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

ZHAO BAO-HENG; YAN MU-LIN

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《中国物理C》（英文）编辑部

2024年10月30日

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

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

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Abstract：
The Yang-Mills field is quantized within the canonical formalism in covariant gauges. The interaction Lagrangian of X and X', i.e. the unphysical components of A_μ, is studied. In this Lagramgian there is only one term contributing to the S matrix elements between physical states. It is the source of the breaking of the unitarity of the physical S matrix. We get the gauge compensating term by solving a simple functional differential equation. If the gauge compensating term is added to the action, the S matrix 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 S matrix is gauge independent and unitary.

References

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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 of X and X', i.e. the unphysical components of A_μ, is studied. In this Lagramgian there is only one term contributing to the S matrix elements between physical states. It is the source of the breaking of the unitarity of the physical S matrix. We get the gauge compensating term by solving a simple functional differential equation. If the gauge compensating term is added to the action, the S matrix 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 S matrix is gauge independent and unitary.