Noncommutativity and Reparametrisation symmetry
Rabin Banerjee, Biswajit Chakraborty, Sunandan Gangopadhyay
TL;DR
This paper presents a systematic method to reveal noncommutative structures in particle mechanics models with reparametrisation symmetry by transforming between gauges, uncovering noncommuting algebras from standard commuting ones.
Contribution
It introduces a general approach to derive noncommutative algebras from commuting ones via gauge transformations in reparametrisation symmetric models.
Findings
Noncommutative structures can be generated through gauge transformations.
A systematic derivation of variable changes relating different gauges.
Application to particle mechanics models with reparametrisation symmetry.
Abstract
We discuss a general method of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. Starting from the commuting algebra in the conventional gauge, it is possible to obtain a noncommuting algebra in a nonstandard gauge. The change of variables relating the algebra in the two gauges is systematically derived using gauge/reparametrisation transformations.
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