Abstract
The work is devoted to a description of the dynamics of proper time as a function of the evolutionary parameter,which can be separated from the Dirac-ADM metric in the Hamiltonian version of the general theory of relativity (GTR) and in conformally invariant, Lichnerowicz variables. In these variables, the GTR is equivalent to the conformally invariant, Penrose-Chernikov-Tagirov, scalar-field theory, with a quantity proportional to the scale factor playing the role of the scalar field. Identifying such a scalar field with the modulus of the Higgs field in the standard model, which unifies the electrvweak and strong interactions, makes it possible to formulate a unified,conformally invariant theory in which the vacuum average of the scalar field is determined by integrals of motion of cosmological evolution.
Similar content being viewed by others
References
C.M. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation, W. H. Freeman and Co., San Francisco (1973).
M. P. Ryan, Jr., and L. C. Shapley,Homogeneous Relativistic Cosmologies, Princeton Series on Physics, Princeton Univ. Press, Princeton (1975).
M. P. Ryan,Hamiltonian Cosmology, Lecture Notes in Physics, No. 13, Springer-Verlag, Berlin-Heidelberg-New York (1972).
P. A. M. Dirac,Lectures on Quantum Mechanics, Belfer Graduate School of Science, Yeshiva Univ., New York (1994).
C. Misner,Phys. Rev.,186, 1319 (1969).
A. M. Khvedelidze, V. V. Papoyan, and V. N. Pervushin,Phys. Rev.,D51, 5654 (1995); V. N. Pervushin and T. Tovmassian (Towmasjan),Int. J. Mod. Phys.,D4, 105 (1995); S. Gogilidze, A. Khvedelidze, Yu. Palii, V. Papoyan, and V. Pervushin, “Gravitation and cosmology,” gr-qc/9705036, 3, 17 (1997).
V. Pervushin, V. Papoyan, S. Gogilidze, A. Khvedelidze, Yu. Palii, and V. Smirichinskii(Smirichinski),Phys. Lett.,B365, 35 (1996).
A. Khvedelidze, Yu. Palii, V. Papoyan, and V. Pervushin,Phys. Lett.,B402, 263 (1997).
J. W. York, Jr.,Phys. Rev. Lett.,26, 1658 (1971).
K. Kuchar,J. Math. Phys.,13, 768 (1972).
P. A. M. Dirac,Proc. R. Soc,A246, 333 (1959);Phys. Rev.,114, 924 (1958); R. Arnowitt, S. Deser, and C. W. Misner,Phys. Rev.,117, 1595 (I960).
A. Lichnerowicz,Math. Pure Appl.,B37, 23 (1944).
V. N. Pervushin and V. I. Smirichinskii (Smirichinski),Phys. At. Nucl.,61, 142 (1998); ibid.62 (in press).
V. V. Papoyan, V. N. Pervushin, and V. I. Smirichinskii (Smirichinski),Astrophysics (in press).
T. Levi-Civita,Prace Mat.-Fiz.,17, 1 (1906); S. Shanmugadhasan,J. Math. Phys.,14, 677 (1973).
S. A. Gogilidze, A. M. Khvedelidze, and V. N. Pervushin,Phys. Rev.,D53, 2160 (1996).
S. A. Gogilidze, A. M. Khvedelidze, and V. N. Pervushin,J. Math. Phys.,37, 1760 (1996).
F. Wilczek,Erice Lectures on Cosmology, NS-ITP-81-91, Lectures delivered at the Ettore Majorana Summer School, Erice (1981).
M. Pavlovski (Pawlowski) and R. Raczka,Found. Phys.,24, 1305 (1994).
V. N. Pervushin, V. I. Smirichinskii (Smirichinski), and M. Pavlovski (Pawlowski), 1CTP preprint IC/97/189, Trieste (1997); V. N. Pervushin and V. 1. Smirichinskii (Smirichinski),Mod. Phys. Lett.,A13, 119 (1998).
R. Penrose,Relativity, Groups and Topology, Gordon and Breach, London (1964); N. A. Chemikov and E. A. Tagirov,Ann. Inst. Henri Poincaré,9, 109 (1968).
A. A. Friedmann,Z. Phys.,10, 377 (1922).
J. A. Wheeler,Batelle Recontres 1967, Lectures in Mathematics and Physics, C. De Witt and J. A. Wheeler (eds.), W. A. Benjamin, New York (1968); B. C. De Witt,Phys. Rev.,160, 1113 (1967).
Y. Fujii,Phys. Rev., D9, 874 (1974); P. Minkowski,Phys. Lett.,B71, 419 (1977); T. Matsuki,Prog. Theor. Phys.,59, 235 (1978); A. D. Linde,Pis’ma Zh. éksp. Teor. Fiz.,30, 479 (1979); A. Zee,Phys. Rev. Lett.,42, 417 (1979); ibid.44, 703 (1980); L. Smollin.Nucl. Phys.,B160, 253 (1979).
H. Dehnen and K. H. Frommen,Int. J. Theor. Phys.,32, 1135 (1993).
J. V. Narlikar,Astrofizika e Cosmologia, Gravitazione, Quanti e Relativita, G. Barbera, Firenze (1979).
Author information
Authors and Affiliations
Additional information
Translated from Astrofizika, Vol. 42, No. 1, pp. 137–154, January–March, 1999.
Rights and permissions
About this article
Cite this article
Pavlovski, M., Papoyan, V.V., Pervushin, V.N. et al. Dynamics of proper time in the theory of gravitation and conformal unification of interactions. Astrophysics 42, 101–113 (1999). https://doi.org/10.1007/BF02700918
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02700918