Quantum Noether identities for non-local transformationsin higher-order derivatives theories
Chinese Center of Advanced Science and Technology (CCAST) (World Laboratory), 100080, Beijing, P.R. China
2 Department of Applied Physics, Beijing Polytechnic University, 100022, Beijing, P.R. China
3 Department of Physics, Guizhou University, 550025, Guiyang, P.R. China
Based on the phase-space generating functional of the Green function for a system with a regular/singular higher-order Lagrangian, the quantum canonical Noether identities (NIs) under a local and non-local transformation in phase space have been deduced, respectively. For a singular higher-order Lagrangian, one must use an effective canonical action I eff P in quantum canonical NIs instead of the classical I P in classical canonical NIs. The quantum NIs under a local and non-local transformation in configuration space for a gauge-invariant system with a higher-order Lagrangian have also been derived. The above results hold true whether or not the Jacobian of the transformation is equal to unity or not. It has been pointed out that in certain cases the quantum NIs may be converted to conservation laws at the quantum level. This algorithm to derive the quantum conservation laws is significantly different from the quantum first Noether theorem. The applications of our formulation to the Yang-Mills fields and non-Abelian Chern-Simons (CS) theories with higher-order derivatives are given, and the conserved quantities at the quantum level for local and non-local transformations are found, respectively.
© Springer-Verlag, 2003