We are taught that gauge transformations in classical and quantum mechanics
do not change the physics of the problem. Nevertheless here we discuss three
broad scenarios where under gauge transformations: (i) conservation laws are
not preserved in the usual manner; (ii) non-gauge-invariant quantities can be
associated with physical observables; and (iii) there are changes in the
physical boundary conditions of the wave function that render it
non-single-valued. We give worked examples that illustrate these points, in
contrast to general opinions from classic texts. We also give a historical
perspective on the development of Abelian gauge theory in relation to our
particular points. Our aim is to provide a discussion of these issues at the
graduate level.
Description
How do gauge transformations make an influence on conserved quantities
%0 Journal Article
%1 berche2016gauge
%A Berche, Bertrand
%A Malterre, Daniel
%A Medina, Ernesto
%D 2016
%K qm
%T Gauge transformations and conserved quantities in classical and quantum mechanics
%U http://arxiv.org/abs/1606.05748
%X We are taught that gauge transformations in classical and quantum mechanics
do not change the physics of the problem. Nevertheless here we discuss three
broad scenarios where under gauge transformations: (i) conservation laws are
not preserved in the usual manner; (ii) non-gauge-invariant quantities can be
associated with physical observables; and (iii) there are changes in the
physical boundary conditions of the wave function that render it
non-single-valued. We give worked examples that illustrate these points, in
contrast to general opinions from classic texts. We also give a historical
perspective on the development of Abelian gauge theory in relation to our
particular points. Our aim is to provide a discussion of these issues at the
graduate level.
@article{berche2016gauge,
abstract = {We are taught that gauge transformations in classical and quantum mechanics
do not change the physics of the problem. Nevertheless here we discuss three
broad scenarios where under gauge transformations: (i) conservation laws are
not preserved in the usual manner; (ii) non-gauge-invariant quantities can be
associated with physical observables; and (iii) there are changes in the
physical boundary conditions of the wave function that render it
non-single-valued. We give worked examples that illustrate these points, in
contrast to general opinions from classic texts. We also give a historical
perspective on the development of Abelian gauge theory in relation to our
particular points. Our aim is to provide a discussion of these issues at the
graduate level.},
added-at = {2016-07-02T12:29:10.000+0200},
author = {Berche, Bertrand and Malterre, Daniel and Medina, Ernesto},
biburl = {https://www.bibsonomy.org/bibtex/232f97c2a4741ae7ab83e291895a83b75/vindex10},
description = {How do gauge transformations make an influence on conserved quantities},
interhash = {14e8b1b9cbf2bda356c0495e9b26f772},
intrahash = {32f97c2a4741ae7ab83e291895a83b75},
keywords = {qm},
note = {cite arxiv:1606.05748},
timestamp = {2016-07-02T12:29:10.000+0200},
title = {Gauge transformations and conserved quantities in classical and quantum mechanics},
url = {http://arxiv.org/abs/1606.05748},
year = 2016
}