Discourses in Mathematics and Its Applications, No. 4 1995

Heat Kernel Techniques and Quantum Gravity

Edited by S. A. Fulling

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Conference Schedule . . . . . . . . . . . . . . . . . . . . . . . . . iv Heat Equation and Heat Content Asymptotics . . . . . . . . . . . . . . 1

Peter B. Gilkey Euclidean Maxwell Theory in the Presence of Boundaries . . . . . . . . . 11

Giampiero Esposito Zeta-Function Technique on Manifolds with Boundaries and its

Applications in Quantum Cosmology . . . . . . . . . . . . . . . . . 23

A.Yu. Kamenshchik Quantum Electrodynamics and Quantum Gravity . . . . . . . . . . . . . 35

Leonard Parker Computational Challenges in Heat Kernel Calculations . . . . . . . . . . 47

Steven M. Christensen Heat Kernel Technique for Nonminimal Operators . . . . . . . . . . . . 65

V.P. Gusynin An Improved Heat Kernel Expansion From Wordline Path Integrals …. 87

P. Haberl, D. Fliegner, M.G. Schmidt and C. Schubert Structural Aspects of the Exponential Expansion of the Heat Kernel … 101

G. Kennedy and S.A. Fulling New Algebraic Methods for Calculating in Heat Kernel and the

Effective Action in Quantum Gravity and Gauge Theories . . . . . . . 115

Ivan G. Avramidi Heat Kernels, Dirac Operators and Stochastic Calculus in Superspace … 141

Alice Rogers Superfield Effective Potential . . . . . . . . . . . . . . . . . . . . . 151

I.L. Buchbinder, S.M. Kuzenko, A.Yu. Petrov and I.V. Yarevskaya

(continued)

Covariant Curvature Expansion and Trace Anomaly

in Four Dimensions . . . . . . . . . . . . . . . . . . . . . . . . 163 A.O. Barvinsky, G.A. Vilkovisky, Yu.V. Gusev and V.V. Zhytnikov

Heat Kernel and Loop Currents by the Generating-Function Method … 189 Andrei Barvinsky and Yuri Gusev

Heat Kernels and Polytopes . . . . . . . . . . . . . . . . . . . . . 203 J.S. Dowker

Cosmic String in Thermal Bath and Casimir Effect

in Accelerated Frame . . . . . . . . . . . . . . . . . . . . . . . 217 V.P. Frolov, A. Pinzul and A.I. Zelnikov

Backreaction Effects in Black Hole Spacetimes: How Quantum Fields Affect the Geometries, Temperatures and Entropies of Static Black Holes . . . . . . . . . . . . . . . . . . . . . . . 227

Paul R. Anderson, Hooman Bahrani, William A. Hiscock, Daniel J. Loranz, David A. Samuel, Janet Whitesell and James W. York, Jr.

On the Influence of Spacetime Properties in ϕ^{4}

Scalar Field Theories . . . . . . . . . . . . . . . . . . . . . . . 239 E. Elizalde, K. Kirsten, G. Cognola, L. Vanzo and S. Zerbini

Average Action in the Einstein Universe . . . . . . . . . . . . . . . 253 A. Bonanno

Correlations, Decoherence, Dissipation, and Noise

in Quantum Field Theory . . . . . . . . . . . . . . . . . . . . . 261 Esteban Calzetta and B.L. Hu

Lower-Dimensional Black Holes: Inside and Out . . . . . . . . . . . . 303 R.B. Mann

Classical and Quantum Mechanics of Black Holes in Generic

2-D Dilation Gravity . . . . . . . . . . . . . . . . . . . . . . . 333 J. Gegenberg, G. Kunstatter and Louis-Martinez

Black Hole Entropy . . . . . . . . . . . . . . . . . . . . . . . . . 347 Valeri Frolov

Black Hole Entropy in Higher-Curvature Gravity . . . . . . . . . . . . 365 Ted Jacobson, Gungwon Kang and Robert C. Myers

(continued)

Two Topics Concerning Black Holes: Extremality of the Energy,

Fractality of the Horizon . . . . . . . . . . . . . . . . . . . . . . 387 Rafael D. Sorkin

Gravitating, Gravitational and Dilatonic Sphalerons . . . . . . . . . . . 409 George Lavrelashvili

Symmetries of Heterotic String Effective Theory in Three

and Two Dimensions . . . . . . . . . . . . . . . . . . . . . . . 421 D.V. Gal’tsov

The Gromov–Lawson–Rosenberg Conjecture: When Do Manifolds

Admit Metrics Of Positive Scalar Curvature? . . . . . . . . . . . . 449 Peter B. Gilkey

Information Loss in Black Holes and/or Conscious Beings? . . . . . . . 461 Don N. Page