Non-linear effects in path integrals and quantization of constrained systems

Eqab M. Rabei

Werner Kerler A

Lorena Parra‐Rodríguez, J. David Vergara

In this work we analyze several physical systems in the context of polymer quantum mechanics using path integrals. First we introduce the group averaging method to quantize constrained systems with path integrals and later we use this procedure to compute the effective actions for the polymer non-relativistic particle and the polymer harmonic oscillator. We analyze the measure of the path integral and we describe the semiclassical dynamics of the systems.

Eyad Hasan Hasan

The Lagrangian with linear acceleration can be considered as a model of singular system. The constrained Hamiltonian systems with linear acceleration are investigated by using the Hamilton-Jacobi method. The Hamilton-Jacobi function is constructed by applying the integrability condition on this function to obtain the path integral quantization. It is shown that the equations of motion can be obtained from the action integral

Manan Sengupta

The concept of constrained Hamiltonian dynamical systems and their quantization, introduced by Dirac, constitutes one of the most fundamental contributions to the development of the canonical formalism in recent times. Dirac’s concepts were later incorporated into the path-integral formulation of quantum mechanics by Faddeev, which played an important role in understanding some subtle aspects in the quantization of non-Abelian gauge theory. An example is given from nonrelativistic quantum mechanics which illustrates the formalism through simple analogy.