Bosonization based on Clifford algebras and its gauge theoretic interpretation
Abstract We study the properties of a bosonization procedure based on Clifford algebra valued degrees of freedom, valid for spaces of any dimension. We present its interpretation in terms of fermions in presence of ℤ2 gauge fields satisfying a modified Gauss’ law, resembling Chern-Simons-like theori...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-12-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2020)118 |
| _version_ | 1819059901537714176 |
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| author | A. Bochniak B. Ruba |
| author_facet | A. Bochniak B. Ruba |
| author_sort | A. Bochniak |
| collection | DOAJ |
| description | Abstract We study the properties of a bosonization procedure based on Clifford algebra valued degrees of freedom, valid for spaces of any dimension. We present its interpretation in terms of fermions in presence of ℤ2 gauge fields satisfying a modified Gauss’ law, resembling Chern-Simons-like theories. Our bosonization prescription involves constraints, which are interpreted as a flatness condition for the gauge field. Solution of the constraints is presented for toroidal geometries of dimension two. Duality between our model and (d − 1)- form ℤ2 gauge theory is derived, which elucidates the relation between the approach taken here with another bosonization map proposed recently. |
| first_indexed | 2024-12-21T14:18:28Z |
| format | Article |
| id | doaj.art-ce0bb3c35997455aa5389cd701dff28f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-21T14:18:28Z |
| publishDate | 2020-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-ce0bb3c35997455aa5389cd701dff28f2022-12-21T19:00:52ZengSpringerOpenJournal of High Energy Physics1029-84792020-12-0120201213610.1007/JHEP12(2020)118Bosonization based on Clifford algebras and its gauge theoretic interpretationA. Bochniak0B. Ruba1Institute of Theoretical Physics, Jagiellonian University in KrakówInstitute of Theoretical Physics, Jagiellonian University in KrakówAbstract We study the properties of a bosonization procedure based on Clifford algebra valued degrees of freedom, valid for spaces of any dimension. We present its interpretation in terms of fermions in presence of ℤ2 gauge fields satisfying a modified Gauss’ law, resembling Chern-Simons-like theories. Our bosonization prescription involves constraints, which are interpreted as a flatness condition for the gauge field. Solution of the constraints is presented for toroidal geometries of dimension two. Duality between our model and (d − 1)- form ℤ2 gauge theory is derived, which elucidates the relation between the approach taken here with another bosonization map proposed recently.https://doi.org/10.1007/JHEP12(2020)118Gauge SymmetryLattice Quantum Field TheoryTopological States of MatterChern-Simons Theories |
| spellingShingle | A. Bochniak B. Ruba Bosonization based on Clifford algebras and its gauge theoretic interpretation Journal of High Energy Physics Gauge Symmetry Lattice Quantum Field Theory Topological States of Matter Chern-Simons Theories |
| title | Bosonization based on Clifford algebras and its gauge theoretic interpretation |
| title_full | Bosonization based on Clifford algebras and its gauge theoretic interpretation |
| title_fullStr | Bosonization based on Clifford algebras and its gauge theoretic interpretation |
| title_full_unstemmed | Bosonization based on Clifford algebras and its gauge theoretic interpretation |
| title_short | Bosonization based on Clifford algebras and its gauge theoretic interpretation |
| title_sort | bosonization based on clifford algebras and its gauge theoretic interpretation |
| topic | Gauge Symmetry Lattice Quantum Field Theory Topological States of Matter Chern-Simons Theories |
| url | https://doi.org/10.1007/JHEP12(2020)118 |
| work_keys_str_mv | AT abochniak bosonizationbasedoncliffordalgebrasanditsgaugetheoreticinterpretation AT bruba bosonizationbasedoncliffordalgebrasanditsgaugetheoreticinterpretation |