Quantum particle on a Mobius strip, coherent states and projection operators

TL;DR

This paper constructs coherent states for a quantum particle on a Möbius strip, relating them to fermionic phase space, and compares these states with previous cylinder-based models, analyzing geometrical and projection operator aspects.

Contribution

It introduces a novel construction of coherent states on a Möbius strip and explores their relation to fermionic phase space and existing models.

Findings

Coherent states for a particle on a Möbius strip are explicitly constructed.

The relation between these states and fermionic phase space is established.

Comparison with cylinder quantization models highlights differences and similarities.

Abstract

The coherent states for a quantum particle on a M\"{o}bius strip are constructed and their relation with the natural phase space for fermionic fields is shown. The explicit comparison of the obtained states with previous works where the cylinder quantization was used and the spin 1/2 was introduced by hand is given, and the relation between the geometrical phase space, constraints and projection operators is analyzed and discussed.