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Extended dualization: a method for the bosonization of anomalous fermion systems in arbitrary dimension

机译:扩展对偶化:一种用于任意维数的异常费米子系统的玻化的方法

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摘要

The technique of extended dualization developed in this paper is a path-integral method for the bosonization of quantized fermion systems in arbitrary dimension D. In its original (minimal) form, dualization is restricted to models wherein it is possible to define a dynamical quantized conserved charge. We generalize the usual dualization prescription to include systems with dynamical non-conserved quantum currents. Bosonization based on this extended dualization requires the introduction of an additional rank 0 (scalar) field together with the usual antisymmetric tensor field of rank (D-2). Our generalized dualization prescription permits one to clearly distinguish the arbitrariness in the bosonization from the arbitrariness in the quantization of the system. We study the bosonization of the most general quantization of the massive Thirring model in arbitrary dimension. Dualization permits one to bosonize this model trivially by invoking the bosonization of the free massive Dirac fermion. We also apply our extended dualization to the bosonization of the Chiral Schwinger model. For this model, minimal dualization is inadequate. We show that two independent scalar fields are required to describe the chiral current in the most general quantization of the Chiral Schwinger model.
机译:本文开发的扩展对偶化技术是一种路径积分方法,用于对任意维D上的量化费米子系统进行玻化。在其原始(最小)形式中,对偶化仅限于可以定义动态量化守恒的模型收费。我们将通常的对偶处方推广为包括具有动态非守恒量子电流的系统。基于这种扩展的二元化的玻色化需要引入一个额外的秩0(标量)场以及通常的秩为(D-2)的反对称张量场。我们的广义二元化处方使人们可以清楚地区分玻色化中的任意性与系统量化中的任意性。我们研究任意维度中大规模Thirring模型的最广义量化的玻色化。对偶化允许人们通过调用自由的大量狄拉克费米子的玻化来简单地对该模型进行玻化。我们还将扩展的对偶化应用于手性Schwinger模型的玻色化。对于此模型,最小化二元化是不够的。我们表明,需要两个独立的标量场来描述手性Schwinger模型的最一般量化中的手性电流。

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