Ward Identities in Canonical Formalism for a System with Singular Higher-Order Lagrangian

Li, Ziping

doi:10.1209/0295-5075/27/8/002

Cited by 9 publications

(3 citation statements)

References 14 publications

(3 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, investigation of the symmetry properties of the system in the phase space has more basic sense. Based on the invariance of the phase-space generating functional of the Green function for a system with a singular first-order Lagrangian under the local transformation of canonical variables in extended phase space, the canonical Ward identity (CWI) for such a system has been studied by one of the authors in a previous work [17]; for a system with a singular higher-order Lagrangian a brief discussion has also been given [18]. The global quantal canonical symmetry for a system with a singular first-order Lagrangian had also been considered [19].…”

Section: Introductionmentioning

confidence: 99%

Magnetoresistance — the Kapitza legacy

Pippard

1994

Phys.-Usp.

View full text Add to dashboard Cite

Based on the phase-space generating functional of the Green function for a constrained Hamiltonian system with a singular higher-order Lagrangian, the canonical Ward identities for such a system under the local and global transformation have been derived, respectively. The quantal conserved charge (QCC) under the global symmetry transformation is also deduced. In general, these QCCs are different from the Noether charge in classical theory. A comparison of these quantal conservation laws with those deriving from the configuration-space path integral for gauge-invariant theories is discussed. We give a preliminary application of our results to Yang-Mills (YM) theory and Chern-Simons (CS) theory with higher-order derivatives. A new form of gauge-ghost proper vertices and new conserved charges at the quantum level are obtained for the YM theory; the quantal Becchi-Rouet-Stora (BRS) conserved charges and conserved angular momentum are also derived for CS theory. The advantage of our canonical formalism is that we do not carry out the integration over the canonical momenta in the phase-space path integral as usually performed.

show abstract

Section: Introductionmentioning

confidence: 99%

Magnetoresistance — the Kapitza legacy

Pippard

1994

Phys.-Usp.

View full text Add to dashboard Cite

show abstract

“…Recently the global/local canonical symmetries for a system with a regular/singular Lagrangian in classical/quantum theory have been studied. The classical canonical Noether theorems/Neother identities and Poincaré-Cartan integral invariant are established [3][4][5][6], the canonical ward identities [7][8][9], the quantum canonical Noether theorem [10][11][12][13][14][15] /Noether identities [16] and Poincaré-Cartan integral invariant [17] in quantum theories are also formulated and some applications are given.…”

mentioning

confidence: 99%

The Transformation Properties at the Quantum Level in Field Theories for a Gauge-Invariant System with a Higher-Order Lagrangian

Gao

2008

Int J Theor Phys

Self Cite

View full text Add to dashboard Cite

Based on the configuration-space generating functional of the Green functions for the gauge-invariant system in higher-order derivatives theories, the equations of the transformation properties at the quantum level have been derived. It follows that the sufficient conditions are found which implies that there exists the conservation laws and the expressions of the quantal conserved laws are also given. Applying the results to the non-Abelian Chern-Simons higher-order derivatives theories, the quantal BRST conserved charge and other conserved charges are found, the transformation properties of the conformal transformation at the quantum level is discussed, the quantal conserved angular momentum is derived, it is pointed out that fractional spin in this system may be also preserved in quantum theories. But the connection between the symmetries and conservation laws in classical theories are not always preserved in quantum theories.

show abstract

“…From expression (3), the phase space generating functional for this model can be written as [17], [6] Z…”

mentioning

confidence: 99%

Quantal conserved laws in the non-Abelian higher-derivative Chern-Simons theories

Bao

1997

Europhys. Lett.

Self Cite

View full text Add to dashboard Cite

Based on the phase space generating functional of the Green function for a system with a singular higher-order Lagrangian, the quantal conserved laws (QCL) have been derived under the global symmetry transformation in the extended phase space. The application of the results to non-Abelian higher-derivative Chern-Simons theories (NAHDCST) is studied; the quantal BRS conserved quantity and conserved angular momentum are obtained. This quantal conserved angular momentum differs from classical Noether one.

show abstract

Ward Identities in Canonical Formalism for a System with Singular Higher-Order Lagrangian

Cited by 9 publications

References 14 publications

Magnetoresistance — the Kapitza legacy

Magnetoresistance — the Kapitza legacy

The Transformation Properties at the Quantum Level in Field Theories for a Gauge-Invariant System with a Higher-Order Lagrangian

Quantal conserved laws in the non-Abelian higher-derivative Chern-Simons theories

Contact Info

Product

Resources

About