Composite boson dominance in relativistic field theories

Abstract

We apply a new bosonization technique to relativistic field theories of fermions whose partition function is dominated by bosonic composites, and derive the effective action for these bosons. The derivation respects all symmetries, including gauge invariance, with the exception of Euclidean invariance which must be checked a posteriori. We use a lattice regularization which should make applications to gauge theories easier. We test the method on a fermion field theory with quartic interaction in the limit when the number of flavours N f is large, and show that it reproduces the exact results in the bosonic sector, namely condensation of a composite boson with the right mass which breaks the discrete chiral invariance of the model. Moreover we determine the structure function of the condensed composite, whose spatial part turns out to be identical to that of the Cooper pairs of the BCS model of superconductivity.

Semivariational approach to QCD at finite temperature and baryon density

“…[10,11]. Hence, under the assumption that the composite operators which dominate the partition function have a large index of nilpotency, an approximate projection operator in the Fock space of the fermions can be defined…”

“…In the evaluation of the trace on the fermionic Fock space the only difference with respect to [11] is the presence of the operatorV t . But I notice that the product of operatorsV tTt+1 has an expression similar to that of T t+1…”

“…The notation is somewhat different from that of [11]. It is remarkable that S mesons has been evaluated exactly [11], so that the only approximations in the partition function are the physical assumption of boson dominance and the form of the projector over the meson subspace.…”

“…The notation is somewhat different from that of [11]. It is remarkable that S mesons has been evaluated exactly [11], so that the only approximations in the partition function are the physical assumption of boson dominance and the form of the projector over the meson subspace. Since the projector depends on the structure functions Φ x,K , the effective action is a functional of these functions which are determined by a variational calculation on the quantities of interest.…”

“…Evaluating the integral in the above equation by the saddle point method, as done in [11] for P m , we see that P m−q is approximately a projector if we assume tr…”