6533b7d9fe1ef96bd126b9b9

RESEARCH PRODUCT

Differential Regularization of a Non-relativistic Anyon Model

N. RiusGustavo S. LozanoDaniel Z. Freedman

subject

High Energy Physics - TheoryPhysicsFOS: Physical sciencesLie groupFísicaRenormalization groupSymmetry groupLambdaRenormalizationHigh Energy Physics - Theory (hep-th)Quantum mechanicsRegularization (physics)Gauge theoryBoson

description

Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the $\phi {}^{*} \phi {}^{*} \phi \phi$ 4-point function, which is the only primitively divergent Green's function, are obtained up to 3-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the $\beta$-function is investigated. If the renormalization scheme is fixed to agree with a previous 1-loop calculation, the 2- and 3-loop contributions to $\beta(\lambda,e)$ vanish, and $\beta(\lambda,e)$ itself vanishes when the ``self-dual'' condition relating $\lambda$ to the gauge coupling $e$ is imposed.

10.1103/physrevd.49.1054http://hdl.handle.net/10550/42598