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The Planar Thirring Model with Kähler-Dirac Fermions

Simon Hands

Symmetry, Volume: 13, Issue: 8, Start page: 1523

Swansea University Author: Simon Hands

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DOI (Published version): 10.3390/sym13081523

Abstract

Kähler’s geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U(N)⊗U(N) field transformations and has a parity-invariant mass term, which are symme...

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Published in: Symmetry
ISSN: 2073-8994
Published: MDPI AG 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57935
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first_indexed 2021-09-17T08:53:32Z
last_indexed 2021-10-19T03:22:52Z
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spelling 2021-10-18T13:21:44.2021385 v2 57935 2021-09-17 The Planar Thirring Model with Kähler-Dirac Fermions b34293f7370adc1d2cac9b93717a61c7 Simon Hands Simon Hands true false 2021-09-17 FGSEN Kähler’s geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U(N)⊗U(N) field transformations and has a parity-invariant mass term, which are symmetries shared in common with staggered lattice fermions. The formalism is used to construct a version of the Thirring model with contact interactions between conserved Noether currents. Under reasonable assumptions about field rescaling after quantum corrections, a more general interaction term is derived, sharing the same symmetries but now including terms which entangle spin and taste degrees of freedom, which exactly coincides with the leading terms in the staggered lattice Thirring model in the long-wavelength limit. Finally, truncated versions of the theory are explored; it is found that excluding scalar and pseudoscalar components leads to a theory of six-component fermion fields describing particles with spin 1, with fermion and antifermion corresponding to states with definite circular polarisation. In the UV limit, only transverse states with just four non-vanishing components propagate. Implications for the description of dynamics at a strongly interacting renormalisation group fixed point are discussed. Journal Article Symmetry 13 8 1523 MDPI AG 2073-8994 interacting fermions; field theories in dimensions other than four; staggered lattice fermions; renormalisation group fixed point 19 8 2021 2021-08-19 10.3390/sym13081523 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University STFC Consolidated Grant ST/T000813/1 2021-10-18T13:21:44.2021385 2021-09-17T09:45:05.8658948 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Physics Simon Hands 1 57935__20900__77881566804e483f9848fa9d66188685.pdf 57935.pdf 2021-09-17T09:52:37.3768210 Output 333803 application/pdf Version of Record true © 2021 by the author. This is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license true eng https://creativecommons.org/licenses/by/4.0/
title The Planar Thirring Model with Kähler-Dirac Fermions
spellingShingle The Planar Thirring Model with Kähler-Dirac Fermions
Simon Hands
title_short The Planar Thirring Model with Kähler-Dirac Fermions
title_full The Planar Thirring Model with Kähler-Dirac Fermions
title_fullStr The Planar Thirring Model with Kähler-Dirac Fermions
title_full_unstemmed The Planar Thirring Model with Kähler-Dirac Fermions
title_sort The Planar Thirring Model with Kähler-Dirac Fermions
author_id_str_mv b34293f7370adc1d2cac9b93717a61c7
author_id_fullname_str_mv b34293f7370adc1d2cac9b93717a61c7_***_Simon Hands
author Simon Hands
author2 Simon Hands
format Journal article
container_title Symmetry
container_volume 13
container_issue 8
container_start_page 1523
publishDate 2021
institution Swansea University
issn 2073-8994
doi_str_mv 10.3390/sym13081523
publisher MDPI AG
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Physics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Physics
document_store_str 1
active_str 0
description Kähler’s geometric approach in which relativistic fermion fields are treated as differential forms is applied in three spacetime dimensions. It is shown that the resulting continuum theory is invariant under global U(N)⊗U(N) field transformations and has a parity-invariant mass term, which are symmetries shared in common with staggered lattice fermions. The formalism is used to construct a version of the Thirring model with contact interactions between conserved Noether currents. Under reasonable assumptions about field rescaling after quantum corrections, a more general interaction term is derived, sharing the same symmetries but now including terms which entangle spin and taste degrees of freedom, which exactly coincides with the leading terms in the staggered lattice Thirring model in the long-wavelength limit. Finally, truncated versions of the theory are explored; it is found that excluding scalar and pseudoscalar components leads to a theory of six-component fermion fields describing particles with spin 1, with fermion and antifermion corresponding to states with definite circular polarisation. In the UV limit, only transverse states with just four non-vanishing components propagate. Implications for the description of dynamics at a strongly interacting renormalisation group fixed point are discussed.
published_date 2021-08-19T04:14:03Z
_version_ 1763753950500093952
score 11.037581

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