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| Preface | |
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| Action principle in classical mechanics | |
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| Euler-Lagrange equations | |
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| Hamilton's principle | |
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| Hamilton's equations | |
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| Canonical transformations | |
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| Conservation laws and symmetries | |
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| Notes | |
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| Action principle in classical field theory | |
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| Continuous systems | |
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| Lagrangian and Hamiltonian formulation for continuous systems | |
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| Some examples | |
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| Functional differentiation and Poisson brackets for field theory | |
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| Noether's theorem | |
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| The stress-energy-momentum tensor | |
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| Gauge invariance | |
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| Fields of general spin | |
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| The Dirac equation | |
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| Notes | |
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| Action principle in quantum theory | |
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| States and observables | |
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| Schwinger action principle | |
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| Equations of motion and canonical commutation relations | |
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| Position and momentum eigenstates | |
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| Simple harmonic oscillator | |
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| Real scalar field | |
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| Complex scalar field | |
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| Schrodinger field | |
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| Dirac field | |
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| Electromagnetic field | |
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| Notes | |
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| The effective action | |
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| Introduction | |
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| Free scalar field in Minkowski spacetime | |
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| Casimir effect | |
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| Constant gauge field background | |
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| Constant magnetic field | |
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| Self-interacting scalar field | |
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| Local Casimir effect | |
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| Notes | |
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| Quantum statistical mechanics | |
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| Introduction | |
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| Simple harmonic oscillator | |
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| Real scalar field | |
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| Charged scalar field | |
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| Non-relativistic field | |
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| Dirac field | |
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| Electromagnetic field | |
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| Notes | |
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| Effective action at finite temperature | |
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| Condensate contribution | |
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| Free homogeneous non-relativistic Bose gas | |
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| Internal energy and specific heat | |
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| Bose gas in a harmonic oscillator confining potential | |
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| Density of states method | |
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| Charged non-relativistic Bose gas in a constant magnetic field | |
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| The interacting Bose gas | |
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| The relativistic non-interacting charged scalar field | |
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| The interacting relativistic field | |
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| Fermi gases at finite temperature in a magnetic field | |
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| Trapped Fermi gases | |
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| Notes | |
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| Further applications of the Schwinger action principle | |
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| Integration of the action principle | |
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| Application of the action principle to the free particle | |
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| Application to the simple harmonic oscillator | |
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| Application to the forced harmonic oscillator | |
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| Propagators and energy levels | |
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| General variation of the Lagrangian | |
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| The vacuum-to-vacuum transition amplitude | |
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| More general systems | |
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| Notes | |
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| General definition of the effective action | |
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| Generating functionals for free field theory | |
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| Interacting fields and perturbation theory | |
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| Feynman diagrams | |
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| One-loop effective potential for a real scalar field | |
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| Dimensional regularization and the derivative expansion | |
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| Renormalization of [lambda phi superscript 4] theory | |
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| Finite temperature | |
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| Generalized CJT effective action | |
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| CJT approach to Bose-Einstein condensation | |
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| Notes | |
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| Mathematical appendices | |
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| Review of special relativity | |
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| Interaction picture | |
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| Bibliography | |
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| Index | |