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Numerical results for U (1) gauge theory on 2d and 4d non‐commutative spaces
Author(s) -
Bietenholz W.,
Bigarini A.,
Hofheinz F.,
Nishimura J.,
Susaki Y.,
Volkholz J.
Publication year - 2005
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.200510199
Subject(s) - commutative property , gauge theory , gauge (firearms) , loop (graph theory) , wilson loop , physics , plane (geometry) , quantum gauge theory , space (punctuation) , phase space , limit (mathematics) , mathematical physics , complex plane , theoretical physics , mathematics , pure mathematics , geometry , quantum mechanics , gauge fixing , mathematical analysis , gauge boson , combinatorics , computer science , archaeology , history , operating system
We present non‐perturbative results for U (1) gauge theory in spaces, which include a non‐commutative plane. In contrast to the commutative space, such gauge theories involve a Yang‐Mills term, and the Wilson loop is complex on the non‐perturbative level. We first consider the 2d case: small Wilson loops follow an area law, whereas for large Wilson loops the complex phase rises linearly with the area. In four dimensions the behavior is qualitatively similar for loops in the non‐commutative plane, whereas the loops in other planes follow closely the commutative pattern. In d = 2 our results can be extrapolated safely to the continuum limit, and in d = 4 we report on recent progress towards this goal.