Abstract
It is shown that the perturbative expansions of the correlation functions of a relativistic quantum field theory at finite temperature are uniquely determined by the equations of motion and standard axiomatic requirements, including the KMS condition. An explicit expression as a sum over generalized Feynman graphs is derived. The canonical formalism is not used, and the derivation proceeds from the beginning in the thermodynamic limit. No doubling of fields is invoked. An unsolved problem concerning existence of these perturbative expressions is pointed out.
Similar content being viewed by others
References
Kapusta, J.I.: Finite-Temperature Field Theory. Cambridge: Cambridge University Press, 1989
Landsman, N.P., van Weert Ch.G.: Real- and imaginary-time field theory at finite temperature and density. Phys. Reps.145, 141 (1987)
Haag, R.: Local Quantum Physics. Berlin, Heidelberg, New York: Springer, 1992
Umezawa, H., Matsumoto, H., Tachiki, M.: Thermo Field Dynamics and Condensed States. Amsterdam: North-Holland, 1982; Umezawa, H.: Advanced Field Theory. New York: American Institute of Physics, 1993
Landsman, N.P.: Non-shell unstable particles in thermal field theory. Ann. Phys. (NY)186, 141 (1988)
Steinmann, O.: Perturbation theory of Wightman functions. Commun. Math. Phys.152, 627 (1993)
Zimmermann, W., In: Local operator products and renormalization in quantum field theory. Lectures on Elementary Particles and Quantum Field Theory. Deser, S., Pendleton, H. (eds.) Cambridge, MA: MIT Press, 1971
Keldysh, L.V.: Diagram technique for nonequilibrium processes. Sov. Phys. JETP20, 1018 (1964)
Ostendorf, A.: Feynman rules for Wightman functions. Ann. Inst. H. Poincaré40, 273 (1984)
Streater, R.F., Wightman, A.S.: PCT, Spin & Statistics, and All That. Chapter 2–3. Reading, MA: Benjamin/Cummings, 1978
Author information
Authors and Affiliations
Additional information
Communicated by G. Felder
Rights and permissions
About this article
Cite this article
Steinmann, O. Perturbative quantum field theory at positive temperatures: An axiomatic approach. Commun.Math. Phys. 170, 405–415 (1995). https://doi.org/10.1007/BF02108335
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02108335