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Schwinger Action Principle and Effective Action

ISBN-10: 0521876761

ISBN-13: 9780521876766

Edition: 2008

Authors: David J. Toms

List price: $184.99
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This book is an introduction to the Schwinger action principle in quantum mechanics and quantum field theory, with applications to a variety of different models including Bose-Einstein condensation, the Casimir effect, and trapped Fermi gases. The book begins with a brief review of the action principle in classical mechanics and classical field theory. It then moves on to quantum field theory, focussing on the effective action method. This is introduced as simply as possible by using the zero-point energy of the simple harmonic oscillator as the starting point. The book concludes with a more complete definition of the effective action, and demonstrates how the provisional definition used earlier is the first term in the systematic loop expansion. The renormalization of interacting scalar field theory is presented to two-loop order. This book will interest graduate students and researchers in theoretical physics who are familiar with quantum mechanics.
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Book details

List price: $184.99
Copyright year: 2008
Publisher: Cambridge University Press
Publication date: 11/15/2007
Binding: Hardcover
Pages: 508
Size: 7.00" wide x 9.50" long x 1.25" tall
Weight: 2.244
Language: English

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