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| Avramidi I.G. — Heat Kernel and Quantum Gravity |
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| Предметный указатель |
Abel — Plan summation 117
action 9 78
Action of higher-derivative quantum gravity 85
Action, classical 13 18 77 85
Action, Euclidean 5 7 102 106 109—112
Action, gravitational 4
Affine parameter 21 22
Analytical continuation 17 19 52 53 59 60 65 66 117
Anomaly 3
Anomaly, conformal 68
Anti-commutator 39
Asymptotic expansion 6 20 34 48 51 52 70 74
Asymptotic expansion of effective action 48 76
Asymptotic expansion of evolution function 51
Asymptotic expansion of Green function 14
Asymptotic expansion of transfer function 34 68 69 73
Asymptotic expansion of transfer function in De Sitter space 73
asymptotic freedom 5 7 102—105 107 108
Asymptotic states 107
Back-reaction 2
Background field 2 3 10—12 51 53 55 60 74 79 80 108
Background field gauge 80
Background field method 1 5
Background field on-shell 108
Background field reparametrization invariant 81
Background metric 48 88
Background metric sflat 99
Bernoulli numbers 71
Bernoulli polynomials 70
Bessel function 74
Bianci identity 61
Black hole 48
Borel function 52 53 73 74
Borel Hum 6 52 53
Borel seriaH 53
Borel summation 52
boundary conditions 10 14
Boundary conditions for formfactors 59 65
Boundary conditions, causal 65
Branching point 59 65 74
Causal structure of space-time 1
Causality 3 4 10
Change of field variables 109
Characteristic length scale 17
Christoffel symbols 22 81 83 84 100 114
Chronological ordering 10
Co-differentiation 46
Coincidence limit 16 21 22 24
Coincidence limit of De Witt coefficients 34
Coincidence limit of derivatives of parallel displacement operator 24
Coincidence limit of derivatives of world function 24 25
Coincidence limit of Green function 6 17 19 20 59 97
Coincidence limit of symmetrized covariant derivatives 36
Coincidence limit of transfer function 15 68 72
Commutator of covariant derivatives 22 26 46 91 96
Completeness of eigenfunctions 24
Complex power of differential operator 116
Compton wave length 3 17
Condensed De Witt’s notation 9
Configuration space 77 78 80 84 111 114
Configuration space complex 106
Configuration space physical 78 84
Conformal condensate 107
Conformal Hector of EinHtflln gravity 106
Conformal Hector of higher-derivative quantum gravity 5 7 107
Conformal invariance 68
Conformal mode 107 108
Conformally invariant models 108
Conjugate points 15
Connection 5 14 22 82 83
Connection in configuration space 12 81 82 115
Connection, affine 22
Connection, gauge-invariant 80
Connection, non-metric 83 98
Constraints 1 109
Constraints, first type 77
Coordinate transformation 14 22
Cosmological constant 4 85 106—108
Cosmological scenario 123
Counter-ter ms 3 18
Coupling constant 5 7 18 101
Coupling constant of scalar field with gravity 46 104
Coupling constant, conformal 85 102 103 105 107
Coupling constant, cosmological 85 103—105
Coupling constant, effective (running) 101
Coupling constant, Einstein 85 101 102 105 106
Coupling constant, essential 101
Coupling constant, matter 104 105
Coupling constant, non-essential 18 101 102
Coupling constant, renormalized 18
Coupling constant, topological 85 102 105
Coupling constant, Weyl 85 102 105
Covariance 53
Covariance of effective action 80
Covariant derivatives 14 22
Covariant derivatives, symmetrized 24 42
Covariant Fourier components 55
Covariant Fourier integral 5 25 26 54
Covariant Fourier integral for Dirac delta-function 27
Covariant Fourier integral for formfactors 57
Covariant Fourier integral for Green function 54
Covariant Fourier integral for propagator 107
