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| Elizalde E., Odintsov A.D., Romeo A. — Zeta Regularization Techiques with Applications |
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| Предметный указатель |
action 10
Analytic continuation of Epstein multidimensional zeta function 97
Analytic continuation of Riemann zeta function 2
Background field 11
Bekenstein — Hawking entropy 182
Bernoulli numbers 88
Black hole degeneracy 182
Boundary conditions antiperiodic 148
Boundary conditions Dirichlet 99
Boundary conditions electromagnetic 100
Boundary conditions Hawking 117
Boundary conditions Neumann 99
Boundary conditions no-boundary 119
Boundary conditions of our universe 120
Boundary conditions periodic 103
Boundary conditions Robin 115
Boundary conditions zero-thickness 108
Bunch formulas 113
Candelas’s conjecture 118
Casimir and Polder formula 82
Casimir effect 79
Casimir effect experiments 82
Casimir effect for em field in spherical shell 113
Casimir effect for massive scalar field 112
Casimir effect for massless scalar field 110
Casimir effect sign 102
Casimir energy density 96
Casimir energy density table 103
Chowla — Selberg formula 46
Christoffel symbols 117
Conformal invariance 116
Conformally coupled fields 116
Constant background field 64
Covariant Laplacian 86
Cut-off additional 107
Cut-off frequency 88
Cut-off momentum 89
Cut-off space 89
De Witt covariant gauge 269
Dedekind’s modular form 124
Dehn surgery 184
Determinant 9
Dirac operator 139
Dirac p-brane action 190
Dual symmetry 234
Effective action divergences 273
Effective action gauge-fixing independent 264
Eigenfunction 11
Eigenmode multiplicities 125
Eigenvalue 11
Euler — Mac Laurin summation formula 91
Euler — Mascheroni constant 148
Fock operators 85
Fourier basis 86
Fourier — Haxish — Chandra transformation 136
Fuchsian group 137
Fundamental invariant 135
Gamma function integration 15
Gamma function poles 28
Gamma function reflection formula 28
Geodesic distance 135
Grand, unified theories 147
Group of isometries 135
Group, centralizer 136
Group, co-compact 137
Group, conjugacy class 136
Group, free 136
Group, invariant operator 136
Group, rank 135
Hagedorn temperature 234
Hamaker — De Boer equation 83
Heegaard splittings 184
Hodge operator 100
Howe — Tucker p-brane action 190
Hyperbolic space 135
Hyperbolic topologies 169
Imaginary time compactification 148
Induced 2D gravity 262
Jacobi’s inversion formula 149
Kaluza — Klein spacetime 162
Kaluza — Klein spacetime, toroidal 166
| Klein — Gordon knot 184
Klein — Gordon operator 94
Klein — Gordon, eigenmode 88
Lens space 184
Lifschitz theory 82
Link 184
Lobachevsky plane 150
London theory 82
Massless vector photons 100
McDonald function 218
Meinardus theorem 176 178
Mellin — Barnes representation 211 213 214
Modes, transverse electric (or Dirichlet) 92
Modes, transverse magnetic (or Neumann) 92
Moebius transformation 137
NIL 186
Normal ordering 84
Partition function 146
Path integral techniques 143
Pauli matrices 139
Plana summation formula 93
Poincare half plane 135
Poincare metric 135
Primitive closed geodesics 139
Principal part prescription 86
Radiation gauge 100
Regularization of eigenmode summations 87
Regularization, zeta 73
Renormalization 278
Renormalization group 146
Renormalization parameter 149
Riemann’s conjecture 3
Scalar field in thermal equilibrium 146
Schild’s string action 191
Seeley — De Witt coefficients 145 164
Selberg trace formula 135
Selberg zeta function 154
Selberg zeta function, factorization formulas 153 155 158 161
Spinor field in thermal equilibrium 148
Spontaneous compactification 267
Stiefel — Whitney class 148
Strictly hyperbolic subgroup 141
Summation, additional contribution 29
Summation, change of order 24
Theta function 6 7
Theta function, identity 8
Thurston theorem 186
Trace anomaly 261
Ultrastatic spacetime 85
Vacuum energy 84
Vacuum energy density for cylinders 128
Vacuum energy density for Riemann surfaces 124
Vacuum energy density for untwisted fields 152
Vacuum energy density, stabilization 128
Vacuum pressure 96
Van der Waals force 82
Van der Waals force, retarded 82
Volume element 12
Wess — Zumino — Witten term 174 175
Weyl spinors 139
zero modes 149
Zeta function alternating 26
Zeta function analytic continuation 2
Zeta function convergence 2
Zeta function for Laplacian 121
Zeta function for Laplacian on a hemisphere 121
Zeta function for Laplacian on Riemann spheres 121
Zeta function of operator 9
Zeta function regularization 73
Zeta function regularization vs dimensional 73
Zeta function regularization vs heat-kernel 73
Zeta function, Epstein 5 167
Zeta function, Epstein, reflection formulas 6
Zeta function, Epstein, zeros 8
Zeta function, Hurwitz 4
Zeta function, Hurwitz, derivatives 12 20
Zeta function, integral representation 94
Zeta function, multiple 43
Zeta function, Riemann 1
Zeta function, Riemann, generalized 4
Zeta function, zeros 3
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