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On the Algebraic Structure of Globally or Locally SU (2) Invariant Lattice Field Theories
Author(s) -
Rühl W.
Publication year - 1982
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.19820300203
Subject(s) - mathematics , computation , lattice (music) , invariant (physics) , pure mathematics , gauge theory , mathematical physics , algebraic number , product (mathematics) , physics , mathematical analysis , geometry , algorithm , acoustics
Abstract The local contribution to the action of the O (3) σ model in D = 2 or pure SU (2) gauge models in D ≧ 3 dimensions are expanded and integrated on the group. There results a field of variables j , a 3 nj coefficient W ({ j }) with n → ∞ and dynamical factors f ( j , β). We prove that for the gauge models a local decomposition of W ({ j }) into a product of 3 nj coefficients with n = 2 D ( D – 2) exists. We study generating functions for W ({ j }) or the 3 nj coefficients and develop an algorithm for their computation. Some of these generating functions are explicitly calculated.