Covariant Taylor series 5 23 24 26 28 30 31 36 83
Covariant Taylor series for De Witt coefficients 34
Covariant Taylor series in configuration space 81
Curvature 31 36 42
Curvature covariantly constant 68
Curvature of De Sitter space 109 122
Curvature of space-time 96
Curved space 5
De Sitter space 7 33 69 94 108—110 112 114 123
De Witt coefficients 3—6 16 34—36 53 55 56 68 69
De Witt coefficients  42
De Witt coefficients  66
De Witt coefficients ![$[a_{(n-2)/2}]$](/math_tex/cf68be12a33655017c12c386cdf02fe582.gif) 60
De Witt coefficients ![$[a_{3}]$](/math_tex/791b8c75715eedead03b2316f12a7ee382.gif) 6 37 38 42
De Witt coefficients ![$[a_{4}]$](/math_tex/6b67e1f4aa353de10dbfddabc91af33c82.gif) 6 37 38 42 46 48
De Witt coefficients for spinor field 48
De Witt coefficients in De Sitter space 69 71
De Witt coefficients in first order in background fields 57
De Witt coefficients in second order in background fields 61
De Witt projector 82
Degrees of freedom 116
Degrees of freedom of higher-derivative quantum gravity 116
Determinant of differential operator 7 79 116 118
Determinant of ghost operator 113 115
Determinant of integro-differential operator 98
Diagrammatic technique 5 11 13 36 37
Diagrammatic technique covariant 55
Diagrammatic technique for De Witt coefficients 55 56
Diagrammatic technique for effective action 81
Diagrammatic technique of perturbation theory 1
Diffeomorphism group 1 9 84
Differential operator 3 14 24 25 35 84 88 116—119 121 122
Differential operator constrained 111
Differential operator elliptic 3
Differential operator minimal 14 100
Differential operator non-minimal 91
Dimension anomalous 18 102
Dimension background 53 55 95 96
Dimension of coupling constant 18
Dimension of space-time 92
Dimension, physical 19
Dirac delta-function 11 13 27 78 84
Dirac matrices 46
Disc of convergence 52 53
distribution 17
D’Alambert operator 14
Effective action 1—5 11—13 48 49 64—68 75 76 78—81 93 95 98 100 101 104 109 116 119—122
Effective action gauge-invariant 2 79 80
| Effective action in De Witt gauge 114 115
Effective action in minimal gauge 105 106
Effective action in second order in background fields 63 65
Effective action in two dimensions 67 68
Effective action non-analytic 6
Effective action non-locai 3 6 48 65
Effective action of massless field 66
Effective action off-shell 2 12 79 80 82
Effective action on De Sitter space 7 108 112 113 121
Effective action on-shell 12 82 94 116 121
Effective action one-loop 3 6 13 15 19 20 46 47 61 74 79 85 93—95 108 119
Effective action renormalized 4 18 42 48 64 67 74 101
Effective action reparametrization invariant 2 12 81
Effective action, Vilkovisky’s 2 6 7 12 81—83 98—101 105 106 114—116 120 121
Effective equations 2 12 80 109 122
Effective equations, Vilkovisky’s 7
Effective potential 7 108
Effective potential of higher-derivative quantum gravity 108
Effective potential one-loop 108
Effective potential Vilkovisky’s 7
Eigenfunctions 23 24 28 34
Eigenfunctions, dual 23 26
Eigenfunctions, orthonormal 24
Eigenmatrix 31
Eigenvalue 23 116
Einstein equations 1 48
Einstein equations in two dimensions 67
Einstein gravity 83 115
Energy-momentum tensor 15 48
Energy-momentum tensor effective 48
Entire function 53 57 63 68 73 74
Equations of motion 85
Equations of motion classical 12 77 108
Euclidean action of higher-derivative quantum gravity 106 107
Euclidean sector of space-time 55 109
Euler bet a-function 57
Euler characteristic 107 109
Euler constant 20
Euler gamma-function 58 70 71
Evolution equation 14
Evolution function 14 15 51
Expansion covariant 5
Expansion in background dimension 3 95
Expansion in eigenfunctions 34
Expansion in extremal 100 119
