The quantal Poincaré-Cartan integral invariantfor singular higher-order Lagrangian in field theories
Department of Applied Physics, Beijing Polytechnic University, 100022, Beijing, P.R. China
2 Chinese Center of Advanced Science and Technology (CCAST) (World Laboratory), 100080, Beijing, P.R. China
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Based on the phase-space generating functional of the Green function for a system with a regular/singular higher-order Lagrangian, the quantal Poincaré-Cartan integral invariant (QPCII) for the higher-order Lagrangian in field theories is derived. It is shown that this QPCII is equivalent to the quantal canonical equations. For the case in which the Jacobian of the transformation may not be equal to unity, the QPCII can still be derived. This case is different from the quantal first Noether theorem. The relations between QPCII and a canonical transformation and those between QPCII and the Hamilton-Jacobi equation at the quantum level are also discussed.
© Springer-Verlag, 2005