A Dimakis et al 1993 J. Phys. A: Math. Gen. 26 1927 doi:10.1088/0305-4470/26/8/019
A Dimakis, F Muller-Hoissen and T Striker
Show affiliationsThe authors study consistent deformations of the classical differential calculus on algebras of functions (and, more generally, commutative algebras) such that differentials and functions satisfy nontrivial commutation relations. For a class of such calculi it is shown that the deformation parameters correspond to the spacings of a lattice. These differential calculi generate a lattice on a space continuum. The whole setting of a lattice theory can then be deduced from the continuum theory via deformation of the standard differential calculus. In this framework one just has to express the Lagrangian for the continuum theory in terms of differential forms. This expression then also makes sense for the deformed differential calculus. There is a natural integral associated with the latter. Integration of the Lagrangian over a space continuum then produces the correct lattice action for a large class of theories. This is explicitly shown for the scalar field action and the action for SU(m) gauge theory.
81T75 Noncommutative geometry methods (See also 46L85, 46L87, 58B34)
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
Issue 8 (21 April 1993)
A Dimakis et al 1993 J. Phys. A: Math. Gen. 26 1927
B Derrida et al 1993 J. Phys. A: Math. Gen. 26 1493
N Brunel et al 1992 J. Phys. A: Math. Gen. 25 5017
A W Sandvik 1992 J. Phys. A: Math. Gen. 25 3667
Y S Yang and C J Thompson 1991 J. Phys. A: Math. Gen. 24 L279
E B Lin 1991 J. Phys. A: Math. Gen. 24 L1045
M Wilkinson et al 1991 J. Phys. A: Math. Gen. 24 175
V Pasquier 1987 J. Phys. A: Math. Gen. 20 L221
K Svozil 1987 J. Phys. A: Math. Gen. 20 3861
J L Cardy 1986 J. Phys. A: Math. Gen. 19 L1093