Quantal global symmetry for a gauge-invariant system

Li, Ziping; Gao, H.B.

doi:10.1007/bf02435801

Int J Theor Phys

1997

DOI: 10.1007/bf02435801

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Quantal global symmetry for a gauge-invariant system

Ziping Li

H.B. Gao

Abstract: Based on the configuration-space generating functional obtained by using the Faddeev-Popov trick for a gauge-invariant system, the Ward identities for global transformation are derived. The conservation laws at the quantum level for global symmetry transformation are also deduced. A preliminary application of the present formulation to non-Abelian Chem-Simons (CS) theory is given. The Ward identity and quantal BRS charge under the BRS transformation are deduced. The quantal conserved angular momentum is obtain… Show more

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Cited by 3 publications

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“…[ , ] Z J K is invariant under the transformation (32), and this yields the following canonical Ward identity [8] :…”

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BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

Huang

Jiang

2007

SCI CHINA SER G

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According to the method of path integral quantization for the canonical constrained system in Becchi-Rouet-Stora-Tyutin scheme, the supersymmetric electromagnetic interaction system was quantized. Both the Hamiltonian of the supersymmetric electromagnetic interaction system in phase space and the quantization procedure were simplified. The BRST generator was constructed, and the BRST transformations of supersymmetric fields were gotten; the effective action was calculated, and the generating functional for the Green function was achieved; also, the gauge generator was constructed, and the gauge transformation of the system was obtained. Finally, the Ward-Takahashi identities based on the canonical Noether theorem were calculated, and two relations between proper vertices and propagators were obtained. supersymmetric electromagnetic interaction, BRST quantization, Ward identitySupersymmetric theory is an attractive theory in the interface of particle physics and cosmology, because it can provide answers to many thorny topics in particle physics and cosmology, for example: (1) the gauge hierarchy problem may be solved by weak-scale supersymmetry [1] ; (2) grand unification becomes more meaningful than the case without supersymmetry, and the coupling constants of the weak, electromagnetic and strong interactions become the same at 100 Plank scale in the framework of supersymmetric standard model [2] ; (3) supersymmetry provides new stable particles (superpartner, for example, neutrolino and gravitino), which may make up an im-

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“…[ , ] Z J K is invariant under the transformation (32), and this yields the following canonical Ward identity [8] :…”

mentioning

confidence: 99%

“…3, we construct the BRST generator, and discuss the relations between BRST and gauge generator. We calculate the Ward-Takahashi identities based on the canonical Noether theorem [8] , and give its applications. Finally, we make the summaries and conclusions.…”

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confidence: 99%

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

Huang

Jiang

2007

SCI CHINA SER G

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Quantal Noether Identities and Their Applications

2006

Int J Theor Phys

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Based on the phase-space generating functional of the Green function for a system with a regular/singular Lagrangian, the quantal canonical Noether identities (NI) under the local and non-local transformation in extended phase have been derived, respectively. The result holds true whether the Jacobian of the transformation is equal to unity or not. Based on the configuration-space generating functional of the gauge-invariant system obtained by using Faddeev-Popov (FP) trick, the quantal NI under the local and non-local transformation in configuration space have been also deduced. It is showed that for a system with a singular Lagriangian one must use the effective action in the quantal NI instead of the classical action in corresponding classical NI. It is pointed out that in certain cases, the quantal NI may be converted into the quantal (weak) conservation laws by using the quantal equations of motion. This algorithm to derive the quantal conservation laws differs from the quantal first Noether theorem. The preliminary applications of this formulation to Yang-Mills (YM) fields and non-Abelian Chern-Simons (CS) theories are given. The quantal conserved quantities for non-local transformation in YM fields are obtained. The conserved BRS and PBRS quantities at the quantum level in non-Abelian CS theories are also found. The property of fractional spin in CS theories is discussed.

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Transformation Properties of Dynamical Systems at the Quantum Level

Jiang

2007

Int J Theor Phys

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Based on the generating functional of Green function for a dynamical system, the general equations of transformation properties at the quantum level are derived. In some cases they can be reduced to the quantum Noether theorem. In some other cases they can be reduced to momentum theorem or angular momentum theorem etc. at the quantum level. An example is presented and it shows that the classical conservation laws don't always preserve in quantum theories.KEY WORDS: symmetry and conservation laws; constrained Hamiltonian systems; path integral quantization.

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Quantal global symmetry for a gauge-invariant system

Cited by 3 publications

References 16 publications

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

BRST quantization and canonical Ward identity of the supersymmetric electromagnetic interaction system

Quantal Noether Identities and Their Applications

Transformation Properties of Dynamical Systems at the Quantum Level

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