Euclidean Quantum Gravity on Manifolds with Boundary

1. Front Matter

   Pages i-xiii

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2. General Formalism

   1. Front Matter

      Pages 1-1

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   2. The Role of Boundaries in Modern Physics

      • Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone

      Pages 2-37

   3. Schwinger-DeWitt Asymptotic Expansion

      • Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone

      Pages 38-50

   4. Effective Action in Quantum Field Theory

      • Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone

      Pages 51-79

   5. Covariant Quantization of Gauge Theories

      • Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone

      Pages 80-105

   6. The Zeta-Function

      • Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone

      Pages 106-130

   7. Boundary Conditions

      • Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone

      Pages 131-158

3. Gauge Fields and Gravitation

   1. Front Matter

      Pages 159-159

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   2. Euclidean Maxwell Theory

      • Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone

      Pages 160-217

   3. Simple Supergravity

      • Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone

      Pages 218-250

   4. Euclidean Quantum Gravity

      • Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone

      Pages 251-298

4. Back Matter

   Pages 299-322

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This book reflects our own struggle to understand the semiclassical behaviour of quantized fields in the presence of boundaries. Along many years, motivated by the problems of quantum cosmology and quantum field theory, we have studied in detail the one-loop properties of massless spin-l/2 fields, Euclidean Maxwell the­ ory, gravitino potentials and Euclidean quantum gravity. Hence our book begins with a review of the physical and mathematical motivations for studying physical theories in the presence of boundaries, with emphasis on electrostatics, vacuum v Maxwell theory and quantum cosmology. We then study the Feynman propagator in Minkowski space-time and in curved space-time. In the latter case, the corre­ sponding Schwinger-DeWitt asymptotic expansion is given. The following chapters are devoted to the standard theory of the effective action and the geometric im­ provement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the problem of boundary conditions in one-loop quantum theory. For this purpose, we study in detail Dirichlet, Neumann and Robin boundary conditions for scalar fields, local and non-local boundary conditions for massless spin-l/2 fields, mixed boundary conditions for gauge fields and gravitation. This is the content of Part I. Part II presents our investigations of Euclidean Maxwell theory, simple super­ gravity and Euclidean quantum gravity.

• Gravity
• Minkowski space
• manifold
• quantum field theory
• quantum mechanics
• relativity

• National Institute for Nuclear Physics, Naples, Italy

  Giampiero Esposito

• Department of Physical Sciences, University of Naples, Naples, Italy

  Giampiero Esposito

• Nuclear Safety Institute, Russian Academy of Sciences, Moscow, Russia

  Alexander Yu. Kamenshchik

• National Institute for Nuclear Physics, Rome, Italy

  Giuseppe Pollifrone

• Department of Physics, “La Sapienza” University, Rome, Italy

  Giuseppe Pollifrone

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