Gaugeon formalism for the second-rank antisymmetric tensor gauge fields

Abstract

We present a BRST symmetric gaugeon formalism for the two-form gauge fields. A set of vector gaugeon fields is introduced as a quantum gauge freedom. One of the gaugeon fields satisfies a higher derivative field equation; this property is necessary to change the gauge-fixing parameter of the two-form gauge field. A naive Lagrangian for the vector gaugeon fields is itself invariant under a gauge transformation for the vector gaugeon field. The Lagrangian of our theory includes the gauge-fixing terms for the gaugeon fields and corresponding Faddeev-Popov ghosts terms. * endo@sci.kj.yamagata-u.ac.jp 1 I. INTRODUCTION The standard formalism of canonically quantized gauge theories [1-5] does not consider quantum-level gauge transformations. There is no quantum gauge freedom, since the quantum theory is defined only after the gauge fixing. Within the broader framework of Yokoyama's gaugeon formalism [6], we can consider quantum gauge transformations as q-number gauge transformations. In this formalism, quantum gauge freedom is provided by an extra field, called a gaugeon field. The gaugeon formalism has been developed so far for various gauge fields, such as, Abelian gauge fields [6-11], non-Abelian gauge fields [12-19], Higgs models [20, 21], chiral gauge theories [22], Schwinger's model [23], spin-3/2 gauge fields [24], string theories [25,26], and gravitational fields [27,28].Recently, gaugeon formalisms for the Abelian two-form gauge fields are considered by Upadhyay and Panigrahi [29] (in the framework of the "very special relativity" [30]), and by Dwivedi [31]. They introduced a vector gaugeon field which would play a role of the quantum gauge freedom of the two-form gauge field. The vector gaugeon field itself has a property of gauge fields. It has a gauge invariance. In fact, the Lagrangians given in Refs. [29,31] are invariant under the gauge transformation of the vector gaugeon field. So, we should fix the gauge before quantizing the vector gaugeon field. However, the authors of Refs. [29,31] did not fix the gauge. Thus, their vector gaugeon field was not quantized.Namely, their theories are incomplete as a gaugeon formalism for the two-form gauge fields; they do not permit the quantum level gauge transformation, which is an essential ingredient of the gaugeon formalism.The aim of this paper is quantizing the vector gaugeon field and obtaining a correct gaugeon theory for the two-form gauge field. This paper is organized as follows. In sect. 2, we first review the standard formalism for the covariantly quantized two-form gauge field. Then, we show that the vector gaugeon field must be a massless dipole field, that is, its propagator have a term proportional to 1/(p 2 ) 2 .In sect. 3, we covariantly fix the gauge of the massless dipole vector field and quantize the system. In section 4, incorporating the massless dipole vector field as the gaugeon field, we present a correct gaugeon theory of the two-form gauge field. Section 5 is devoted to summary and comments.