Abstract
We construct a quantum kinetic theory of a weakly interacting critical boson gas using the expectation values of products of Heisenberg field operators in the grand canonical ensemble. Using a functional representation for the Wick theorem for time-ordered products, we construct a perturbation theory for the generating functional of these time-dependent Green’s functions at a finite temperature. We note some problems of the functional-integral representation and discuss unusual apparent divergences of the perturbation expansion. We propose a regularization of these divergences using attenuating propagators. Using a linear transformation to variables with well-defined scaling dimensions, we construct an infrared effective field theory. We show that the structure of the regularized model is restored by renormalization. We propose a multiplicatively renormalizable infrared effective model of the quantum dynamics of a boson gas.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. M. Lifshitz and L. P. Pitaevskii, Physical Kinetics [in Russian], Nauka, Moscow (1979); English transl., Pergamon, Oxford (1981).
M. Bonitz, Quantum Kinetic Theory, Springer, Heidelberg (2016).
L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics, Benjamin, New York (1962).
L. V. Keldysh, “Diagram technique for nonequilibrium processes,” Sov. Phys. JETP, 20, 1018–1026 (1965).
P. Danielewicz, “Quantum theory of nonequilibrium processes, I,” Ann. Phys., 152, 239–304 (1984).
K.-C. Chou, Z.-B. Su, B.-L. Hao, and L. Yu, “Equilibrium and nonequilibrium formalisms made unified,” Phys. Rep., 118, 1–131 (1985).
J. Rammer and H. Smith, “Quantum field-theoretical methods in transport theory of metals,” Rev. Mod. Phys., 58, 323–359 (1986).
N. P. Landsman and Ch. G. van Weert, “Real- and imaginary-time field theory at finite temperature and density,” Phys. Rep., 145, 141–249 (1987).
M. Wagner, “Expansions of nonequilibrium Green’s functions,” Phys. Rev. B, 44, 6104–6117 (1991).
A. N. Vasiliev, Functional Methods in Quantum Field Theory and Statistical Physics [in Russian], Leningrad Univ. Press, Leningrad (1976); English transl., Gordon and Breach, Amsterdam (1998).
L. Ts. Adzhemyan, A. N. Vasil’ev, M. Gnatich, and Yu. M. Pis’mak, “Quantum field renormalization group in the theory of stochastic Langmuir turbulence,” Theor. Math. Phys., 78, 260–271 (1989).
A. N. Vasil’ev, The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics [in Russian], Petersburg Inst. Nucl. Phys. Press, St. Petersburg (1998); English transl., CRC, Boca Raton, Fla. (2004).
U. C. Täuber and S. Diehl, “Perturbative field-theoretical renormalization group approach to driven-dissipative Bose-Einstein criticality,” Phys. Rev. X, 4, 021010 (2014); arXiv:1312.5182v2 [cond-mat.stat-mech] (2013).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Conflict of interest
The authors declare no conflicts of interest.
This research was supported by the Academy of Finland (Grant No. 325408).
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 200, No. 3, pp. 507–521, September, 2019.
Rights and permissions
About this article
Cite this article
Honkonen, J., Komarova, M.V., Molotkov, Y.G. et al. Kinetic Theory of Boson Gas. Theor Math Phys 200, 1360–1373 (2019). https://doi.org/10.1134/S0040577919090095
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0040577919090095