Abstract
The structure of divergences of the vacuum mean <T> energy-momentum tensor is investigated by a simple model (a linear massive scalar field with nonconformal coupling in a spatially plane isotropic universe). The class R of physically permissible vacuums [0> is isolated; when∥0>⊂R the tensor <T> contains only standard local (power-law and logarithmic) divergences; in the general case the condition that the Hamiltonian be diagonal and the “quantum equivalence principle” lead to ∥0>⊂R . The nongeometric structure of power-law divergences, which does not allow their elimination by renormalization of the constants in the generalized gravitational action, is established by a new regularization method (covariant smoothing of a δ-function). It is shown that all local divergences are eliminated by renormalization according to the Pauli-Villars scheme; it gives the same final results as do the adiabatic and n-wave computational procedures.
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Literature cited
B. De Witt, Phys. Rev.,19, 295 (1975).
A. A. Grib, S. G. Mamaev, and V. M. Mostepanenko, Quantum Effects in Intense External Fields [in Russian], Atomizdat, Moscow (1980).
K. A. Bronnikov and V. G. Lapchinskii (V. G. Lapchinsky), Phys. Lett.,117B, 387 (1982).
Y. Fujii, Phys. Lett.,107B, 51 (1981).
M. B. Voloshin and A. D. Dolgov, Yad. Fiz.,35, 213 (1982).
N. A. Chernikov and E. A. Tagirov, Ann. Inst. H. Poincare,9A, 109 (1968); K. A. Bronnikov and E. A. Tagirov, Preprint JINR R2-4151, Dubna (1968).
B. Chakraborty, J. Math. Phys.,14, 188 (1973).
N. N. Bogolyubov and D. V. Shirkov, Introduction to the Theory of Quantized Fields [in Russian], Nauka, Moscow (1973).
M. Castagnino et al., Nuovo Cimento,60A, 138 (1980).
A. A. Kharkov, Phys. Lett., 87A, 223 (1982);88A, 109 (1982).
S. G. Mamev and V. M. Mostepanenko, Yad. Fiz.,37, No. 5, 1323 (1983).
M. Brown and C. Dutton, Phys. Rev.,D18, 4422 (1978).
J. L. Synge, Relativity: The General Theory, Elsevier (1960).
I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press (1966).
A. Duncan, Phys. Rev.,D17, 964 (1978).
T. S. Bunch, J. Phys. A,13, 1297 (1980).
C. Bernard and A. Duncan, Ann. Phys. (N.Y.),107, 201 (1977).
A. Vilenkin, Nuovo Cimento,44A, 441 (1978).
Ya. B. Zel'dovich and A. A. Starobinskii, Zh. Eksp. Teor. Fiz.,61, 2161 (1971).
L. Parker and S. A. Fulling, Phys. Rev.,D9, 341 (1974).
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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 24–29, December, 1983.
The author is sincerely grateful to Profs. K. P. Stanyukovich, Yu. S. Vladimirov, V. G. Lapchinskii, V. N. Mel'nikov, S. G. Mamaev, V. M. Mostepanenko, and other colleagues for fruitful discussions.
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Bronnikov, K.A. Divergences in a nonsteady universe. Soviet Physics Journal 26, 1083–1088 (1983). https://doi.org/10.1007/BF00894638
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DOI: https://doi.org/10.1007/BF00894638