Symmetry in phase space for a system with a singular higher-order Lagrangian

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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 obtained and the fractional spin for CS theories is discussed.

“…It is easy to check that ~ and ~gh are invariant under the transformation (34) (Li, 1995). The Jacobian of the transformation (34) is equal to unity (Kuang and Yi, 1980).…”

Section: Q = F D2x L-2 Eijajal~bicb "T-i(do~)+cata~ -I~+cata(dodp)mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 97%

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Quantal global symmetry for a gauge-invariant system

Gao

1997

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“…where "≈" [25][26][27] different from "=" [28,29] denotes (14) limited on hyper-surface of primary constraints. Therefore, the above equations can be rewritten as…”

Section: In Extended Hamiltonian Formalismmentioning

confidence: 99%

Total Hamiltonian and Extended Hamiltonian for Constrained Hamilton Systems

Wang

Ning

et al. 2008

For constrained Hamiltonian systems, the motion equations are deduced from total Hamiltonian and extended Hamiltonian with Lagrangian multipliers depending on time t and canonical variables q i and p i . When the multipliers reduced to only depend on time t, the motion equations exactly agree with the old results. Under the same conditions (Lagrangian multipliers depend on time t and canonical variables q i and p i ), the relation equations of coefficients in the generator of gauge transformation are deduced, but the equations have an additive term besides the well-known results. This additive term is from Lagrangian multipliers depending on canonical variables, and it might perform the gauge symmetries that needs to be discussed further.

“…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

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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.