Discretization in noncommutative field theory. (English) Zbl 1416.81090

Acatrinei, Ciprian Sorin

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 20th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 2–7, 2018. Sofia: Avangard Prima; Sofia: Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering. Geom. Integrability Quantization 20, 65-78 (2019).

Summary: A discretization scheme provided by the noncommutativity of space is reviewed. In the representation chosen here the radial coordinate is rendered discrete, allowing fields to be put on a lattice in a natural way. Noncommutativity is traded for a controllable type of nonlocality of the field dynamics, which in turn allows fermions to be free of lattice artefacts. Exact, singularity-free solutions are found interpreted, and their continuum limit is well-defined.
For the entire collection see [Zbl 1408.53003].

MSC:

81R60	Noncommutative geometry in quantum theory
81T10	Model quantum field theories
81T27	Continuum limits in quantum field theory
33E20	Other functions defined by series and integrals
39A12	Discrete version of topics in analysis
33C80	Connections of hypergeometric functions with groups and algebras, and related topics
33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
05A10	Factorials, binomial coefficients, combinatorial functions

Keywords:

discrete space; field theory; noncommutative geometry