A general method for deriving e ective Lagrangians is used to establish a continuous bosonization of a fermionic theory. This is achieved by i n troducing new elds in the path integral, and choosing di erent gauges in an equivalent v ersion of the theory containing also a bosonic eld. We illustrate this idea by showing the equivalence of fermions and bosons in (1+1) dimensions. We also demonstrate a smooth transition in space from a bosonic to a fermionic representation, providing a new class of soft Cheshire Cat bag models, as well as a smooth transition in momentum space introducing e ective l o w and high energy elds.

The (1+1)-dimensional bosonization relations for fermionic mass terms are derived by choosing a specific gauge in an enlarged gauge-invariant theory containing both fermionic and bosonic fields. The fermionic part of the generating functional subject to the gauge constraint can be cast into the form of a strongly coupled Schwinger model, which can be solved exactly. The resulting bosonic theory coupled to the scalar sources then exhibits directly the bosonic counterparts of the fermionic densitiesψψ andψγ 5 ψ.

We present a general scheme for extracting effective degrees of freedom from an underlying fundamental Lagrangian, through a series of well-defined transformations in the functional integral of the cut-off theory. This is done by introducing collective fields in a gauge-symmetric manner. Through appropriate gauge fixings of this symmetry one can remove long-distance degrees of freedom from the underlying theory, replacing them by the collective fields. Applying this technique to QCD, we set out to extract the long-distance dynamics in the pseudoscalar flavour singlet sector through a gauging (and subsequent gauge fixing) of the U (1) A flavour symmetry which is broken by the anomaly. By this series of exact transformations of a cut-off generating functional for QCD, we arrive at a theory describing the long-distance physics of a pseudoscalar flavour singlet meson coupled to the residual quark-gluon degrees of freedom. As examples of how known low-energy physics can be reproduced in this formulation, we rederive the Witten-Veneziano relation between the η ′ mass and the topological susceptibility, now for any value of the number of colours N c . The resulting effective Lagrangian contains an axial vector field, which shares the relevant features with the Veneziano ghost. This field is responsible for removing the η ′ degree of freedom from the fundamental QCD Lagrangian.

No abstract

Qualitons, topological excitations with the quantum numbers of quarks, may provide an accurate description of what is meant by constituent quarks in QCD. Their existence hinges crucially on an effective Lagrangian description of QCD in which a pseudoscalar colour-octet of fields enters as a new variable. We show here how such new fields may be extracted from the fundamental QCD Lagrangian using the gaugesymmetric collective field technique.