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DeWitt B.S. — The global approach to quantum field theory (Vol. 1)
DeWitt B.S. — The global approach to quantum field theory (Vol. 1)

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Название: The global approach to quantum field theory (Vol. 1)

Автор: DeWitt B.S.

Аннотация:

There exists an anomaly today in the pedagogy of physics. When expounding the fundamentals of quantum field theory physicists almost universally fail to apply the lessons that relativity theory taught them early in the twentieth century. Although they usually carry out their calculations in a covariant way, in deriving their culational rules they seem unable to wean themselves from canonical methods and Hamiltonians, which are holdovers from the nineteenth century and are tied to the cumbersome C + 1)-dimensional baggage of conjugate momenta, bigger-than-physical Hilbert spaces, and constraints. There seems to be a feeling that only canonical methods are "safe"; only they guarantee unitarity. This is a pity because such a belief is wrong, and it makes the foundations of field theory unnecessarily cluttered. One of the unfortunate results of this belief is that physicists, over the years, have almost totally neglected the beautiful covariant replacement for the canonical Poisson bracket that Peierls invented in 1952.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 528

Добавлена в каталог: 27.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$GL (n, \mathbb{R})$, generators of      102 253
$\beta$-function for $\lambda\varphi^4$ model      925
$\beta$-function for quantum electrodynamics      735
$\beta$-function for Yang — Mills field      760
$\mathbb{C}_a$      977
$\mathbb{C}_c$      977
$\mathbb{R}_a$      978
$\mathbb{R}_c$      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 $S_{,i}$      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 $\mathbb{R}_a$      981
Delta function on $\mathbb{R}_c$      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-$\frac{3}{2}$ 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 $(k^2)^r$      1020
Fourier transform on $\mathbb{R}_a$      981
Fourier transform on $\mathbb{R}_c$      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
1 2 3 4
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