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arXiv:nucl-th/0405045 · Physical Review C

Boson dominance in nuclei

F. Palumbo

Published Jul 7, 2005• 10 citations
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Abstract

We present a new method of bosonization of fermion systems applicable when the partition function is dominated by composite bosons. By restricting the partition function to such states, we obtain a Euclidean bosonic action from which we derive the Hamiltonian. Such a procedure respects all the fermion symmetries, particularly the fermion number conservation, and provides a boson mapping of all fermion operators.

DOI
10.1103/physrevc.72.014303

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We present a new method of bosonization of fermion systems applicable when the partition function is dominated by composite bosons. By restricting the partition function to such states, we obtain a Euclidean bosonic action from which we derive the Hamiltonian. Such a procedure respects all the fermion symmetries, particularly the fermion number conservation, and provides a boson mapping of all fermion operators.
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We test a new approach to bosonization in relativistic field theories and many-body systems, based on the use of fermionic composites as integration variables in the Berezin integral defining the partition function of the system. The method appears promising since at zeroth order it correctly describes the propagators of the composites, which can be evaluated in a number of significant cases. Still to be established is a general procedure for deriving the free action of the composites starting from the one of the constituents. To shed light on this problem and to explore further features of the method we study a simplified version of the BCS model. In this simple case the action of the composites can indeed be obtained: whether this result can be generalized it remains hewever to be seen. Yet an interesting property of the wave operators appearing in the free actions of bilinear composites already emerges from the simple problem we have treated: here the wave operators do not describe any time evolution, even though they generate the right propagators. This outcome relates to the basic properties of the integrals over the even elements of a Grassmann algebra where the composites live, which entails that the propagators are no longer the inverse of the wave operators.
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We discuss a generalization of the conventional bosonization procedure to the case of current-current interactions which have a natural representation in terms of current instead of fermion-number-density operators. A consistent bosonization procedure requires a geometrical quantization of the Hamiltonian action of ${\mathit{W}}_{\mathrm{\ensuremath{\infty}}}$ on its coadjoint orbits. An integrable example of a nontrivial realization of this symmetry is presented by the Calogero-Sutherland model. For an illustrative nonintegrable example we consider transverse gauge interactions and calculate the fermion Green function.