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Introduction to Quantum Effects in Gravity

ISBN-10: 0521868343

ISBN-13: 9780521868341

Edition: 2007

Authors: Viatcheslav Mukhanov, Sergei Winitzki

List price: $130.00
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This is the first introductory textbook on quantum field theory in gravitational backgrounds intended for undergraduate and beginning graduate students in the fields of theoretical astrophysics, cosmology, particle physics, and string theory. The book covers the basic (but essential) material of quantization of fields in an expanding universe and quantum fluctuations in inflationary spacetime. It also contains a detailed explanation of the Casimir, Unruh, and Hawking effects, and introduces the method of effective action used for calculating the back-reaction of quantum systems on a classical external gravitational field. The broad scope of the material covered will provide the reader with a thorough perspective of the subject. Every major result is derived from first principles and thoroughly explained. The book is self-contained and assumes only a basic knowledge of general relativity. Exercises with detailed solutions are provided throughout the book.
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Book details

List price: $130.00
Copyright year: 2007
Publisher: Cambridge University Press
Publication date: 6/14/2007
Binding: Hardcover
Pages: 284
Size: 6.75" wide x 9.50" long x 0.75" tall
Weight: 1.584
Language: English

Canonical quantization and particle production
Overview: a taste of quantum fields
Classical field
Quantum field and its vacuum state
The vacuum energy
Quantum vacuum fluctuations
Particle interpretation of quantum fields
Quantum field theory in classical backgrounds
Examples of particle creation
Reminder: classical and quantum theory
Lagrangian formalism
Functional derivatives
Hamiltonian formalism
Quantization of Hamiltonian systems
Hilbert spaces and Dirac notation
Operators, eigenvalue problem and basis in a Hilbert space
Generalized eigenvectors and basic matrix elements
Evolution in quantum theory
Driven harmonic oscillator
Quantizing an oscillator
The "in" and "out" states
Matrix elements and Green's functions
From harmonic oscillators to fields
Quantum harmonic oscillators
From oscillators to fields
Quantizing fields in a flat spacetime
The mode expansion
Vacuum energy and vacuum fluctuations
The Schrodinger equation for a quantum field
Reminder: classical fields
The action functional
Real scalar field and its coupling to the gravity
Gauge invariance and coupling to the electromagnetic field
Action for the gravitational and gauge fields
Energy-momentum tensor
Quantum fields in expanding universe
Classical scalar field in expanding background
Mode expansion
Bogolyubov transformations
Hilbert space; "a- and b-particles"
Choice of the physical vacuum
The instantaneous lowest-energy state
Ambiguity of the vacuum state
Amplitude of quantum fluctuations
Comparing fluctuations in the vacuum and excited states
An example of particle production
Quantum fields in the de Sitter universe
De Sitter universe
Bunch-Davies vacuum
Fluctuations in inflationary universe
Unruh effect
Accelerated motion
Comoving frame of accelerated observer
Quantum fields in inertial and accelerated frames
Bogolyubov transformations
Occupation numbers and Unruh temperature
Hawking effect. Thermodynamics of black holes
Hawking radiation
Schwarzschild solution
Kruskal-Szekeres coordinates
Field quantization and Hawking radiation
Hawking effect in 3 + 1 dimensions
Thermodynamics of black holes
Laws of black hole thermodynamics
The Casimir effect
Vacuum energy between plates
Regularization and renormalization
Path integrals and vacuum polarization
Path integrals
Evolution operator. Propagator
Propagator as a path integral
Lagrangian path integrals
Propagators for free particle and harmonic oscillator
Free particle
Quadratic potential
Euclidean path integral
Ground state as a path integral
Effective action
Driven harmonic oscillator (continuation)
Green's functions and matrix elements
Euclidean Green's function
Introducing effective action
Calculating effective action for a driven oscillator
Matrix elements
The effective action "recipe"
Effective action in external gravitational field
Euclidean action for scalar field
Effective action as a functional determinant
Reformulation of the eigenvalue problem
Zeta function
Heat kernel
Calculation of heat kernel
Perturbative expansion for the heat kernel
Matrix elements
Trace of the heat kernel
The Seeley-DeWitt expansion
Results from effective action
Renormalization of the effective action
Finite terms in the effective action
EMT from the Polyakov action
Conformal anomaly
Mathematical supplement
Functionals and distributions (generalized functions)
Green's functions, boundary conditions, and contours
Euler's gamma function and analytic continuations
Backreaction derived from effective action
Mode expansions cheat sheet
Solutions to exercises