Thermal quantum field theory : algebraic aspects and applications /
This monograph presents recent developments in quantum field theory at finite temperature. By using Lie groups, ideas from thermal theory are considered with concepts of symmetry, allowing for applications not only to quantum field theory but also to transport theory, quantum optics and statistical...
| Други автори: | Khanna, F. C. |
|---|---|
| Формат: | Електронна книга |
| Език: | English |
| Публикувано: |
New Jersey :
World Scientific,
℗♭2009.
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| Предмети: | |
| Онлайн достъп: |
http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305192 |
| Подобни документи: |
Print version::
Thermal quantum field theory. |
Съдържание:
- pt. I. General principles. 1. Elements of thermodynamics. 1.1. Kinematical aspects of thermal physics. 1.2. Dynamical aspects of thermal physics. 1.3. Equations of state. 1.4. The meaning of intensive variables. 1.5. Thermodynamical potentials. 1.6. Gibbs-Duhem relation. 1.7. Second derivatives. 1.8. Example : ideal gas and generalizations. 1.9. Stability conditions and phase transitions. 2. Elements of statistical mechanics. 2.1. Macro- and micro-physics. 2.2. Liouville-von Neumann equation. 2.3. Gibbs ensembles. 2.4. Wigner function formalism. 3. Partition function and path integral. 3.1. Partition function and the propagator. 3.2. Path integral in quantum mechanics. 3.3. Classical elds. 3.4. Canonical quantization of scalar fields. 3.5. Path integral for a scalar field. 5.6. Canonical quantization of the Dirac field. 3.7. Path integral for the Dirac field. 4. Zero temperature interacting fields. 4.1. Generating functional for bosons. 4.2. The effective action. 4.3. Gauge fields. 4.4. Generating functional for gauge fields. 4.5. U(1) gauge theory. 4.6. SU(3) gauge theory. 4.7. Scattering amplitudes. 4.8. S-matrix in the canonical approach
- pt. II. Thermal fields. 5. Thermofield dynamics : kinematical symmetry algebraic basis. 5.1. Thermal Hilbert space. 5.2. The meaning of the doubling : thermo-algebras. 5.3. Tilde and non-tilde operators. 5.4. Liouville-von Neumann equation. 5.5. Physical implications of thermo-algebras. 6. Thermal oscillators : bosons and fermions. 6.1. Boson oscillators. 6.2. Fermion oscillators. 6.3. TFD and spin 1/2 lattices. 7. Thermal Poincare and Galilei groups. 7.1. The Poincare group. 7.2. Relativistic density matrices. 7.3. The Galilei group. 7.4. Galilean density matrices. 7.5. Lagrangians. 8. Thermal Propagator. 8.1. Thermal Klein-Gordon field. 8.2. Thermal Dirac field. 8.3. Doubled notation for bosons. 8.4. Generating functional for bosons. 8.5. Generating functional for fermions. 8.6. Thermal gauge fields. 9. Scattering process at finite temperature. 9.1. Scattering matrix in TFD. 9.2. Reaction rates. 9.3. Decay of particles and generalized Cutkosky rules. 9.4. Decay of Higgs meson. 9.5. The detailed balance. 9.6. Scattering cross-section of 1+2->1'+2'. 9.7. Fermion-boson scattering. 10. Topics on renormalization theory. 10.1. Ultraviolet divergences. 10.2. Regularization. 10.3. Renormalization. 10.4. Bogoliubov recurrence. 10.5. Temperature eects. 11. Ward-Takahashi relations and gauge symmetry. 11.1. Ward relation. 11.2. Ward-Takahashi relations. 11.3. Applications of generalized Ward-Takahashi relations. 11.4. Transverse Ward-Takahashi relations. 11.5. Transverse W-T relation in momentum space. 11.6. W-T relations and spontaneous symmetry breaking
- pt. III. Applications to quantum optics. 12. Thermalized states of a field mode. 12.1. Thermalized states. 12.2. Physical interpretation. 12.3. Other possibilities of thermalized states. 13. Nonclassical properties of thermal quantum states. 13.1. Photon statistics. 13.2. Quadrature squeezing. 13.3. Atomic population inversion. 13.4. Phase space representation. 14. SU(2) and SU(1,1) systems : entanglement. 14.1. Maximum entanglement. 14.2. Maximally entangled states and SU(1,1) symmetry. 14.3. Maximally entangled states and SU(2) symmetry. 14.4. Entanglement of a system with fixed spin. 14.5. Entanglement of two-boson squeezed states. 14.6. Coherent fermion states and density matrix operators. 14.7. Entanglement of two-mode squeezed fermion states
- pt. IV. Compactified fields. 15. Compactified fields. 15.1. Compactification and topology. 15.2. Generalized Bogoliubov transformation. 15.3. Field theory. 15.4. Feynman rules. 16. Casimir effect for the electromagnetic field. 16.1. The vacuum state of the electromagnetic field. 16.2. The Casimir effect. 16.3. Casimir-Boyer model. 17. Casimir Effect for fermions. 17.1. Casimir effect in [symbol]. 17.2. Compactification in higher dimensions. 17.3. Casimir effect for two plates. 17.4. Casimir effect for a waveguide. 17.5. Casimir effect for a box. 17.6. Casimir effect for a non-interacting massless QCD. 18. Compactified [symbol] theory. 18.1. Compactification of a d-dimensional subspace. 18.2. Subtraction scheme. 18.3. The zero-temperature compactified model. 18.4. The compactified model at finite temperature : spontaneous symmetry breaking. 19. Phase transitions in confined systems : application to superconducting films. 19.1. Overview. 19.2. Second-order phase transition in superconducting films. 19.3. Mass renormalization and transition temperature. 19.4. Critical behavior of type-II superconducting films in a magnetic field. 20. Second-order phase transition in wires and grains. 20.1. Compactification of a d-dimensional subspace. 20.2. Critical behavior for wires. 20.3. Critical behavior for grains. 20.4. Boundary effects on the coupling constant. 20.5. Effects of the boundary-corrected coupling constant on the critical behavior. 20.6. Universal behavior of size-effects in second-order phase transitions. 21. First-order phase transitions in confined systems. 21.1. Effective potential with compactification of a d-dimensional subspace. 21.2. The film, the wire and the grain
- pt. V. Applications to open systems. 22. Thermo-algebras in phase space : quantum and classical systems. 22.1. Wigner function for the Schrodinger field. 22.2. Wigner function for the Klein-Gordon field. 22.3. Wigner function for the Dirac field. 22.4. Representations for classical systems. 22.5. Classical unitary representations. 22.6. Liouville equation for the oscillator. 22.7. Non-relativistic symmetries in the Schonberg-Fock space. 22.8. Classical relativistic representation. 22.9. Boltzmann equation and non-relativistic limit. 23. Real-time method for nonequilibrium quantum mechanics. 23.1. Schrodinger, Heisenberg and Liouville pictures. 23.2. Linear model for phase transition. 23.3. Nonlinear model for phase transition. 23.4. Beyond the Hartree approximation for nonlinear model. 23.5. TFD for time-dependent boson system. 24. Dressed and bare state approaches to the thermalization process. 24.1. The model. 24.2. The thermalization process in bare coordinates. 24.3. Dressed coordinates and dressed states. 24.4. Thermal behavior for a cavity of arbitrary size with dressed coordinates. 24.5. The limit of arbitrarily large cavity : unbounded space.