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From classical mechanics with doubled degrees of freedom to quantum field theory for nonconservative systems. (English) Zbl 1302.81144
Summary: The (\(2\times 2\))-matrix structure of Green’s functions is a common feature for the real-time formalisms of quantum field theory under thermal situations, such as the closed time path formalism and Thermo Field Dynamics (TFD). It has been believed to originate from quantum nature. Recently, Galley has proposed the Hamilton’s principle with initial data for nonconservative classical systems, doubling each degree of freedom. We show that the Galley’s Hamilton formalism can be extended to quantum field and that the resulting theory is naturally identical with nonequilibrium TFD.

81T28 Thermal quantum field theory
81S05 Commutation relations and statistics as related to quantum mechanics (general)
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
70H25 Hamilton’s principle
70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems
Full Text: DOI
[1] Galley, C. R., Phys. Rev. Lett., 110, 174301, (2013)
[2] Schwinger, J.; Keldysh, L. V.; Kadanoff, L. P.; Baym, G.; Danielewiecz, P.; Chou, K.; Su, Z.; Hao, B.; Yu, L., Quantum statistical mechanics, J. Math. Phys., Sov. Phys. JETP, Ann. Phys., Phys. Rep., 118, 1, (1985), Benjamin New York
[3] Takahashi, Y.; Umezawa, H., Collect. Phenom., 2, 55-80, (1975), This paper is reprinted in Int. J. Mod. Phys. B 10 (1996) 1755-1805
[4] Umezawa, H.; Matsumoto, H.; Tachiki, M., Thermo field dynamics and condensed states, (1982), North-Holland Amsterdam, New York, London
[5] Umezawa, H., Advanced field theory — micro, macro, and thermal physics, (1993), AIP New York
[6] Nakamura, Y.; Yamanaka, Y., Ann. Phys., 326, 1070-1083, (2011)
[7] Nakamura, Y.; Yamanaka, Y., Ann. Phys., 331, 51-69, (2013)
[8] Celeghini, E.; Rasetti, M.; Vitiello, G., Ann. Phys., 215, 156-170, (1992)
[9] Blasone, M.; Vitiello, G.; Jizba, P., Quantum field theory and its macroscopic manifestations: boson condensation, ordered patterns and topological defects, (2011), Imperial College Press London
[10] Arimitsu, T.; Guida, M.; Umezawa, H.; Arimitsu, T.; Umezawa, H.; Yamanaka, Y.; Papastamatiou, N. J., Europhys. Lett., Physica, 148A, 27, (1988)
[11] Umezawa, H.; Yamanaka, Y., Adv. Phys., 37, 531-557, (1988)
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