Introduction to Quantum Effects in Gravity
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...
Search in google:
Quantum field theory for undergraduates and graduates in theoretical astrophysics, cosmology, particle physics, and string theory.
Preface ixCanonical quantization and particle production 1Overview: a taste of quantum fields 3Classical field 3Quantum field and its vacuum state 4The vacuum energy 7Quantum vacuum fluctuations 8Particle interpretation of quantum fields 9Quantum field theory in classical backgrounds 9Examples of particle creation 10Reminder: classical and quantum theory 13Lagrangian formalism 13Functional derivatives 15Hamiltonian formalism 17Quantization of Hamiltonian systems 19Hilbert spaces and Dirac notation 20Operators, eigenvalue problem and basis in a Hilbert space 22Generalized eigenvectors and basic matrix elements 26Evolution in quantum theory 29Driven harmonic oscillator 33Quantizing an oscillator 33The "in" and "out" states 35Matrix elements and Green's functions 38From harmonic oscillators to fields 42Quantum harmonic oscillators 42From oscillators to fields 43Quantizing fields in a flat spacetime 45The mode expansion 48Vacuum energy and vacuum fluctuations 50The Schrodinger equation for a quantum field 51Reminder: classical fields 54The action functional 54Real scalar field and its coupling to the gravity 56Gauge invariance and coupling to the electromagnetic field 58Action for the gravitational and gauge fields 59Energy-momentum tensor 61Quantum fields in expanding universe 64Classical scalar field in expanding background 64Mode expansion 66Quantization 67Bogolyubov transformations 68Hilbert space; "a- and b-particles" 69Choice of the physical vacuum 71The instantaneous lowest-energy state 71Ambiguity of the vacuum state 74Amplitude of quantum fluctuations 78Comparing fluctuations in the vacuum and excited states 80An example of particle production 81Quantum fields in the de Sitter universe 85De Sitter universe 85Quantization 88Bunch-Davies vacuum 90Fluctuations in inflationary universe 92Unruh effect 97Accelerated motion 97Comoving frame of accelerated observer 100Quantum fields in inertial and accelerated frames 103Bogolyubov transformations 106Occupation numbers and Unruh temperature 107Hawking effect. Thermodynamics of black holes 109Hawking radiation 109Schwarzschild solution 110Kruskal-Szekeres coordinates 111Field quantization and Hawking radiation 115Hawking effect in 3 + 1 dimensions 118Thermodynamics of black holes 120Laws of black hole thermodynamics 121The Casimir effect 124Vacuum energy between plates 124Regularization and renormalization 125Path integrals and vacuum polarization 129Path integrals 131Evolution operator. Propagator 131Propagator as a path integral 132Lagrangian path integrals 137Propagators for free particle and harmonic oscillator 138Free particle 139Quadratic potential 139Euclidean path integral 142Ground state as a path integral 144Effective action 146Driven harmonic oscillator (continuation) 146Green's functions and matrix elements 146Euclidean Green's function 148Introducing effective action 150Calculating effective action for a driven oscillator 152Matrix elements 154The effective action "recipe" 157Backreaction 158Effective action in external gravitational field 159Euclidean action for scalar field 161Effective action as a functional determinant 163Reformulation of the eigenvalue problem 164Zeta function 166Heat kernel 167Calculation of heat kernel 170Perturbative expansion for the heat kernel 171Matrix elements 172Trace of the heat kernel 176The Seeley-DeWitt expansion 178Results from effective action 180Renormalization of the effective action 180Finite terms in the effective action 183EMT from the Polyakov action 185Conformal anomaly 187Mathematical supplement 193Functionals and distributions (generalized functions) 193Green's functions, boundary conditions, and contours 202Euler's gamma function and analytic continuations 206Backreaction derived from effective action 212Mode expansions cheat sheet 216Solutions to exercises 218Index 272
\ From the Publisher"... A groundbreaker in being an introductory text on quantum field theory in gravitational backgrounds, intended for undergraduate and beginning graduate students." \ Lewis H. Ryder, Mathematical Reviews\ "The treatment is clear throughout and the mathematical manipulations straightforward. This book is to be greatly recommended to anyone with an interest in contemporary theoretical cosmology; it is a most valuable contribution to the literature on the early universe."\ Contemporary Physics\ \ \
