CRAVITATION AND SPINOR GAUGE FIELD

LIU YAO-YANG

Chinese Physics C> 1982, Vol. 6> Issue(3) : 306-316

CRAVITATION AND SPINOR GAUGE FIELD

LIU YAO-YANG

University of Science and Technology of China

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Abstract：
Basing on the Lorentz covariance and SO (4, 2) symmetry of Dirac theory, anobvious covariant theory of spinor gauge field is obtained by expanding the Lorentztransformation to general coordinate tranformation and making the SO (4, 2) to belocalized. We have proved that, by the gauge independence, the symmetrygroup is reduced to the localized rotation of Lorentz group in Riemann space automa-tically. So our theory is the natural generalization of Dirac theory in curved space.We have also proved that, the spinor gauge field can not appear in flat space, thenthe existence of spinor gauge field is closely related to the curvature. The differencesbetween our theory and Utiyama and Kibble theories are also discussed, and it is poin-ted out that the so-called scalar property of Dirac wave function in general relativity isa misunderstanding caused by the unobvious covariance of those theories, even inthose theories We can not distinguish what is the genuine gauge. field and what is theeffect of the structure of space. In obvious covariant theory this paradox disappears.

References

[1]

C. N. Yang and R. L. Mills, Phys. Rev., 96(1954),191.[2] E. S. Abers and B. W. Lee, Phys. Reports, 9(1973),1.[3] A. Einstein, Ann. der physik, 49(1916),769.[4] R. Ltiyama, Phys. Rev., 101(1956),1597.[5] D. Brill and J. A. Wheeler, Rev. Mod. Phys., 29(1957), 465.[6] T.W.B.Kibble, J. Math. Phys. 2(1961), 212.F. W. Hehl, P. Von der Heyde, G. D. gerlick, and J.M.Neater, Rev. Mod. Phys., 48(1976),393.[7] 刘耀阳,高能物理与核物理,1(1981), 17.[8] M.J. G. Veltman,in Methad in Field Theory, eds. R.Balian and J. Zin-Juatin (1976, North-Holland Publishing Company, Amsterdam: New York.Oxford).[9] A. O. Barut, Phys. Rev., 135(1964), B839.[10] H. Weyl, Zeits. Phys,56(1929), 330.[11] A. Belavin, A. Polyakov, A. Schwartz and Y. Tyupkin, Phys. Lett., 59B(1975), 85.[12] 我要特别感谢杨振宁教授提醒我注意到这一点.[13] B. Weinberg, Gravitation and Cosmology: Principles ,and Applieatione of the General Theory of Relativity (Wiley New York, 1972).[14] C.N.Yang,Phys .Lett., 33(1974), 445.

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LIU YAO-YANG. CRAVITATION AND SPINOR GAUGE FIELD[J]. Chinese Physics C, 1982, 6(3): 306-316.

LIU YAO-YANG. CRAVITATION AND SPINOR GAUGE FIELD[J]. Chinese Physics C, 1982, 6(3): 306-316. shu

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Received: 1980-10-13
Revised: 1900-01-01

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沈阳化工大学材料科学与工程学院沈阳 110142

CRAVITATION AND SPINOR GAUGE FIELD

LIU YAO-YANG

University of Science and Technology of China

Received Date: 1980-10-13
Accepted Date: 1900-01-01
Available Online: 1982-06-05

Abstract: Basing on the Lorentz covariance and SO (4, 2) symmetry of Dirac theory, anobvious covariant theory of spinor gauge field is obtained by expanding the Lorentztransformation to general coordinate tranformation and making the SO (4, 2) to belocalized. We have proved that, by the gauge independence, the symmetrygroup is reduced to the localized rotation of Lorentz group in Riemann space automa-tically. So our theory is the natural generalization of Dirac theory in curved space.We have also proved that, the spinor gauge field can not appear in flat space, thenthe existence of spinor gauge field is closely related to the curvature. The differencesbetween our theory and Utiyama and Kibble theories are also discussed, and it is poin-ted out that the so-called scalar property of Dirac wave function in general relativity isa misunderstanding caused by the unobvious covariance of those theories, even inthose theories We can not distinguish what is the genuine gauge. field and what is theeffect of the structure of space. In obvious covariant theory this paradox disappears.