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Baez J.C., Segal I.E., Zhou Z. — Introduction to algebraic and constructive quantum field theory
Baez J.C., Segal I.E., Zhou Z. — Introduction to algebraic and constructive quantum field theory



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Название: Introduction to algebraic and constructive quantum field theory

Авторы: Baez J.C., Segal I.E., Zhou Z.

Аннотация:

The authors present a rigorous treatment of the first principles of the algebraic and analytic core of quantum field theory. Their aim is to correlate modern mathematical theory with the explanation of the observed process of particle production and of particle-wave duality that heuristic quantum field theory provides. Many topics are treated here in book form for the first time, from the origins of complex structures to the quantization of tachyons and domains of dependence for quantized wave equations. This work begins with a comprehensive analysis, in a universal format, of the structure and characterization of free fields, which is illustrated by applications to specific fields. Nonlinear local functions of both free fields (or Wick products) and interacting fields are established mathematically in a way that is consistent with the basic physical constraints and practice. Among other topics discussed are functional integration, Fourier transforms in Hilbert space, and implementability of canonical transformations. The authors address readers interested in fundamental mathematical physics and who have at least the training of an entering graduate student. A series of lexicons connects the mathematical development with the underlying physical motivation or interpretation. The examples and problems illustrate the theory and relate it to the scientific literature.


Язык: en

Рубрика: Физика/Квантовая теория поля/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 291

