A Condensation of Interacting Bosons in Two Dimensional Space

S. G. Rajeev

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arXiv · hep-th/9905120

A Condensation of Interacting Bosons in Two Dimensional Space

S. G. Rajeev

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Abstract

We develop a theory of non-relativistic bosons in two spatial dimensions with a weak short range attractive interaction. In the limit as the range of the interaction becomes small, there is an ultra-violet divergence in the problem. We devise a scheme to remove this divergence and produce a completely finite formulation of the theory. This involves reformulating the dynamics in terms of a new operator whose eigenvalues give the {\it logarithm} of the energy levels. Then, a mean field theory is developed which allows us to describe the limit of a large number of bosons. The ground state is a new kind of condensate (soliton) of bosons that breaks translation invariance spontaneously. The ground state energy is negative and its magnitude grows {\it exponentially} with the number of particles, rather than like a power law as for conventional many body systems.

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S. G. Rajeev. 1999-05-17. A Condensation of Interacting Bosons in Two Dimensional Space. https://arxiv.org/abs/hep-th/9905120

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