From lattice gauge theories to hydrogen atoms
We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space Hp of pure SU(2)2+1 lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms. One hydrogen atom is assigned to every plaquette of the lattice. A complete...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2015-10-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269315005602 |
| _version_ | 1811193156986732544 |
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| author | Manu Mathur T.P. Sreeraj |
| author_facet | Manu Mathur T.P. Sreeraj |
| author_sort | Manu Mathur |
| collection | DOAJ |
| description | We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space Hp of pure SU(2)2+1 lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms. One hydrogen atom is assigned to every plaquette of the lattice. A complete orthonormal description of the Wilson loop basis in Hp is obtained by all possible angular momentum Wigner couplings of hydrogen atom energy eigenstates |n l m〉 describing electric fluxes on the loops. The SU(2) gauge invariance implies that the total angular momenta of all hydrogen atoms vanish. The canonical transformations also enable us to rewrite the Kogut–Susskind Hamiltonian in terms of fundamental Wilson loop operators and their conjugate electric fields. The resulting loop Hamiltonian has a global SU(2) invariance and a simple weak coupling (g2→0) continuum limit. The canonical transformations leading to the loop Hamiltonian are valid for any SU(N). The ideas and techniques can also be extended to higher dimension. |
| first_indexed | 2024-04-12T00:03:51Z |
| format | Article |
| id | doaj.art-494a6526dec442dd9e44f16b2c7eaa0d |
| institution | Directory Open Access Journal |
| issn | 0370-2693 1873-2445 |
| language | English |
| last_indexed | 2024-04-12T00:03:51Z |
| publishDate | 2015-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-494a6526dec442dd9e44f16b2c7eaa0d2022-12-22T03:56:10ZengElsevierPhysics Letters B0370-26931873-24452015-10-01749C13714310.1016/j.physletb.2015.07.050From lattice gauge theories to hydrogen atomsManu MathurT.P. SreerajWe construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space Hp of pure SU(2)2+1 lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms. One hydrogen atom is assigned to every plaquette of the lattice. A complete orthonormal description of the Wilson loop basis in Hp is obtained by all possible angular momentum Wigner couplings of hydrogen atom energy eigenstates |n l m〉 describing electric fluxes on the loops. The SU(2) gauge invariance implies that the total angular momenta of all hydrogen atoms vanish. The canonical transformations also enable us to rewrite the Kogut–Susskind Hamiltonian in terms of fundamental Wilson loop operators and their conjugate electric fields. The resulting loop Hamiltonian has a global SU(2) invariance and a simple weak coupling (g2→0) continuum limit. The canonical transformations leading to the loop Hamiltonian are valid for any SU(N). The ideas and techniques can also be extended to higher dimension.http://www.sciencedirect.com/science/article/pii/S0370269315005602 |
| spellingShingle | Manu Mathur T.P. Sreeraj From lattice gauge theories to hydrogen atoms Physics Letters B |
| title | From lattice gauge theories to hydrogen atoms |
| title_full | From lattice gauge theories to hydrogen atoms |
| title_fullStr | From lattice gauge theories to hydrogen atoms |
| title_full_unstemmed | From lattice gauge theories to hydrogen atoms |
| title_short | From lattice gauge theories to hydrogen atoms |
| title_sort | from lattice gauge theories to hydrogen atoms |
| url | http://www.sciencedirect.com/science/article/pii/S0370269315005602 |
| work_keys_str_mv | AT manumathur fromlatticegaugetheoriestohydrogenatoms AT tpsreeraj fromlatticegaugetheoriestohydrogenatoms |