Feynman Path Integral Formulation

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References 333 Williams, R. M., 1986, Class. Quantum Grav. 3, 853–869. Wilson, K. G., 1971a, Phys. Rev. B 4, 3174. Wilson, K. G., 1971b, Phys. Rev. B 4, 3184. Wilson, K. G., and M. E. Fisher, 1972, Phys. Rev. Lett. 28, 240. Wilson, K. G., 1973, Phys. Rev. D 7, 2911. Wilson, K. G., 1974, Phys. Rev. D 10, 2445. Wilson, K. G., 1975, Rev. Mod. Phys. 47, 773. Wong, C. Y., 1971, J. Math. Phys. 12, 70. Zakharov, V. I., 1970, JETP Lett. 12, 312; Pisma Zh. Eksp. Teor. Fiz. 12, 447 (1970). Zavada, P., 1998, Commun. Math. Phys. 192, 261 [funct-an/9608002]. Zinn-Justin, J., 2002, Quantum Field Theory and Critical Phenomena, fourth edition (Oxford University Press, New York, 2002). Zinn-Justin, J., 2005, <strong>Path</strong> <strong>Integral</strong>s in Quantum Mechanics (Oxford University Press, Oxford, 2005).
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Quantum Gravitation
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Prof. Dr. Herbert W. Hamber Univers
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Preface Almost a century has gone b
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Preface ix mately leading to the Ei
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Preface xi thereof) have meaning an
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Acknowledgements Over the years I h
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xvi Contents 4 Hamiltonian and Whee
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Chapter 1 Continuum Formulation 1.1
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1.3 Wave Equation 3 One important a
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1.3 Wave Equation 5 e 01 + e 31 = 0
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1.3 Wave Equation 7 Fig. 1.1 Lowest
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1.3 Wave Equation 9 with s μν = 1
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1.4 Feynman Rules 11 One can exploi
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1.4 Feynman Rules 13 and the gravit
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1.4 Feynman Rules 15 where the p 1
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1.5 One-Loop Divergences 17 D = 2 +
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1.5 One-Loop Divergences 19 R 2 =
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1.6 Gravity in d Dimensions 21 1.6
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1.6 Gravity in d Dimensions 23 ∇
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1.7 Higher Derivative Terms 25 case
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1.7 Higher Derivative Terms 27 theo
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1.7 Higher Derivative Terms 29 ∫
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1.7 Higher Derivative Terms 31 trln
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1.8 Supersymmetry 33 treated pertur
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1.8 Supersymmetry 35 and Σ’s has
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1.9 Supergravity 37 δA μ = −2g
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1.9 Supergravity 39 The first order
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1.10 String Theory 41 of the string
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1.10 String Theory 43 Solutions to
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1.10 String Theory 45 and for the o
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1.10 String Theory 47 with [dg ab ]
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1.11 Supersymmetric Strings 49 One
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1.11 Supersymmetric Strings 51 of c
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1.11 Supersymmetric Strings 53 ∫
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Chapter 2 Feynman Path Integral For
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2.2 Sum over Paths 57 ∫ ∞ A(q i
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2.4 Gravitational Functional Measur
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2.5 Conformal Instability 65 ∫ I
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Chapter 3 Gravity in 2+ε Dimension
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3.2 Perturbatively Non-renormalizab
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3.3 Non-linear Sigma Model in the L
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3.3 Non-linear Sigma Model in the L
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3.4 Self-coupled Fermion Model 83 3
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3.5 The Gravitational Case 85 with
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3.5 The Gravitational Case 87 × ×
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3.5 The Gravitational Case 89 Next
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3.5 The Gravitational Case 91 1993a
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3.6 Phases of Gravity in 2+ε Dimen
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3.7 Running of α(μ) in Gauge Theo
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3.7 Running of α(μ) in Gauge Theo
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104 4 Hamiltonian and Wheeler-DeWit
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142 5 Semiclassical Gravity ordinar
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144 5 Semiclassical Gravity Î[g μ
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146 5 Semiclassical Gravity An alte
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148 5 Semiclassical Gravity with TT
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150 5 Semiclassical Gravity [ ] d d
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152 5 Semiclassical Gravity the cas
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154 5 Semiclassical Gravity essenti
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156 5 Semiclassical Gravity conserv
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158 5 Semiclassical Gravity ∫ E (
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160 5 Semiclassical Gravity of the
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162 5 Semiclassical Gravity One can
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164 5 Semiclassical Gravity that lo
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166 5 Semiclassical Gravity But the
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168 5 Semiclassical Gravity Fig. 5.
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170 6 Lattice Regularized Quantum G
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226 7 Analytical Lattice Expansion
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Chapter 8 Numerical Studies 8.1 Non
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8.2 Observables, Phase Structure an
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8.3 Invariant Local Gravitational A
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8.4 Invariant Correlations at Fixed
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8.5 Wilson Lines and Static Potenti
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8.5 Wilson Lines and Static Potenti
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8.7 Physical and Unphysical Phases
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8.8 Numerical Determination of the
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8.8 Numerical Determination of the
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8.9 Renormalization Group and Latti
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8.10 Curvature Scales 301 for gravi
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8.11 Gravitational Condensate 303 w
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306 9 Scale Dependent Gravitational
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Page 684: References Abbott, L., 1982, Introd
Page 688: References 327 Das, A., 1977, Phys.
Page 692: References 329 Hartle, J. B., 1985,
Page 696: References 331 Parisi, G., 1979, Ph
Page 704: Index 1/N expansion, 82 2 + ε expa
Page 708: Index 337 effective action, 152, 22
Page 712: Index 339 lattice supermetric, 135
Page 716: Index 341 scalar-graviton vertex, 1
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Feynman Path Integral Formulation

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