Adler S.L. — Quantum theory as emergent phenomenon :: Электронная библиотека попечительского совета мехмата МГУ

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Adler S.L. — Quantum theory as emergent phenomenon

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Название: Quantum theory as emergent phenomenon

Автор: Adler S.L.

Аннотация:

Develops a new approach to the conceptual foundations of quantum mechanics.

Язык:

Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 225

Добавлена в каталог: 08.12.2009

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Предметный указатель

$A_{rs}$ , defined      48
$A_{rs}$ , generalized choice of      51
$A_{rs}$ , simplest choice of      49 51 161
$A_{rs}$ , time-reversal invariance condition on      50—51
$D = n_{B}+n_{F}$ defined      30
$l_{eff}$       15 16 130 140 157
$l_{eff}$ , decomposition of general matrix with respect to      101—102
$l_{eff}$ , reduction of Hilbert space modulo      100—105
$n_{B}$ , $n_{F}$ defined as numbers of bosonic, fermionic canonical coordinates      27
$W^{Rl}_{s}$ and $W^{Ll}_{s}$ defined      122
$\gamma$ matrices for Dirac equation      (see also Dirac)
$\gamma$ matrices for Dirac equation, representation covananl identities for      202—203
$\gamma_{1}$ , matrices for “M” model      70—71
$\gamma_{1}$ , matrices for “M” model, identities for      203
$\widetilde{C}$       14—20 39 42—52 54—55 60 62 117
$\widetilde{C}$ , anti-self-adjoint      15 45 117
$\widetilde{C}$ , average in canonical ensemble      84—85 129
$\widetilde{C}$ , average in unitary fixed ensemble      105 129 157
$\widetilde{C}$ , conservation discovered by Millard x      19 43
$\widetilde{C}$ , construction of global unitary generators from      45
$\widetilde{C}$ , current for      54—55 60 66 69
$\widetilde{C}$ , dependence on non-commulative parts of phase space variables      48
$\widetilde{C}$ , equipartition of      16 19 117 133
$\widetilde{C}$ , fermionic part of      49
$\widetilde{C}$ , fluctuations of      17 129 146—147 154 158
$\widetilde{C}$ , invariance properties of      47
$\widetilde{C}$ , Noether formulation      44 54 55
$\widetilde{C}$ , Poincare invariance of      47 136—137
$\widetilde{C}$ , rate of growth with system size      146—147
$\widetilde{C}$ , self-adjoint component of      15 48—52 83 159—160 162
$\widetilde{C}$ , supersymmetric Yang — Mills model expression      69 141—143
$\widetilde{C}$ , time-reversal properties of      50—52
$\widetilde{C}$ , traceless      45
$\widetilde{C}$ , Wess—Zumino model expression      66
$\widetilde{C}$ , “M” model expression      71
Adjoint, assigmenl of fermionic variables      40—41 44 45 48—52
Adjoint, condition on fermionic trace Hamiltonian      40—41
Adjoint, properties of operator derivative      26
Adjoint, rule for products      23 193—194
Anticommutation relations, canonical of quantum theory      14 34—38 75 147
Anticommutation relations, canonical, effective or emergent      12 16 76 117 133 137—138 141 144 147
Anticommutation relations, canonical, local structure of      10 190
Anticommutation relations, canonical, not assumed      21 75
Anticommutator, notation defined as {X, F)      14 24
Approximations leading to quantum theory      (see Quantum theory approximations)
Averages, $\langle\mathcal{O}\rangle_{AV_{J}}$ defined      88
Averages, $\langle\mathcal{O}\rangle_{AV}$ defined      83—84
Averages, $\langle\mathcal{O}\rangle_{\widehat{AV}}$ and $\langle\mathcal{O}\rangle_{\widehat{AV, J}}$ defined      119
Averages, over unitary fixed ensemble      108 111—112
Ax-Kochen approach      (see Quantum theory)
Axial gauge, defined      93—94
Axial gauge, trace Hamiltonian      95
B-mesons      178—179
Becchi — Rouet — Stora — Tyutin (BRST) invariance      94 98—100 112 114 208—211
Becchi — Rouet — Stora — Tyutin (BRST) invariance, nilpotence of      99 209 211
Bell inequalities      6 7 17 119 151—155
Bilinear fermionic structure      40—41
Bohmian approach      (see Quantum theory)
Boldface, defined to indicate trace quantities      24
Bom rule      5 6 8 13 17 151 154 156 169—174
Boson oi bosonic, commutators in $\widetilde{C}$       14 16
Boson oi bosonic, creation and annihilation operators      148
Boson oi bosonic, type (even grade) defined      22—23
Boson-fermion balance      12 17 20 118 139 142 144—147 154
Brownian motion      13 17 154 156—192
Canonical, algebra not trace class      133