Expansion near mass shell 95
Exterior derivative 46
Extremal 77 85 95—99 109
Field components bosonic 9
Field components confcravarianfc 9
Field components covariant 9
Field components fermionic 9
Field configurations 77
Field renormalization constant 18 102
Field variables anti-commuting 79
Field variables constrained 110 111 115
Field variables dynamical 77
Field variables gauge-invariant 78 110
Field variables Grassmanian 9
Field variables group 78
Field variables non-physical 83 110 111
Field variables unconstrained 110
Finite part of effective action 121
Flat space expansion 107
Formfactors 6 58 59 63 65
Functional derivative 68 83
Functional derivative covariant 81 98
Functional derivative, left 10
Functional derivative, right 11
Functional determinant 47 119
Functional determinant of minimal differential operator 47
Functional determinant,  -function regularized 117
Functional formulation of quantum field theory 5
Functional integral 10 12 78 81 106 107
Functional integral, Gaussian 12 79
Functional Legendre transform 11
Functional measure 10 12 13 78 115
Functional super determinant 13
Functional supertrace 13
Functional trace 116
Functional trace of transfer function 62
Gauge condition 77—80 101 105 109
Gauge condition, covariant 5
Gauge condition, De Donder — Fock — Landau 88 115
Gauge condition, De Witt 79 88 95 99 112 113
Gauge condition, harmonic 88 98 115
Gauge condition, minimal 88 92 97 100
Gauge condition, orthogonal 83 114
Gauge field theory 9 12
Gauge field theory non — Abelian 83
Gauge fixing 2 9 79 82
Gauge fixing operator 79
Gauge fixing parameters 93
Gauge fixing tensor 93 96
Gauge fixing term 112
Gauge group 1 77 78 80 84
Gauge invariance 77 82
Gauge parameters 95 113 114
Gauge parameters, minimal 100
Gauge trainformation 77 80 82
Gauge trainformation of constrained fields 110
Gauge trainformation of unconstrained fields 110
Gell — Mann — Low beta-functions 3 18 101 104 105
General relativity 1
Generating functional 1 10 11
Generators of gauge transformations 77 78 80 82 84
Geodesic 15 21—23
Geodesic distance 15
Geodesic in configuration space 80
Ghost fields 4 9
Ghost fields Faddeev — Popov 79
Ghost fields Nielsen — Kallosh 79
Ghost operator 88 113 115
Ghost operator on De Sitter space 112
Ghost propagators 96
Ghost states 107
Gravitational field 1 4 6 46 48 49 84 105
Gravitational field, background 2 3
Gravitational field, linearized 2
Gravitational loop 2
Gravitational propagator 96
Graviton 116
Green function 2 3 12—15 17 19 47 49 51 53 55 59 60 70 71 73 96 97 99
Green function in De Sitter space 69
Green function in first order in background fields 58
Green function of massless field 59
Green function of matter field 46
Green function of minimal operator 46
Green function, causal (Feynman) 15 55 58 59
Green function, conformally invariant 6 60
Green function, exact 54
Green function, free 54
Green function, renormalized 58 60
Ground state 117
Ground state of higher-derivative quantum gravity 107
Group parameter 77
Group variables 78
Heat kernel 14
High-energy asymptotics 6 68 101
High-energy asymptotics of conformal coupling 7
High-energy asymptotics of conformal sector 109
High-energy asymptotics of coupling constants 6 101
High-energy asymptotics of formfactors 6 59 60 65 67
High-energy asymptotics of Green function 51
High-energy asymptotics of higher-derivative quantum gravity 4 5 18 104
Higher-derivative quantum gravity 2 4—7 12 83 85 101 105—108 116
Higher-derivative quantum gravity, conformally invariant 5
Hypersurface 33
Imaginary part of effective action 48 65 116 122
Imaginary part of formfactors 6 59 65
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