge conjugation 726
Charge group 82
Charge group for Yang — Mills field 769
Charges (conserved) 81
Charges (conserved) in presence of external fields 98
Charges (conserved), flow invariance of 83 99
Charges (conserved), Peierls bracket of 82 90 92 98
Chern number 781
Chern — Simons secondary characteristic 778
Chiral anomaly 582
Chiral anomaly, heat kernal and zeta function derivation of 568ff
Chiral coupling 568
Chiral coupling, noninvariance under space inversion 711
Chiral coupling, noninvariance under time reversal 721
Chronological ordering operator 166
Chronological product 167
Chronological product, chronological products involving 177
Classical dynamical system 3ff
Classical dynamical system, trajectory or history of 3
Closed-time-path formalism see “In—in” formalism
Cluster decomposition principle 439—40
Coarse graining 202
Coherent Green’s function 42ff
Coherent Green’s function, use of in theory of finite disturbances 61ff
Coherent states (or relative vacua) 432
Coherent states (or relative vacua) for Fermi doublet 825—826
Coherent states (or relative vacua) for Fermi oscillator 842
Coherent states (or relative vacua) for Вose oscillator 850
Coincidence limits 277ff 282 284—285 533—534 536
Collapse of state vector 158
Combination law for path integrals 229
Comma notation for differentiation 8
Commutation law for functional differentiation 8—9
Compact universes and linearization constraints 95ff
Compensation term in measurement theory 122
Condensed notation 9ff
Conditional invariants 25
Configuration space 3
Confinement (evidence for) 766—767
Conformal charges 111—112
Conformal flatness 1038ff
Conformal flatness in dimensions greater than three 1040—1041
Conformal flatness in three dimensions 1040
Conformal flatness in two dimensions 1039
Conformal flatness, spacetimes of isotropic curvature 1042
Conformal group, global 110ff
Conformal group, local 109
Conformal Killing vector fields 110ff
Conformally invariant scalar field 318
Conformally invariant scalar field, trace anomaly for 563
Conformally invariant spinor field 352
| Conformally invariant spinor field, trace anomaly for 566—567
Conjugate points 234 266—267 271 273
Connection on a principal bundle 4
Connection on space of gauge field histories 457
Connection on space of gauge field histories for “in-in” formalism 677
Conservation laws 78ff
Conserved currents 80
Contravariant vector operators 180—181
Coordinate indices 341
Correlation functions 411
Counter terms 409
Counter terms, general theory of 700ff
Counter terms, precise definition of 702ff
Counter terms, real valuedness of 419—420
Covariant differentiation with respect to time 254—255
Covariant functional differentiation 255ff
Covariant variation 253—254
Covariant vector operators 181—182
CP invariance 726ff
Creation and annihilation operators, bosonic 324
Creation and annihilation operators, fermionic 368ff
Current algebra 452ff
Current density 80
Current operator 452
Current operator, finiteness of 454
Current operator, physical renormalization of 594ff
Current operator, vacuum expectation value of 594
de Rham cohomology relation to momentum operator 191
de Rham cohomology relation to path integrals 223ff
Decoherence function 203ff
Decoherence of high inertia system 196ff
Decoherence of high inertia system, independent of arrow of time 202
Decoherence of low inertia system 158
Delta function 7
Delta function on 981
Delta function on 980
Delta function, fermionic delta function 372
Delta function, weight of 7
Density operator 158 195 198ff
Detectors 620ff
Detectors, accelerating detectors 622ff
Detectors, monopole detector 620—621
Diffeomorphism group 101ff
Diffeomorphism group, structure constants of 103
Dimensional regularization 547ff
Dimensional regularization in momentum space 689ff
Dimensional regularization of vacuum persistence amplitude for scalar field 547ff
Dimensional regularization of vacuum persistence amplitude for spinor field 552ff
Dirac matrices 342ff
Dirac matrices, analytic continuation in presence of 1035—1037
