Scale Invariance Breaking and Discrete Phase Invariance in Few-Body Problems
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918288575954944 |
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| author | Ohya, Satoshi |
| author_facet | Ohya, Satoshi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09266 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scale Invariance Breaking and Discrete Phase Invariance in Few-Body Problems Ohya, Satoshi Quantum Physics Quantum Gases 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. |
| title | Scale Invariance Breaking and Discrete Phase Invariance in Few-Body Problems |
| topic | Quantum Physics Quantum Gases |
| url | https://arxiv.org/abs/2601.09266 |