Chinese Physics C > 1978, Vol. 2 > Issue(6): 501-510

CANONICAL QUANTIZATION OF GAUGE FIELDS (I)——THE YANG-MILLS FIELD

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The Yang-Mills field is quantized within the canonical formalism in covariant gauges. The interaction Lagrangian of Xand X', i.e. the unphysical components of A _μ, is studied. In this Lagramgian there is only one term contributing to the Smatrix elements between physical states. It is the source of the breaking of the unitarity of the physical Smatrix. We get the gauge compensating term by solving a simple functional differential equation. If the gauge compensating term is added to the action, the Smatrix in the physical state vector space can be expressed in a form which has no couplings of physical and unphysical particles, and so the physical Smatrix is gauge independent and unitary.

References

[1]

B, S. Dewitt, Phys. Rev., 162(1967), 1195, 1239; L. D. Faddeev and V. N. Popov, Phys. Lett.,25B(1967), 29;S. Mandelstam. Phys. Rev., 175(1968), 1580, 1604; E. S. Fradkin and I. V. Tuytin, Phys. Rev., D2(1970), 2841;G. 't Hooft, Nucl. Phys., B33(1971), 173.[2] N. Nakanish. Supp Prog. Theor. Phys., 51(1972), 1.[3] B. Lautrup, Kgl. Danske Vidensk., Mat.Fys., 35(1967), No. 11;N. Nakanishi, Prog. Theor. Phys., 35(1966), 1111;38(1967), 881; H. P. Dürr and E. Rudolph, Nuovo Cimento, 62A.(1696), 411.[4] J. P. Hsu and E. C. G. Sudarshan, Phys. Rev., D9(1974), 1678.[5] N. Gapta, Phys. Rev., D14(1976), 2596.[6] R. E. Cntkosky, J. Math. Phys., 1(1960), 429; M. Veltman, Physica, 29(1963), 1971;G. 't Hooft and M. Veltman, Diagrammar, CERN Report 73/9 (1973).

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ZHAO BAO-HENG and YAN MU-LIN. CANONICAL QUANTIZATION OF GAUGE FIELDS (I)——THE YANG-MILLS FIELD[J]. Chinese Physics C, 1978, 2(6): 501-510.

ZHAO BAO-HENG and YAN MU-LIN. CANONICAL QUANTIZATION OF GAUGE FIELDS (I)——THE YANG-MILLS FIELD[J]. Chinese Physics C, 1978, 2(6): 501-510. shu

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Received: 1978-01-27
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

CANONICAL QUANTIZATION OF GAUGE FIELDS (I)——THE YANG-MILLS FIELD

ZHAO BAO-HENG
YAN MU-LIN

Received Date:1978-01-27
Accepted Date:1900-01-01
Available Online:1978-12-05

Abstract:The Yang-Mills field is quantized within the canonical formalism in covariant gauges. The interaction Lagrangian ofXandX', i.e. the unphysical components of A_μ, is studied. In this Lagramgian there is only one term contributing to theSmatrix elements between physical states. It is the source of the breaking of the unitarity of the physicalSmatrix. We get the gauge compensating term by solving a simple functional differential equation. If the gauge compensating term is added to the action, theSmatrix in the physical state vector space can be expressed in a form which has no couplings of physical and unphysical particles, and so the physicalSmatrix is gauge independent and unitary.