Dirac matrices, Majorana representation 353
Dirac operator (twisted) 359—60
Direct ghost interaction term 526
Dynamical equations 13ff
Dynamical equations, operator dynamical equations 168
Dynamical shell 13
Effective action 411ff
Effective action for gauge fields 483
Effective action for quantum electrodynamics 733—734
Effective action for “in-in” formalism 674
Effective action reduced effective action 494ff
Effective action, as the generator of quantum dynamics 432—433
Effective action, gauge invariant effective action 500
Effective action, structure of 414ff
Effective field equations 413 432
Effective field equations for quantum electrodynamics 744—745
Electric field measurement 125ff
electromagnetic field 902ff
Electromagnetic field in a stationary background 396
Electromagnetic field mode functions for 397 904
Electromagnetic field, conformal invariance of 319
Electromagnetic field, gauge transformation of 902
Electromagnetic field, ghost operator for 903
Emergence of classicality 205ff
Energy canonical form for 295 317 357
Energy in scalar field 295 307
Energy production by weak backgrounds 592
Energy-momentum vector 108
Ensemble interpretation of probabilities 153ff
Environmental modulation function 200
Equal likelihood 147
Equations of small disturbances 30
Ergospheres 336
Euclideanization 697ff
Euclideanization boundary conditions in Euclidean functional integrals 698—699
Euclideanization failure of in quantum gravity 699—700
Everett, Hugh, III 140 144
expectation value 152
External gravitational field 101ff
External gravitational field, minimal coupling to 104
external sources 165
External sources at infinity 436
External sources for gauge fields 483
External sources for “in-in” formation 672
Fermi doublet 822ff
Fermi doublet, coherent states for 825—826
Fermi doublet, functional integral for 830—831
Fermi multiplet 835ff
Fermi oscillator 839ff
Fermi oscillator, coherent states for 842
Fermi oscillator, Feynman propagator for 848
Fermi oscillator, functional integral for 844
Fermi oscillator, mode functions for 840
Feynman functional integral or sum over histories 171ff see
Feynman functional integral or sum over histories, integration by parts in 172 174
Feynman propagator 330ff 372ff
Feynman propagator canonical form for bosonic propagator 332 335
Feynman propagator canonical form for fermionic propagator 376
Feynman propagator fibre-adapted coordinates 457ff
Feynman propagator for Bose oscillator 859
Feynman propagator for Fermi oscillator 848
Feynman propagator for fields in nonstationary backgrounds 392
Feynman propagator for fourth order system 866
Feynman propagator for massive antisymmetric tensor field 881
Feynman propagator for massive linear vector field 876
Feynman propagator for massive spin- field 896
Feynman propagator for massive symmetric tensor field 885
Feynman propagator for scalar field in flat spacetime 874
Feynman propagator for spinor field 372ff 888
Feynman propagator for “in-in” formalien 669
Feynman propagator functional integral representation of 394
Feynman propagator, expansions of 542ff
Fibre bundle 3
Fibre bundle principal bundle 4
Fibre bundle trivial bundle 3 6
Fibre bundle twisted bundle 3
Field components 3
Finite disturbances 60ff
Flow invariance 14ff
Flow invariance of conserved charges 83
Flow invariance of conserved currents 99
Flow invariance of the action 14
flows 14ff
Fock spaces (super) bosonic 322ff
Fock spaces (super) fermionic 368ff
Fock spaces (super) “in” and “out” Fock spaces 381
Fock spaces (super), unitary inequivalence of 328 390 613
Fourier transform of 1020
Fourier transform on 981
Fourier transform on 980
Fourth order system 862ff
Fourth order system, Feynman propagator for 866
Fourth order system, fourth order quantum gravity 700 867
Fourth order system, mode functions for 863
Frame indices 341
Frame patch 341
Frame rotations 342
Full propagator 413
Full quantum shell 500
Full vertex functions 414
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