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Euclidean Quantum Gravity on Manifolds with Boundary

  • Giampiero Esposito
  • Alexander Yu. Kamenshchik
  • Giuseppe Pollifrone

Part of the Fundamental Theories of Physics book series (FTPH, volume 85)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. General Formalism

    1. Front Matter
      Pages 1-1
    2. Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone
      Pages 2-37
    3. Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone
      Pages 38-50
    4. Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone
      Pages 51-79
    5. Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone
      Pages 80-105
    6. Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone
      Pages 106-130
    7. Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone
      Pages 131-158
  3. Gauge Fields and Gravitation

    1. Front Matter
      Pages 159-159
    2. Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone
      Pages 160-217
    3. Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone
      Pages 218-250
    4. Giampiero Esposito, Alexander Yu. Kamenshchik, Giuseppe Pollifrone
      Pages 251-298
  4. Back Matter
    Pages 299-322

About this book

Introduction

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.

Keywords

Gravity Minkowski space manifold quantum field theory quantum mechanics relativity

Authors and affiliations

  • Giampiero Esposito
    • 1
    • 2
  • Alexander Yu. Kamenshchik
    • 3
  • Giuseppe Pollifrone
    • 4
    • 5
  1. 1.National Institute for Nuclear PhysicsNaplesItaly
  2. 2.Department of Physical SciencesUniversity of NaplesNaplesItaly
  3. 3.Nuclear Safety InstituteRussian Academy of SciencesMoscowRussia
  4. 4.National Institute for Nuclear PhysicsRomeItaly
  5. 5.Department of Physics“La Sapienza” UniversityRomeItaly

Bibliographic information