- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Operator description for thermal quantum field theories on an arbitrary path in the real time formalism

Ashok Das1,2 and Pushpa Kalauni3

  • 1Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627-0171, USA
  • 2Institute of Physics, Sachivalaya Marg, Bhubaneswar 751005, India
  • 3Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019, USA

PDF

Phys. Rev. D 93, 125028 – Published 22 June, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.125028

Abstract

We develop an operator description, much like thermofield dynamics, for quantum field theories on a real time path with an arbitrary parameter σ (0≤σ≤β). We point out new features which arise when σ≠β2 in that the Hilbert space develops a natural, modified inner product different from the standard Dirac inner product. We construct the Bogoliubov transformation which connects the doubled vacuum state at zero temperature to the thermal vacuum in this case. We obtain the thermal Green’s function (propagator) for the real massive Klein-Gordon theory as an expectation value in this thermal vacuum (with a modified inner product). The factorization of the thermal Green’s function follows from this analysis. We also discuss, in the main text as well as in two appendices, various other interesting features which arise in such a description.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (27)

  1. J. Schwinger, Brownian motion of a quantum oscillator, J. Math. Phys. 2, 407 (1961); in Proceedings of the 3rd Brandeis Summer Institute in Theoretical Physics, edited by (Brandeis University, Waltham, MA, 1960).
  2. P. M. Bakshi and K. T. Mahanthappa, Expectation value formalism in quantum field theory. I, J. Math. Phys. (N.Y.) 4, 1 (1963).
  3. L. V. Keldysh, Diagram technique for nonequilibrium processes, Sov. Phys. JETP 20, 1018 (1965).
  4. Y. Takahashi and H. Umezawa, Thermofield dynamics, Collective Phenomena 2, 55 (1975), also reprinted in; Thermo field dynamics, Int. J. Mod. Phys. B 10, 1755 (1996).
  5. H. Umezawa, H. Matsumoto, and M. Tachiki, Thermo Field Dynamics and Condensed States (North-Holland, Amsterdam, 1982).
  6. H. Umezawa, Advanced Field Theory: Micro, Macro, and Thermal Physics (AIP Press, New York, 1995).
  7. T. Matsubara, A new approach to quantum-statistical mechanics, Prog. Theor. Phys. 14, 351 (1955).
  8. K. C. Chou, Z. B. Su, B. L. Hao, and L. Yu, Equilibrium and nonequilibrium formalisms made unified, Phys. Rep. 118, 1 (1985).
  9. N. P. Landsman and Ch. G. Van Weert, Real and imaginary-time field theory at finite temperature and density, Phys. Rep. 145, 141 (1987).
  10. M. L. Bellac, Thermal Field Theory (Cambridge University Press, Cambridge, England, 1996).
  11. A. Das, Finite Temperature Field Theory (World scientific, Singapore, 1997).
  12. F. C. Khanna, A. P. C. Malbouisson, J. M. C. Malbouisson, and A. E. Santana, Thermal Quantum Field Theory: Algebraic Aspects and Applications (World Scientific, Singapore, 2009).
  13. H. Matsumoto, Y. Nakano, H. Umezawa, F. Mancini, and M. Marinaro, Thermofield dynamics in interaction representation, Prog. Theor. Phys. 70, 599 (1983).
  14. H. Matsumoto, Y. Nakano, and H. Umezawa, An equivalence class of quantum field theories at finite temperature, J. Math. Phys. (N.Y.) 25, 3076 (1984).
  15. I. Ojima, Gauge fields at finite temperatures: Thermo field dynamics, the KMS condition and their extension to gauge theories, Ann. Phys. (N.Y.) 137, 1 (1981).
  16. T. S. Evans, I. Hardman, H. Umezawa, and Y. Yamanaka, Heisenberg and interaction representation in thermofield dynamics, J. Math. Phys. (N.Y.) 33, 370 (1992).
  17. H. Chu and H. Umezawa, A unified formalism of thermal quantum field theory, Int. J. Mod. Phys. A 09, 2363 (1994).
  18. P. A. Henning and H. Umezawa, Diagonalization of propagators in thermofield dynamics for relativistic quantum fields, Nucl. Phys. B417, 463 (1994).
  19. P. Elmfors and H. Umezawa, Generalizations of the thermal Bogoliubov transformation, Physica A (Amsterdam) 202, 577 (1994).
  20. P. A. Henning, Thermofield dynamics for quantum fields with continuous spectrum, Phys. Rep. 253, 235 (1995).
  21. H. H. Xu, Bogoliubov matrices in thermal field theory, Commun. Theor. Phys. 26, 289 (1996).
  22. A. E. Santana, F. C. Khanna, H. Chu, and Y. C. Chang, Thermal Lie groups, classical mechanics, and thermofield dynamics, Ann. Phys. (N.Y.) 249, 481 (1996).
  23. C. M. Bender and S. Boettcher, Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry, Phys. Rev. Lett. 80, 5243 (1998).
  24. C. M. Bender, S. Boettcher, and P. Meisinger, PT-symmetric quantum mechanics, J. Math. Phys. (N.Y.) 40, 2201 (1999).
  25. A. Mostafazadeh, Pseudo-Hermiticity and generalized PTand CPT-symmetries, J. Math. Phys. (N.Y.) 44, 974 (2003).
  26. A. Das and L. Greenwood, An alternative construction of the positive inner product in non-Hermitian quantum mechanics, Phys. Lett. B 678, 504 (2009).
  27. A. Das and L. Greenwood, An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples, J. Math. Phys. (N.Y.) 51, 042103 (2010).

Outline

Information

Phys. Rev. D 93, 125028– Published 22 June, 2016
  • Received 22 March 2016

© 2016 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation