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Adler S.L. Ч Quantum theory as emergent phenomenon
Adler S.L. Ч Quantum theory as emergent phenomenon



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Ќазвание: Quantum theory as emergent phenomenon

јвтор: Adler S.L.

јннотаци€:

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


язык: en

–убрика: ћеханика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2004

 оличество страниц: 225

ƒобавлена в каталог: 08.12.2009

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный 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      50Ч51
$D = n_{B}+n_{F}$ defined      30
$l_{eff}$      15 16 130 140 157
$l_{eff}$, decomposition of general matrix with respect to      101Ч102
$l_{eff}$, reduction of Hilbert space modulo      100Ч105
$n_{B}$, $n_{F}$ 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      202Ч203
$\gamma_{1}$, matrices for УMФ model      70Ч71
$\gamma_{1}$, matrices for УMФ model, identities for      203
$\widetilde{C}$      14Ч20 39 42Ч52 54Ч55 60 62 117
$\widetilde{C}$, anti-self-adjoint      15 45 117
$\widetilde{C}$, average in canonical ensemble      84Ч85 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      54Ч55 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 146Ч147 154 158
$\widetilde{C}$, invariance properties of      47
$\widetilde{C}$, Noether formulation      44 54 55
$\widetilde{C}$, Poincare invariance of      47 136Ч137
$\widetilde{C}$, rate of growth with system size      146Ч147
$\widetilde{C}$, self-adjoint component of      15 48Ч52 83 159Ч160 162
$\widetilde{C}$, supersymmetric Yang Ч Mills model expression      69 141Ч143
$\widetilde{C}$, time-reversal properties of      50Ч52
$\widetilde{C}$, traceless      45
$\widetilde{C}$, WessЧZumino model expression      66
$\widetilde{C}$, УMФ model expression      71
Adjoint, assigmenl of fermionic variables      40Ч41 44 45 48Ч52
Adjoint, condition on fermionic trace Hamiltonian      40Ч41
Adjoint, properties of operator derivative      26
Adjoint, rule for products      23 193Ч194
Anticommutation relations, canonical of quantum theory      14 34Ч38 75 147
Anticommutation relations, canonical, effective or emergent      12 16 76 117 133 137Ч138 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      83Ч84
Averages, $\langle\mathcal{O}\rangle_{\widehat{AV}}$ and $\langle\mathcal{O}\rangle_{\widehat{AV, J}}$ defined      119
Averages, over unitary fixed ensemble      108 111Ч112
Ax-Kochen approach      (see Quantum theory)
Axial gauge, defined      93Ч94
Axial gauge, trace Hamiltonian      95
B-mesons      178Ч179
Becchi Ч Rouet Ч Stora Ч Tyutin (BRST) invariance      94 98Ч100 112 114 208Ч211
Becchi Ч Rouet Ч Stora Ч Tyutin (BRST) invariance, nilpotence of      99 209 211
Bell inequalities      6 7 17 119 151Ч155
Bilinear fermionic structure      40Ч41
Bohmian approach      (see Quantum theory)
Boldface, defined to indicate trace quantities      24
Bom rule      5 6 8 13 17 151 154 156 169Ч174
Boson oi bosonic, commutators in $\widetilde{C}$      14 16
Boson oi bosonic, creation and annihilation operators      148
Boson oi bosonic, type (even grade) defined      22Ч23
Boson-fermion balance      12 17 20 118 139 142 144Ч147 154
Brownian motion      13 17 154 156Ч192
Canonical, algebra not trace class      133
Canonical, ensemble      12 15Ч17 20 38 76 81Ч88 123
Canonical, quantization      10 13 19 75 190
Canonical, transformations      46Ч47 76Ч80 133 135 200
Chain rule      (see Leibniz rule)
Charmed meson decay      180
Classical mechanics      12 13 198Ч200
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 34Ч38 75 147
Commutation relations, canonical effective or emergent      12 16 76 117 133 137Ч138 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 157Ч158
Conformal invariance      11 58
Conserved quantities      (see Trace dynamics)
Conserved quantities for continuum spacetime theories      52Ч58
Conserved quantities, global unitary invariance of      43 101
Conserved quantities, operator $\widetilde{C}$      42Ч52 (see also $\widetilde{C}$)
Conserved quantities, symmetry under interchange of $q_{F}$ with $p_{F}$      62Ч63
Conserved quantities, trace fermion number N      39Ч42
Conserved quantities, trace Hamiltonian H      29
Conventions for melnc, summation, Grassmann quantities      193Ч194
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 204Ч205
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 109Ч111
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 58Ч60 63
Dirac, gamma matrices      53 63 73 201Ч203
Dynamical variables, УfastФ and УslowФ parts of      128 140Ч141 191
Effective projection in field equations      191
Effective projection in Ч Podolsky Ч Rosen experiments      10
Effective projection, defined      101
Effective projection, four-vector      56Ч57
Effective projection, operator tensor      61
Effective projection, trace tensor      15 55Ч57 60Ч61 131 190-191
Ensemble, Canonical      (see Canonical Ensemble
Ensemble, microcanonical      (see Microcanonical ensemble)
entropy      15 76 85 87 90Ч91
Epsilon symbol $\epsilon^{A}$ defined      78
Epsilon symbol $\epsilon^{B}$, $\epsilon^{r}$, or $\epsilon^{l}$ defined      24Ч25 28 122
Equilbnum ensemble      (see Canonical Ensemble
Equilibrium distribution $\rho$      81Ч82
Equilibrium distribution $\rho$, averages over defined      83Ч84 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 117Ч118 133 190
Equipartition in classical statistical mechanics      117Ч118
Euler-Lagrange equations for continuum theory      52
Euler-Lagrange equations for Dirac fermion      205Ч206