Добавлена в каталог: 23.07.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute continuity      25
Adjoint      258
Adjunction      19 76 258
Affiliation      103 258
Algebraic topology      22
Annihilates      185
Annihilation operator      48 77
Anti-free-field      166
Antidual      262
Antientire function      67
Antiholomorphic polynomial      66
Antiholomorphic spinor      92
Antimonomial      68
Antisymmetric product      50
Antisymmetrization      48
Autocovariance function      47
Banach algebra      258
BoreI function      259
Borel set      259
Boson field: covariant      40
Boson field: free      3 60
Boson field: general      147
Boson field: regular      66
Brownian motion      23 116 206
C*-algebra      259
C*-algebra, graduated      233
c-number      12
Canonical commutation relations      11
Canonical pair      9 11
Canonical system      118
Cauchy data      106
Cauchy problem      259
Causality      233
Characteristic function      20
Clifford algebra      76 83 259
Clifford algebra, holomorphic antiholomorphic element of      89
Clifford algebra, modefinite      150
Clifford algebra, trace on      83
Clifford relations      76
Clifford system      76
Clifford system, complex      78
Clifford system, dual      82
Closure      260
Cocycle      122 140
Cocycle, essential      140
Coherent state      73
Commutor      260
Complex structure, I OS      260
Complex wave representation      60 64 71
Complex wave representation, of fermion Geld      89
Complexification      35 101
Conditional expectation      30
Configuration spice      12
Conjugation      41
Covariance      18
Creation operator      48 71 77
Creator      185
Degree      175
Differential      262
Dirac equation      162
Dirac spinors      162
Direct product      126
Direct sum      262
Direct sum, of distributions      124
Directed system      262
distribution      17
Distribution, algebraically equivalent      26
Distribution, bounded      23
Distribution, continuous      23
Distribution, derivative of      25
Distribution, ergodic      37
Distribution, ergodically quasi-invariant      38
Distribution, isonormal      18 266
Distribution, metrically equivalent      120
Distribution, normal      17
Distribution, of parameter c      18
Distribution, quasi-invariant      28
Distribution, strict      17
Dual couple      9
Dual couple, multiplicative      216
Dual space      4
Duhamel's principle      263
Entire function      67
Ergodicity      24 37 103
Essential linearity      121
Expectation      17
Extension      263
Fatou's lemma      263
Fermion field, free      78
Field energy      59
Finite propagation velocity      236
Fock — Cook representation      60
FORM      198
Fourier — Wiener transformation      43
Free boson representation      41
Functional integration representation      60
Gauge      170
Generating function      34 141
Graduation      161 233
Grassman algebra      82
Grounded Hilbert space      126
Group      264
Group, conformal      261
Group, extended symplectic      39
Group, general linear      264
Group, Heisenberg      14
Group, orthogonal      271
Group, Poincare      264
Group, symplectic      39
Haag's theorem      248
Harmonic oscillator Hamiltonian      42
Harmonic representation      140
Hausdorff — Young inequality      264
Heisenberg pair      10
Heisenberg relations      5
Heisenberg system      6
Hermite polynomials      265
Hoelder's inequality      266
Holes      163
Integration algebra      19
Interacting field      209 238
Irreducibility      11 266
Isotropic subspace      176
Kernel      197
Klein — Cordon equation      159 200 254
Lagrangian subspace      176
Lie algebra      268
Lie — Trotter formula      26&
Locality      245
Mass      200
Mass hyperboloid      256
Maximal abelian algebra      269
Mean      23
Measurable      17
Measure space      269
Mehler kernel      42
Minkowski space      269
Momentum cutoff      243
Monomial      177
Multiplicative unitary transformation      120
Multiplier      122
n-particle subspace      100
Net      269
Newion — Wigner localization      173
Nonsingular transformation      37
Normal product      189
Number operator      58 100
One-form      123
Operator topology      270
Operator: closed      260
Operator: compact      260
Operator: essentially self adjoint      273
Operator: Hermitian      265
Operator: Hilbert — Schmidt      265
Operator: inverse compact      232
Operator: invertible      266
Operator: positivity-preserving      27 232 271
Operator: selfadjoint      273
Operator: trace-class      18 279
Operators, strongly commutative      275
Orthogonal Space      75
Particle representation      8 58
Particle representation of fermion field      80
Polynomial      175
Polynomial, complex-analytic      65
Polynomial, complex-antianalytic      65
Polynomial, real-analytic      65
Positive energy      254
Pre-Hilbert space      5
Predistribution      17
Predistribution, equivalent      17
Probability measure space      269
Proper one-para meter group      234
Pseudo-derivation      90
Pseudo-interacting field      229
q-number      12
Quantization      107
Quantized nonlinear equation      244
Quasi-invariant measure      9
Random variable      16 21 271
Re normalization      174
Real part      41
Real wave representation      60 82
Real wave representation of fermion field      82
Rech — Schieder theorem      172
Regular state      147
Renormalization map      177
Renormalized power system      216
Reproducing kernel      68
Riesz interpolation theorem      273
Scale of spaces      273
Schroedinger equation      155
Schroedinger representation      5
Schroedinger system      5 13
Schwarz reflection principle      273
Second quantization      154
Semirepresentalion      39
Separable space      273
Sequential topology      274
Single-particle energy      59
Single-particle space      3
Skew product      98
Sobolev inequality      274
Spatial cutoff      235
Spectral function      219
Spectral theory      274
Speed      161
Spin representation      140
Stability      107
State      276
State, equilibrium      40
State, invariant      40
Stein interpolation theorem      277
Stochastic independence      31
Stone — Von Neumann theorem      278
Stone — Weierstrass theorem      278
Stone's theorem      277
Strict commutativity      10
Strict positivity      278
Strong operations      121
Symmetric product      50
Symmetrization      48
Symplectic group representation      39
Symplectic transformation, unitarily quantizable      140
Symplectic vector space      4
Tachyons      146 169
Tame function      18
Tame linear mapping      177
Tensor multiplication      48
Tensor multiplication, amisymmetrized      81
Tensor multiplication, symmetrized      48
Tensor, algebraic      50
Tensor, antisymmetric      47
Tensor, covariant      47
Tensor, finite rank      49
Tensor, pure      49
Tensor, symmetric      47 50
Unitarizability      107
Unitarized action      14
Unitarizer      28
Unitary implementability      118 135
Vacuum vector      41
Vacuum vector, physical      209 238
Vacuum, normal      185
Vector, analytic      258
Vector, cyclic      22 261
Vector, differentiate      272
Vector, entire      272
Vector, regular      272
Vector, separating      274
W*-algebra      28
Wave equation      207
Wave representation      58
Weyl algebra: infinitesimal      175
Weyl algebra: modefinite      144
Weyl algebra: space-finite      144
Weyl pair      9
Weyl pair, normal      35
Weyl pair, simple      218
Weyl relations      5
Weyl relations, nonlinear      216
Weyl relations, restricted      9
Weyl system      4
Weyl system, covariant      39
Weyl system, normal      35 41
While noise      206
Wick product      186
Wick's theorem      187—190
Wiener measure      30
Wiener space      134
Wiener transformation      44
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