Canonical, ensemble      12 15—17 20 38 76 81—88 123
Canonical, quantization      10 13 19 75 190
Canonical, transformations      46—47 76—80 133 135 200
Chain rule      (see Leibniz rule)
Charmed meson decay      180
Classical mechanics      12 13 198—200
Clustering and energy-driven stochastic equation      182
Clustering and unitary fixing      105
Clustering in deriving canonical from microcanonical ensemble      90 137
Clustering of Wightman functions      137 208
Commutation relations of quantum theory      14 34—38 75 147
Commutation relations, canonical effective or emergent      12 16 76 117 133 137—138 141 144 147 153
Commutation relations, local slraclure of      10 190
Commutation relations, nol assumed      21 75
Commutator, notation defined as [X, F]      14 24
Completeness relation      150 157—158
Conformal invariance      11 58
Conserved quantities      (see Trace dynamics)
Conserved quantities for continuum spacetime theories      52—58
Conserved quantities, global unitary invariance of      43 101
Conserved quantities, operator $\widetilde{C}$       42—52 (see also $\widetilde{C}$ )
Conserved quantities, symmetry under interchange of $q_{F}$ with $p_{F}$       62—63
Conserved quantities, trace fermion number N      39—42
Conserved quantities, trace Hamiltonian H      29
Conventions for melnc, summation, Grassmann quantities      193—194
Copenhagen interpretation      (see Quantum theory)
Correlation, function g(x) defined      168
Correlation, length $r_{C}$ defined      186
Correlations, in canonical ensemble      87 93
Cosmological blackbody radiation      82 169
Cosmological constant      11 131 191
Cosmology of early universe      190
Covariant derivative      68 204—205
Current algebra      46
Cyclic identities      (see Trace)
Cyclic identities, bilinear      22
Cyclic identities, trilinear      23
Dark matter, energy      191
De Witt-Faddeev-Popov, determinant      95 97 208 209
De Witt-Faddeev-Popov, method      94 106 109—111
Decoherence      4 5
Degenerate manifold      172 173
Density matrix      167 170 172
Density matrix for mixed state      172
Derivative $\delta P/\delta\mathcal{O}$       (see also Trace Operator
Derivative $\delta P/\delta\mathcal{O}$ , defined      24
Derivative $\delta P/\delta\mathcal{O}$ , properties of      24 26
Dirac, fermion      15 39 58—60 63
Dirac, gamma matrices      53 63 73 201—203
Dynamical variables, “fast” and “slow” parts of      128 140—141 191
Effective projection in field equations      191
Effective projection in — Podolsky — Rosen experiments      10
Effective projection, defined      101
Effective projection, four-vector      56—57
Effective projection, operator tensor      61
Effective projection, trace tensor      15 55—57 60—61 131 190-191
Ensemble, Canonical      (see Canonical Ensemble
Ensemble, microcanonical      (see Microcanonical ensemble)
entropy      15 76 85 87 90—91
Epsilon symbol $\epsilon^{A}$ defined      78
Epsilon symbol $\epsilon^{B}$ , $\epsilon^{r}$ , or $\epsilon^{l}$ defined      24—25 28 122
Equilbnum ensemble      (see Canonical Ensemble
Equilibrium distribution $\rho$       81—82
Equilibrium distribution $\rho$ , averages over defined      83—84 88
Equilibrium distribution $\rho$ , fluctuations of conserved quantities in      87 93
Equilibrium distribution $\rho$ , parameters of      83 128 145
Equilibrium distribution $\rho$ , residual unitary invariance of      103
Equilibrium distribution $\rho$ , unitary fixed      108
Equilibrium distribution $\rho$ , vector notation for parameters of      89
Equipartition      16 19 81 117—118 133 190
Equipartition in classical statistical mechanics      117—118
Euler-Lagrange equations for continuum theory      52
Euler-Lagrange equations for Dirac fermion      205—206
Euler’s theorem      41
Euler’s theorem, expectation E[ ] of density matrix      167—168 176
Euler’s theorem, expectation E[ ] of probabilities      176—177
Euler’s theorem, expectation E[ ] of variance      171—172
Euler’s theorem, expectation E[ ], defined      167
Extensive generators      134
Fermion or fermionic, adjoint convention      20 23 193—194
Fermion or fermionic, adjoint properties of canonical variables      40—41 44 48—52 117 148 159
Fermion or fermionic, anticommutators in $\widetilde{C}$       14 16
Fermion or fermionic, creation, annihilation operators $\Psi^{\dag}_{eff}, \Psi_{eff}$ defined      136 147—148
Fermion or fermionic, introduction inlo theory      20

