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arXiv:1510.05865

On the term of the 4-th order with respect to the field operators in the translation-invariant polaron theory

Victor Dmitrievich Lakhno

Published Oct 20, 2015• 0 citations
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Abstract

It is shown that 4-th order term in the translation-invariant polaron theory vanishes.
DOI
10.48550/arxiv.1510.05865

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•Jan 1, 2008•0 citations
We summarize a study of an Abelian gauge theory in 2+1 dimensions, the gauge field being coupled to nonrelativistic Fermions. The Action for the gauge field is a combination of the Maxwell term and a Chern-Simons (CS) term. We study the limit of vanishing Fermions ’ charge, keeping fixed the gauge field mass induced by the CS term. By considering a closed surface, in particular a torus to keep translational invariance, we show that the Fermions do not decouple completely from the gauge field, and in fact they behave as Anyons treated in the-translationally invariant formulation of the- Mean Field approximation. We describe the exact solution of this limiting case. This lecture is based on ref.[1] and on previous work done on the problem of a translational invariant formulation of the Anyon mean field theory and its properties with respect to superfluidity and possibly superconductivity (for a general review of the previous work see ref.[2]). Actually, to discuss those issues in a proper way it is necessary to introduce a suitable mathematical formalism: