A note on broken dilatation symmetry in planar noncommutative theory
A riveting study of Ward-Takahashi identities is presented for a broken dilatation or scale symmetry in a generalized quantum Hall system. On using the “Peierls substitution” scheme, it is shown that noncommutativity between spatial coordinates emerges naturally at a large magnetic field limit. Ther...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2021-10-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S055032132100208X |
| _version_ | 1819043172797382656 |
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| author | Partha Nandi Sankarshan Sahu Sayan Kumar Pal |
| author_facet | Partha Nandi Sankarshan Sahu Sayan Kumar Pal |
| author_sort | Partha Nandi |
| collection | DOAJ |
| description | A riveting study of Ward-Takahashi identities is presented for a broken dilatation or scale symmetry in a generalized quantum Hall system. On using the “Peierls substitution” scheme, it is shown that noncommutativity between spatial coordinates emerges naturally at a large magnetic field limit. Thereafter, we derive a path-integral action for the corresponding noncommutative quantum system and discuss the equivalence between the considered noncommutative system and the generalized Landau problem thus rendering an effective commmutative description. We then derive an expression for the unintegrated scale or dilatation anomaly for the generalized Landau system using Fujikawa's method and is subsequently renormalised. In fact, we identify the Ward-Takahashi identities associated with broken dilatation symmetry to be anomalous which is a purely quantum effect induced from the noncommutative structure between spatial coordinates and therefore non-intuitive in nature. |
| first_indexed | 2024-12-21T09:52:34Z |
| format | Article |
| id | doaj.art-7fe1c22c3b954bf4960fe3af596c7936 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-21T09:52:34Z |
| publishDate | 2021-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-7fe1c22c3b954bf4960fe3af596c79362022-12-21T19:08:09ZengElsevierNuclear Physics B0550-32132021-10-01971115511A note on broken dilatation symmetry in planar noncommutative theoryPartha Nandi0Sankarshan Sahu1Sayan Kumar Pal2S. N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake City, Kolkata 700106, IndiaIndian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, IndiaS. N. Bose National Centre for Basic Sciences, JD Block, Sector III, Salt Lake City, Kolkata 700106, India; Corresponding author.A riveting study of Ward-Takahashi identities is presented for a broken dilatation or scale symmetry in a generalized quantum Hall system. On using the “Peierls substitution” scheme, it is shown that noncommutativity between spatial coordinates emerges naturally at a large magnetic field limit. Thereafter, we derive a path-integral action for the corresponding noncommutative quantum system and discuss the equivalence between the considered noncommutative system and the generalized Landau problem thus rendering an effective commmutative description. We then derive an expression for the unintegrated scale or dilatation anomaly for the generalized Landau system using Fujikawa's method and is subsequently renormalised. In fact, we identify the Ward-Takahashi identities associated with broken dilatation symmetry to be anomalous which is a purely quantum effect induced from the noncommutative structure between spatial coordinates and therefore non-intuitive in nature.http://www.sciencedirect.com/science/article/pii/S055032132100208X |
| spellingShingle | Partha Nandi Sankarshan Sahu Sayan Kumar Pal A note on broken dilatation symmetry in planar noncommutative theory Nuclear Physics B |
| title | A note on broken dilatation symmetry in planar noncommutative theory |
| title_full | A note on broken dilatation symmetry in planar noncommutative theory |
| title_fullStr | A note on broken dilatation symmetry in planar noncommutative theory |
| title_full_unstemmed | A note on broken dilatation symmetry in planar noncommutative theory |
| title_short | A note on broken dilatation symmetry in planar noncommutative theory |
| title_sort | note on broken dilatation symmetry in planar noncommutative theory |
| url | http://www.sciencedirect.com/science/article/pii/S055032132100208X |
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