Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces
High Energy Physics - Theory
2009-11-10 v1
Abstract
We present the exact solution of a scalar field theory defined with noncommuting position and momentum variables. The model describes charged particles in a uniform magnetic field and with an interaction defined by the Groenewold-Moyal star-product. Explicit results are presented for all Green's functions in arbitrary even spacetime dimensionality. Various scaling limits of the field theory are analysed non-perturbatively and the renormalizability of each limit examined. A supersymmetric extension of the field theory is also constructed in which the supersymmetry transformations are parametrized by differential operators in an infinite-dimensional noncommutative algebra.
Cite
@article{arxiv.hep-th/0308043,
title = {Exact Solution of Quantum Field Theory on Noncommutative Phase Spaces},
author = {E. Langmann and R. J. Szabo and K. Zarembo},
journal= {arXiv preprint arXiv:hep-th/0308043},
year = {2009}
}
Comments
70 pages AMSTeX