dorsal/arxiv
View SchemaScale Invariance Breaking and Discrete Phase Invariance in Few-Body Problems
| Authors | Satoshi Ohya |
|---|---|
| Categories | |
| ArXiv ID | 2601.09266vv1 |
| URL | https://arxiv.org/abs/2601.09266 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Scale invariance in quantum mechanics can be broken in several ways. A well-known example is the breakdown of continuous scale invariance to discrete scale invariance, whose typical realization is the Efimov effect of three-body problems. Here we discuss yet another discrete symmetry to which continuous scale invariance can be broken: discrete phase invariance. We first revisit the one-body problem on the half line in the presence of an inverse-square potential -- the simplest example of nontrivial scale-invariant quantum mechanics -- and show that continuous scale invariance can be broken to discrete phase invariance in a small window of coupling constant. We also show that discrete phase invariance manifests itself as circularly distributed simple poles on Riemann sheets of the S-matrix. We then present three examples of few-body problems that exhibit discrete phase invariance. These examples are the one-body Aharonov-Bohm problem, a two-body problem of nonidentical particles in two dimensions, and a three-body problem of nonidentical particles in one dimension, all of which contain a codimension-two ``magnetic'' flux in configuration spaces.
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"abstract": "Scale invariance in quantum mechanics can be broken in several ways. A well-known example is the breakdown of continuous scale invariance to discrete scale invariance, whose typical realization is the Efimov effect of three-body problems. Here we discuss yet another discrete symmetry to which continuous scale invariance can be broken: discrete phase invariance. We first revisit the one-body problem on the half line in the presence of an inverse-square potential -- the simplest example of nontrivial scale-invariant quantum mechanics -- and show that continuous scale invariance can be broken to discrete phase invariance in a small window of coupling constant. We also show that discrete phase invariance manifests itself as circularly distributed simple poles on Riemann sheets of the S-matrix. We then present three examples of few-body problems that exhibit discrete phase invariance. These examples are the one-body Aharonov-Bohm problem, a two-body problem of nonidentical particles in two dimensions, and a three-body problem of nonidentical particles in one dimension, all of which contain a codimension-two ``magnetic\u0027\u0027 flux in configuration spaces.",
"arxiv_id": "2601.09266",
"authors": [
"Satoshi Ohya"
],
"categories": [
"quant-ph",
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],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Scale Invariance Breaking and Discrete Phase Invariance in Few-Body Problems",
"url": "https://arxiv.org/abs/2601.09266",
"version": "v1"
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