Ebook: Euclidean Quantum Gravity on Manifolds with Boundary

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.

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The 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 Maxwell theory and quantum cosmology. The Feynman propagator is then studied in Minkowski space- time and in curved space-time. In the latter case, the corresponding Schwinger-DeWitt asymptotic expansion is given. The following chapters introduce the theory of the effective action and the geometric improvement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the choice of local or non-local boundary conditions in one-loop quantum theory. In the second part, the authors present their investigations of Euclidean Maxwell theory, simple supergravity and Euclidean quantum gravity. The recurring themes are the evaluation of conformal anomalies and one-loop divergences on manifolds with boundary, the relation between covariant and non-covariant formalisms for the quantization of gauge fields and the choice of boundary condition in the one-loop semiclassical analysis of Euclidean quantum gravity and simple supergravity.
Audience: This work will appeal to research workers involved in quantum field theory, relativity and gravitation, electromagnetic theory, cosmology and quantum mechanics.

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The 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 Maxwell theory and quantum cosmology. The Feynman propagator is then studied in Minkowski space- time and in curved space-time. In the latter case, the corresponding Schwinger-DeWitt asymptotic expansion is given. The following chapters introduce the theory of the effective action and the geometric improvement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the choice of local or non-local boundary conditions in one-loop quantum theory. In the second part, the authors present their investigations of Euclidean Maxwell theory, simple supergravity and Euclidean quantum gravity. The recurring themes are the evaluation of conformal anomalies and one-loop divergences on manifolds with boundary, the relation between covariant and non-covariant formalisms for the quantization of gauge fields and the choice of boundary condition in the one-loop semiclassical analysis of Euclidean quantum gravity and simple supergravity.
Audience: This work will appeal to research workers involved in quantum field theory, relativity and gravitation, electromagnetic theory, cosmology and quantum mechanics.
Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
The Role of Boundaries in Modern Physics....Pages 2-37
Schwinger-DeWitt Asymptotic Expansion....Pages 38-50
Effective Action in Quantum Field Theory....Pages 51-79
Covariant Quantization of Gauge Theories....Pages 80-105
The Zeta-Function....Pages 106-130
Boundary Conditions....Pages 131-158
Front Matter....Pages 159-159
Euclidean Maxwell Theory....Pages 160-217
Simple Supergravity....Pages 218-250
Euclidean Quantum Gravity....Pages 251-298
Back Matter....Pages 299-322

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The 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 Maxwell theory and quantum cosmology. The Feynman propagator is then studied in Minkowski space- time and in curved space-time. In the latter case, the corresponding Schwinger-DeWitt asymptotic expansion is given. The following chapters introduce the theory of the effective action and the geometric improvement due to Vilkovisky, the manifestly covariant quantization of gauge fields, zeta-function regularization in mathematics and in quantum field theory, and the choice of local or non-local boundary conditions in one-loop quantum theory. In the second part, the authors present their investigations of Euclidean Maxwell theory, simple supergravity and Euclidean quantum gravity. The recurring themes are the evaluation of conformal anomalies and one-loop divergences on manifolds with boundary, the relation between covariant and non-covariant formalisms for the quantization of gauge fields and the choice of boundary condition in the one-loop semiclassical analysis of Euclidean quantum gravity and simple supergravity.
Audience: This work will appeal to research workers involved in quantum field theory, relativity and gravitation, electromagnetic theory, cosmology and quantum mechanics.
Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
The Role of Boundaries in Modern Physics....Pages 2-37
Schwinger-DeWitt Asymptotic Expansion....Pages 38-50
Effective Action in Quantum Field Theory....Pages 51-79
Covariant Quantization of Gauge Theories....Pages 80-105
The Zeta-Function....Pages 106-130
Boundary Conditions....Pages 131-158
Front Matter....Pages 159-159
Euclidean Maxwell Theory....Pages 160-217
Simple Supergravity....Pages 218-250
Euclidean Quantum Gravity....Pages 251-298
Back Matter....Pages 299-322
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