Mimetic discretization of the Abelian Chern-Simons theory and link invariants

In: Journal of Mathematical Physics (2013), 54:12
 

Abstract

A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the formulation of a theory of differential forms in the lattice, including a consistent definition of the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which correspond to their continuum counterparts are given. A discussion of the discretization of metric structures in the space of transverse vector densities is presented. The study of these metrics could serve to obtain explicit formulae for knot an link invariants in the lattice.

Bibtex

@ARTICLE{di2013mimetic,
    author = {Grau, Javier},
     title = {Mimetic discretization of the Abelian Chern-Simons theory and link invariants},
   journal = {Journal of Mathematical Physics},
    volume = {54},
    number = {12},
      year = {2013},
  abstract = {A mimetic discretization of the Abelian Chern-Simons theory is presented. The study relies on the
              formulation of a theory of differential forms in the lattice, including a consistent definition of
              the Hodge duality operation. Explicit expressions for the Gauss Linking Number in the lattice, which
              correspond to their continuum counterparts are given. A discussion of the discretization of metric
              structures in the space of transverse vector densities is presented. The study of these metrics
              could serve to obtain explicit formulae for knot an link invariants in the lattice.},
       url = {http://arxiv.org/abs/1210.4716}
}