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Avramidi I.G. — Heat Kernel and Quantum Gravity
Avramidi I.G. — Heat Kernel and Quantum Gravity

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Название: Heat Kernel and Quantum Gravity

Автор: Avramidi I.G.

Аннотация:

This book tackles quantum gravity via the so-called background field method and its effective action functional. The author presents an explicitly covariant and effective technique to calculate the de Witt coefficients and to analyze the Schwinger-de Wit asymptotic expansion of the effective action. He also investigates the ultraviolet behaviour of higher-derivative quantum gravity.
The book addresses theoretical physicists, graduate students as well as researchers, but should also be of interest to physicists working in mathematical or elementary particle physics.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 149

Добавлена в каталог: 07.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $A_{3}$      42
De Witt coefficients $A_{n/2}$      66
De Witt coefficients $[a_{(n-2)/2}]$      60
De Witt coefficients $[a_{3}]$      6 37 38 42
De Witt coefficients $[a_{4}]$      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, $\zeta$-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
1 2
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