Treatment of Path Integral for a Particle in One-Dimensional Box--with a Help of Topological Conception

Akira Inomata, Vijay A. Singh

Kleinert, H, Chervyakov, A

We demonstrate the reparametrization invariance of perturbatively defined one-dimensional functional integrals up to the three-loop level for a path integral of a quantum-mechanical point particle in a box. We exhibit the origin of the failure of earlier authors to establish reparametrization invariance which led them to introduce, superfluously, a compensating potential depending on the connection of the coordinate system. We show that problems with invariance are absent by defining path integrals as the $\\epsilon \\to 0$ limits of $1+ \\epsilon$-dimensional functional integrals.

Travis S. Taylor

Quantization is one of the fundamental concepts of modern physics, forming the bedrock of quantum mechanics and quantum field theory. This section delves into the nature of quantum particles, the processes that underlie quantization, and how these principles apply to systems ranging from simple particles in a box to complex many-body systems.

Rainer Dick