Fermion or fermionic, structure of trace Hamiltonian and Lagrangian      39 42
Fermion or fermionic, trace charge or number      39 42 54 60 62 66 69 129
Fermion or fermionic, trace current      53—54 59—60 66 69
Fermion or fermionic, type (odd grade) defined      22
Field strength      68 204
Fierz identities      202
figure      2 12—14 138
Fluctuation(s) in amplified currents      183—184
Fluctuation(s) in conserved quantities      87 93
Fluctuation(s) in energy      181—185
Fluctuation(s) in spacetime geometry      185
Fluctuation(s), accretion induced      181—184
Fluctuation(s), corrections to Ward identities      17 18 127 156—170 190
Four-vector notation      52
Fullerene diffraction      188
Gambler’s ruin      172
Gauge invanance      204 206 210
Gauge, axial      93—96
Gauge, Coulomb      94
Gauge, fixing      16 93—100 104 108
Gauge, nontemporal      94 96
Gauge, potential      68
Gauge, properties of conserved quantities      97
General relativity      11
Generalized Poisson bracket      (see Poisson bracket)
Generalized quantum dynamics      19 (see also Trace dynamics)
Ghost fermions      94 97—100 112—116 208-211
Global unitary invariance      13 20 190
Global unitary invariance of ensemble averages of trace polynomials      107
Global unitary invariance of generators      47 136
Global unitary invariance of matrix models      12 45 76 135 169
Global unitary invariance of trace Hamiltonian and/or Lagrangian      12 14 43 47 48 83
Global unitary invariance, breaking by canonical ensemble      16 20 85 100—102
Global unitary invariance, BRST invariance for fixing      208—211
Global unitary invariance, effect of fixing on Ward identities      116
Global unitary invariance, fixing of      16 20 61 103—116 191
Global unitary invariance, Noether charge $(\widetilde{C})$ for      45 54—55
Global unitary invariance, Noether current or theorem for      54 55
Global unitary invariance, trace generators for      45
Golden Rule      180
Grade      (see Grassmann algebra)
Grassmann algebra or quantities      13 20—24 193—194 206 208—209
Grassmann algebra or quantities, adjoint convention      23 193—194
Grassmann algebra or quantities, even and odd grade sectors      22—23 193
Grassmann algebra or quantities, integrals over      77 193
Gravitation      11 131 180 185 191
Gravitino      73
Hamilton equations for      28 31 198
Hamilton equations for generic trace dynamics      28 31
Hamilton equations, formal integration of      32
Hamilton equations, use to show conservation of $\widetilde{C}$       43—44
Hamiltonian      (see Effective Hamiltonian or trace)
Hamiltonian form of      19 (see also Trace Hamiltonian)
Hamiltonian form of, irreducible      105
Hamiltonian form of, operator gauge invanance in      68 93—100 204 206
Hamiltonian form of, supersymmetric models with      64—74
Hamiltonian form of, symplectic geometry of      30 198—200
Hamiltonian form of, tangent vector field      198—199
Hamiltonian, phase flow      200
Hamiltonian, rest mass dominated      160 173 185
Hamiltonian, vector field      199
Heisenberg picture or evolution      12 14 16 17 118 130—131 135 147 149 158 163
Heisenberg picture or evolution, contrasted with trace dynamics      21 32—38
Heisenberg picture or evolution, lime integrated form      131—132 135
Heisenberg uncertainty relations      138
Hidden variables      6 17 119 152—155
Hierarchy of mass or energy scales      128 143 191
Hierarchy of matrix structures      12 13 138
Hilbert space      12
Hilbert space, complex      2 21—22 194
Hilbert space, quatemionic      2 19 194
Hilbert space, real      2 191 194
Hilbert space, reduction modulo $l_{eff}$       100—105
histories      (see Quantum theory)
Holography      142 185 192
Independent particle picture      163
Internal symmetries      134
Interpretation      (see Quantum theory)
Intertwining identities      205
Ito calculus      164—167 171 176
K defined      85
K defined, role in effective projection      101—2 134 135
K-mesons      178—179
Klein — Gordon scalar      15 39 58—61
Kochen — Specker Iheorem      6 7 17 119 151—153
Lagrangian      (see Trace Matrix
Legendre transformation      40
Leibniz rule (chain rule) for differentiation      25 30 120 125—126 131 166 195—196 199
Lie algebra of trace functionals      30 46 199
Liouville theorem      15 76—81 200
Locality as an emergent property      138
London rigidity      143
Lorentz      (see also Poincare group invanance)
Lorentz, invanance of C      47 131 136—137
Lorentz, nomnvanance of stochastic reduction      169—170
Lorentz, noninvanance of canonical ensemble      82 136
Lorentz, trace      61 131 190
Lorentzian profile      177 179
Lueders rule      156 169 173
Many worlds      (see Quantum theory)
Martingale      172 176—177
Master equation      167—168
Matrix      12 21—24
Matrix models      2 12 13 15 18 21—38 106 109 169 190
Matrix models, Lagrangian and Hamiltonian dynamics      21 27—28
Measure for classical phase space      118
Measure for matnx integration      15 76—81 90 95—97 103 106—107 210—211
Measure for matnx integration, canonical invanance of      77—80
Measure for matnx integration, global unitary invanance of      80—81 106—107
Measure for matnx integration, Haar      103—104
Measure for matnx integration, modified (unitary fixed)      101 103—116 119
Measure for matnx integration, permutation symmetry of      111—112
Measure for matnx integration, shift invanance of      81 115 119
Measurement, apparatus      2—6 9 10 152—153 156 160 162-163 181 184
Measurement, contextual dependence in      152
Measurement, problem      (see Quantum theory)
Mechanics of matnx models      2 12 15 17 39 75
Meissner effect      143
Meromorphic function      13 24
Metric, convention      193
Metric, spacetime      191
microcanonical ensemble      16 19 76 88—93
Microcanonical ensemble, approximation by canonical ensemble      92
Microcanonical ensemble, Ward identities in      123
Mtegraiion measure      (see Measure)
N defined as dimension of Hilbert space      22
N defined as dimension of Hilbert space, relation N=2K      85
N defined as trace fermion number      39 42 Trace
Noether theorem or charge      14 39 42—44 53—57
Noether theorem or charge for internal symmetry      53
Noether theorem or charge for Poincare invariant theory      55—58
Nonlocality      10—11 138 155 190 167—168
Number density $N_{r}(\overrightarrow{y})$ , defined      168
Number density $N_{r}(\overrightarrow{y})$ , mutual commutativity of      173—174
Orthonormality      151 158
Partition function, $Z_{J}$ defined      88
Partition function, conditions for existence      86—87
Partition function, global unitary invanance of      107
Partition function, Z defined      86 106
Pauli spin matrices      51 101 177—178 201
Phase space vanables, classical and non-commutative parts of      47 48 138
Phase space vanables, indices R, R+1 defined      105
Phenomenology of continuous spontaneous localization reduction      185—189
Phenomenology of energy-driven reduction      175—185
Pi zero decay      180
Planck constant      15 16 83 85 102 117 193
Planck constant, sum rule involving      142 146
Planck mass, energy, or scale      11 13 128 144 180—183 185
Poincare group invariance      15 39 47 82—83 104 117 134—137
Poincare group invariance associated Noether charges and currents      55—58

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