Chinese Physics C > 1982, Vol. 6 > Issue(1): 17-24

A METHOD ON DERIVATION OF GAUGE FIELDS

LIU YAO-YANG

University of Science and Technology of China

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Abstract：
Usually the study of gauge field is based on the wave function. By discussing thebehaviour of Dirac particles in gravitation, one has a famous difficulty, that is, thewave functions appear as scalars under general coordinate transformations. In thispaper, a method is suggested to constitute the gauge fields directly from algebraicstructures, Lie algebra and Jordan algebra. We introduce a concept called represen-tation group of algebras, the transformations, of wave function are connected with therepresentation group. The global and local representation groups are connected withglobal and local transformations of wave function respectively. According to thismethod we find that it is equivalent to the usual one for all of the problems concernedwith internal freedom as Yang-Mills field etc. For spinors, one can introduce gravi-tation by changing the algebraic structure, one find that the vierbein is unneccessaryand the wave functions transform as spinors corresponding to Dirac theory. Somerelated problems are also discussed.

References

[1]

C. N. Yang and R. Mills, Phys. Rev., 96(1954), 191.[2] R. Utiyama, Phys. Rev., 101(1956), 1597.[3] H. Weyl, Zeits. Phys., 56(1929), 330; D. Brill and J. A. Wheeler, Rev.Mod. Phys., 59(1957),465.[4] M. J. G. Veltman,"Method in Field Theory",Ede. R. Balian and J. Zin-Justin, 1976(North-Holland, Amsterdam New York Oaford).[5] P. A.M.Dime, The Principles of Quantum Mechanics, 4th. ed. 1958(Oxford Press).[6] В. И. Синрнов, Курс Высшей Математики, ТШ-1, ГИТТЛ, 1954 (Москва).[7] J. D. Bjorken and S. D. Drell, Relativistic Quantum Fields. 1956 (McGraw-Hill Book Company)[8] W. Pauli,Ann. Inst. Poincaré, 6(1936), 106.[9] C. J. Ieham. A. Balam and J. Strathdee. Lett. Nuovo Cim.,5(1972), 969; C. Biraran and K. P. Sinha, Lett. Nuoro Cim.,13(1975),357;Phys. Rep.,51(1979), 111.

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LIU YAO-YANG. A METHOD ON DERIVATION OF GAUGE FIELDS[J]. Chinese Physics C, 1982, 6(1): 17-24.

LIU YAO-YANG. A METHOD ON DERIVATION OF GAUGE FIELDS[J]. Chinese Physics C, 1982, 6(1): 17-24. shu

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Received: 1979-04-03
Revised: 1980-07-05

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沈阳化工大学材料科学与工程学院沈阳 110142

A METHOD ON DERIVATION OF GAUGE FIELDS

LIU YAO-YANG

University of Science and Technology of China

Received Date:1979-04-03
Accepted Date:1980-07-05
Available Online:1982-02-05

Abstract:Usually the study of gauge field is based on the wave function. By discussing thebehaviour of Dirac particles in gravitation, one has a famous difficulty, that is, thewave functions appear as scalars under general coordinate transformations. In thispaper, a method is suggested to constitute the gauge fields directly from algebraicstructures, Lie algebra and Jordan algebra. We introduce a concept called represen-tation group of algebras, the transformations, of wave function are connected with therepresentation group. The global and local representation groups are connected withglobal and local transformations of wave function respectively. According to thismethod we find that it is equivalent to the usual one for all of the problems concernedwith internal freedom as Yang-Mills field etc. For spinors, one can introduce gravi-tation by changing the algebraic structure, one find that the vierbein is unneccessaryand the wave functions transform as spinors corresponding to Dirac theory. Somerelated problems are also discussed.