Quantal symmetry for a system with a singular higher-order Lagrangian

Abstract

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.