Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-06-22
Phys.Rev.D49:1054-1066,1994
Physics
High Energy Physics
High Energy Physics - Theory
22 pages in ReVTEX (with a plaintext PostScript figure appended at end), MIT CTP #2216
Scientific paper
10.1103/PhysRevD.49.1054
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.
Freedman Daniel Z.
Lozano Guadalupe
Rius Nuria
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