EulerТs theorem      41
EulerТs theorem, expectation E[ ] of density matrix      167Ч168 176
EulerТs theorem, expectation E[ ] of probabilities      176Ч177
EulerТs theorem, expectation E[ ] of variance      171Ч172
EulerТs theorem, expectation E[ ], defined      167
Extensive generators      134
Fermion or fermionic, adjoint convention      20 23 193Ч194
Fermion or fermionic, adjoint properties of canonical variables      40Ч41 44 48Ч52 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 147Ч148
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      53Ч54 59Ч60 66 69
Fermion or fermionic, type (odd grade) defined      22
Field strength      68 204
Fierz identities      202
figure      2 12Ч14 138
Fluctuation(s) in amplified currents      183Ч184
Fluctuation(s) in conserved quantities      87 93
Fluctuation(s) in energy      181Ч185
Fluctuation(s) in spacetime geometry      185
Fluctuation(s), accretion induced      181Ч184
Fluctuation(s), corrections to Ward identities      17 18 127 156Ч170 190
Four-vector notation      52
Fullerene diffraction      188
GamblerТs ruin      172
Gauge invanance      204 206 210
Gauge, axial      93Ч96
Gauge, Coulomb      94
Gauge, fixing      16 93Ч100 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 97Ч100 112Ч116 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 100Ч102
Global unitary invariance, BRST invariance for fixing      208Ч211
Global unitary invariance, effect of fixing on Ward identities      116
Global unitary invariance, fixing of      16 20 61 103Ч116 191
Global unitary invariance, Noether charge $(\widetilde{C})$ for      45 54Ч55
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 20Ч24 193Ч194 206 208Ч209
Grassmann algebra or quantities, adjoint convention      23 193Ч194
Grassmann algebra or quantities, even and odd grade sectors      22Ч23 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 $\widetilde{C}$      43Ч44
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 93Ч100 204 206
Hamiltonian form of, supersymmetric models with      64Ч74
Hamiltonian form of, symplectic geometry of      30 198Ч200
Hamiltonian form of, tangent vector field      198Ч199
Hamiltonian, phase flow      200
Hamiltonian, rest mass dominated      160 173 185
Hamiltonian, vector field      199
Heisenberg picture or evolution      12 14 16 17 118 130Ч131 135 147 149 158 163
Heisenberg picture or evolution, contrasted with trace dynamics      21 32Ч38
Heisenberg picture or evolution, lime integrated form      131Ч132 135
Heisenberg uncertainty relations      138
Hidden variables      6 17 119 152Ч155
Hierarchy of mass or energy scales      128 143 191
Hierarchy of matrix structures      12 13 138
Hilbert space      12
Hilbert space, complex      2 21Ч22 194
Hilbert space, quatemionic      2 19 194
Hilbert space, real      2 191 194
Hilbert space, reduction modulo $l_{eff}$      100Ч105
histories      (see Quantum theory)
Holography      142 185 192
Independent particle picture      163
Internal symmetries      134
Interpretation      (see Quantum theory)
Intertwining identities      205
Ito calculus      164Ч167 171 176
K defined      85
K defined, role in effective projection      101Ч2 134 135
K-mesons      178Ч179
Klein Ч Gordon scalar      15 39 58Ч61
Kochen Ч Specker Iheorem      6 7 17 119 151Ч153
Lagrangian      (see Trace Matrix
Legendre transformation      40
Leibniz rule (chain rule) for differentiation      25 30 120 125Ч126 131 166 195Ч196 199
Lie algebra of trace functionals      30 46 199
Liouville theorem      15 76Ч81 200
Locality as an emergent property      138
London rigidity      143
Lorentz      (see also Poincare group invanance)
Lorentz, invanance of C      47 131 136Ч137
Lorentz, nomnvanance of stochastic reduction      169Ч170
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 176Ч177
Master equation      167Ч168
Matrix      12 21Ч24
Matrix models      2 12 13 15 18 21Ч38 106 109 169 190
Matrix models, Lagrangian and Hamiltonian dynamics      21 27Ч28
Measure for classical phase space      118
Measure for matnx integration      15 76Ч81 90 95Ч97 103 106Ч107 210Ч211
Measure for matnx integration, canonical invanance of      77Ч80
Measure for matnx integration, global unitary invanance of      80Ч81 106Ч107
Measure for matnx integration, Haar      103Ч104
Measure for matnx integration, modified (unitary fixed)      101 103Ч116 119
Measure for matnx integration, permutation symmetry of      111Ч112
Measure for matnx integration, shift invanance of      81 115 119
Measurement, apparatus      2Ч6 9 10 152Ч153 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 88Ч93
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 42Ч44 53Ч57
Noether theorem or charge for internal symmetry      53
Noether theorem or charge for Poincare invariant theory      55Ч58
Nonlocality      10Ч11 138 155 190 167Ч168
Number density $N_{r}(\overrightarrow{y})$, defined      168
Number density $N_{r}(\overrightarrow{y})$, mutual commutativity of      173Ч174
Orthonormality      151 158
Partition function, $Z_{J}$ defined      88
Partition function, conditions for existence      86Ч87
Partition function, global unitary invanance of      107
Partition function, Z defined      86 106
Pauli spin matrices      51 101 177Ч178 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      185Ч189
Phenomenology of energy-driven reduction      175Ч185
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 180Ч183 185
Poincare group invariance      15 39 47 82Ч83 104 117 134Ч137
Poincare group invariance associated Noether charges and currents      55Ч58
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