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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.

No abstract

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.