Introduction to quantum effects in gravity

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Introduction to quantum effects in gravity / Viatcheslav Mukhanov and Sergei Winitzki

資料種別:

図書

出版情報:

Cambridge, UK : Cambridge University Press, 2007

形態:

x, 273 p. ; 26 cm

著者名:

ISBN:

9780521868341 [0521868343] (: hardback)

書誌ID:

BA82010462

子書誌情報

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書誌詳細

注記:

Includes bibliographical references and index

主題:

Gravity; Quantum field theory; Quantum gravity

言語:

英語

目次情報:

Preface

Canonical quantization and particle production / Part I：

Overview: a taste of quantum fields / 1：

Classical field / 1.1：

Quantum field and its vacuum state / 1.2：

The vacuum energy / 1.3：

Quantum vacuum fluctuations / 1.4：

Particle interpretation of quantum fields / 1.5：

Quantum field theory in classical backgrounds / 1.6：

Examples of particle creation / 1.7：

Reminder: classical and quantum theory / 2：

Lagrangian formalism / 2.1：

Functional derivatives / 2.1.1：

Hamiltonian formalism / 2.2：

Quantization of Hamiltonian systems / 2.3：

Hilbert spaces and Dirac notation / 2.4：

Operators, eigenvalue problem and basis in a Hilbert space / 2.5：

Generalized eigenvectors and basic matrix elements / 2.6：

Evolution in quantum theory / 2.7：

Driven harmonic oscillator / 3：

Quantizing an oscillator / 3.1：

The "in" and "out" states / 3.2：

Matrix elements and Green's functions / 3.3：

From harmonic oscillators to fields / 4：

Quantum harmonic oscillators / 4.1：

From oscillators to fields / 4.2：

Quantizing fields in a flat spacetime / 4.3：

The mode expansion / 4.4：

Vacuum energy and vacuum fluctuations / 4.5：

The Schrodinger equation for a quantum field / 4.6：

Reminder: classical fields / 5：

The action functional / 5.1：

Real scalar field and its coupling to the gravity / 5.2：

Gauge invariance and coupling to the electromagnetic field / 5.3：

Action for the gravitational and gauge fields / 5.4：

Energy-momentum tensor / 5.5：

Quantum fields in expanding universe / 6：

Classical scalar field in expanding background / 6.1：

Mode expansion / 6.1.1：

Quantization / 6.2：

Bogolyubov transformations / 6.3：

Hilbert space; "a- and b-particles" / 6.4：

Choice of the physical vacuum / 6.5：

The instantaneous lowest-energy state / 6.5.1：

Ambiguity of the vacuum state / 6.5.2：

Amplitude of quantum fluctuations / 6.6：

Comparing fluctuations in the vacuum and excited states / 6.6.1：

An example of particle production / 6.7：

Quantum fields in the de Sitter universe / 7：

De Sitter universe / 7.1：

Bunch-Davies vacuum / 7.2：

Fluctuations in inflationary universe / 7.3：

Unruh effect / 8：

Accelerated motion / 8.1：

Comoving frame of accelerated observer / 8.2：

Quantum fields in inertial and accelerated frames / 8.3：

Occupation numbers and Unruh temperature / 8.4：

Hawking effect. Thermodynamics of black holes / 9：

Hawking radiation / 9.1：

Schwarzschild solution / 9.1.1：

Kruskal-Szekeres coordinates / 9.1.2：

Field quantization and Hawking radiation / 9.1.3：

Hawking effect in 3 + 1 dimensions / 9.1.4：

Thermodynamics of black holes / 9.2：

Laws of black hole thermodynamics / 9.2.1：

The Casimir effect / 10：

Vacuum energy between plates / 10.1：

Regularization and renormalization / 10.2：

Path integrals and vacuum polarization / Part II：

Path integrals / 11：

Evolution operator. Propagator / 11.1：

Propagator as a path integral / 11.2：

Lagrangian path integrals / 11.3：

Propagators for free particle and harmonic oscillator / 11.4：

Free particle / 11.4.1：

Quadratic potential / 11.4.2：

Euclidean path integral / 11.4.3：

Ground state as a path integral / 11.4.4：

Effective action / 12：

Driven harmonic oscillator (continuation) / 12.1：

Green's functions and matrix elements / 12.1.1：

Euclidean Green's function / 12.1.2：

Introducing effective action / 12.1.3：

Calculating effective action for a driven oscillator / 12.1.4：

Matrix elements / 12.1.5：

The effective action "recipe" / 12.1.6：

Backreaction / 12.1.7：

Effective action in external gravitational field / 12.2：

Euclidean action for scalar field / 12.2.1：

Effective action as a functional determinant / 12.3：

Reformulation of the eigenvalue problem / 12.3.1：

Zeta function / 12.3.2：

Heat kernel / 12.3.3：

Calculation of heat kernel / 13：

Perturbative expansion for the heat kernel / 13.1：

Trace of the heat kernel / 13.1.1：

The Seeley-DeWitt expansion / 13.3：

Results from effective action / 14：

Renormalization of the effective action / 14.1：

Finite terms in the effective action / 14.2：

EMT from the Polyakov action / 14.2.1：

Conformal anomaly / 14.3：

Mathematical supplement / Appendix 1：

Functionals and distributions (generalized functions) / A1.1：

Green's functions, boundary conditions, and contours / A1.2：

Euler's gamma function and analytic continuations / A1.3：

Backreaction derived from effective action / Appendix 2：

Mode expansions cheat sheet / Appendix 3：

Solutions to exercises / Appendix 4：

Index

Preface

Canonical quantization and particle production / Part I：

Overview: a taste of quantum fields / 1：

Classical field / 1.1：

Quantum field and its vacuum state / 1.2：

The vacuum energy / 1.3：

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