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Prog. Theor. Phys. Vol. 73 No. 6 (1985) pp. 1560-1572
Chiral Symmetry Breaking in Quantum Gravity in Flat Background Spacetime
Osamu Abe
Department of Physics, Hokkaido University, Sapporo 060
(Received December 3, 1984)
Abstract:
The possibility that chiral symmetry is broken dynamically in quantum gravity in flat background spacetime is investigated by solving the Schwinger-Dyson equation and by the use of the effective potential formalism both in the Hartree-Fock approximation. It is found partially by analytic method and partially by numerical computation that chiral symmetry is unbroken either in the case where the value of ξ, the gauge parameter, is greater than 1 and the value of the momentum cutoff ΛG is less than the maximal one ΛM or in the case where ξ<1 and ΛG≤ΛC, the critical one. When ξ<1 and ΛC< ΛG≤ΛM, chiral symmetry is broken dynamically. No real solution is obtained in the case where ΛG>ΛM. The obtained value of the maximal cutoff ΛM is almost equal to Planck's mass in both Landau- and Feynman-like gauges.
URL :
http://ptp.ipap.jp/link?PTP/73/1560/
DOI : 10.1143/PTP.73.1560
References:
- T. Maskawa and H. Nakajima, Prog. Theor. Phys. 52 (1974), 1326[PTP].
-
K. D. Lane, Phys. Rev. D10 (1974), 1353[APS].
D. J. Gross and A. Neveu, Phys. Rev. D10 (1974), 3235[APS].
- M. E. Peskin, Chiral Symmetry and Chiral Symmetry Breaking, in Recent Advances in Field Theory and Statistical Mechanics, ed. J.-B. Zuber and R. Stora (North Holland, Amsterdam, 1982).
-
J. M. Cornwall, R. Jackiw and E. Tomboulis, Phys. Rev. D10 (1974), 2428[APS].
- J. P. Schauder, Studia Math. 2 (1930).
N. Dunford and J. Schwartz, Linear Operator I: General Theory (Interscience, New York, 1958).
- See, e.g. J. Glimm and A. Jaffe, Quantum Physics (Springer-Verlag, New York, 1981), p. 49.
- O. Abe and Y. Hoshino, Phys. Lett. 139B (1984), 167.
-
H. B. Nielsen and M. Ninomiya, Nucl. Phys. B185 (1981), 20[Elsevier];
ibid. B193 (1981), 173[Elsevier].
- See, e.g., M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968), p. 370.
