Abstract
An explicit expression is obtained for the Green's functions of a massive scalar field for nonnull temperatures and density in the form of a series in powers of m/T. The equivalence of the spectral-geometric approach and the temperature technique of Matsubara and Bernard is demonstrated. Corrections to the Stefan-Boltzmann law are obtained on the basis of the calculated Green's functions. The energy density is calculated in regions of high and low temperatures. The formulas obtained can prove to be useful in the discussion of the phase transition hadrons-quark-gluon plasma.
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N. N. Bogolyubov and S. V. Tyablikov, Dokl. Akad. Nauk SSSR,126, No. 1, 53–56 (1959).
E. S. Fradkin, Trudy FIAN,29, 7–138 (1965).
N. Birrell and P. Davies, Quantum Fields in Curved Space, Cambridge University Press, Cambridge (1982).
B. S. DeWitt, Dynamical Theory of Groups and Fields, Gordon and Breach, New York (1965).
J. S. Dowker and G. Kennedy, J. Phys. All., 895–920 (1978).
A. Cabo and A. E. Shabad, Trudy FIAN,192, 153–203 (1988).
A. S. Vshivtsev, Yu. M. Loskutov, and V. V. Skobelev, Tr. Mat. Fiz.,84, No. 3, 372–387 (1990).
N. P. Landsman and C. G. van Weert, Phys. Rep.,145, No. 3–4, 141–249 (1987).
N. Hurt, Geometric Quantization in Action, D. Reidel Publishing Co., Boston (1983).
T. Matsubara, Progr. Theor. Phys.,14, 351–376 (1955).
C. W. Bernard, Phys. Rev.,D9, 3312–3319 (1974).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Moscow (1962).
D. Mumford, Lectures on Theta-Functions, Birkhauser, Boston (1983).
H. Bateman and A. Erdelyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York (1953).
A. S. Vshivtsev and V. K. Peres-Fernandes, Dokl. Akad. Nauk SSSR,309, No. 1, 70–73 (1989).
D. Prorok, Preprint ITPUWr 732/89 (1989).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 32–40, July, 1991.
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Vshivtsev, A.S., Zhukovskii, V.C. & Starinets, A.O. Green's temperature functions of massive scalar particles for finite matter density. Soviet Physics Journal 34, 589–596 (1991). https://doi.org/10.1007/BF00897986
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DOI: https://doi.org/10.1007/BF00897986