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