Antisymmetric Tensor Gauge Field in General Covariant Gauges

Abstract

Recently, Townsend has shown that there exist similarity and dissimilarity between the mode counting of spin 3/2 field and that of antisymmetric tensor gauge field. 11 Especially, one cannot find a mechanism of introducing extra two modes in contrast to the case of spin 3/2 theory where an additional extra Majorana spinor ghost has been introduced by Nielsen. 21 Nielsen adopted the ordinary form of Faddeev-Popov (FP) ghosts c*(rD)c+N(rD)N. On the other hand, Rata iand Kugo 31 have proposed a new formalism of supergravity by adopting the unconventional form of FP ghost ic*(ro) (rD)c. Since the ghosts c and c* of Hata-Kugo obey the second order differential equations, all their components are independent and give rise to eight modes of FP ghosts. There should then exist eight unphysical modes of spin 3/2 field sector which compensate eight modes of FP ghosts. Such an unphysical sector is constructed by introducing the Lagrangian multiplier spinor field B which plays a role of fixing the gauge. The unphysical modes consist of four longitudinal components of cj; 11 and four components of B, and their number is equal to that of FP ghosts. Fronsdal and Hata41 have further shown that such a type of formalism is necessary to construct the interacting theory of higher spin fields so that the unitarity ,:of the physical S-matrix is assured. The present author 51 has also shown that the axial anomaly for the gravitino in the background curved space is obtained by B field not by ghost fields in Hata-Kugo formalism. It is, therefore, desirable to discuss the mode counting of the quantized antisymmetric tensor gauge field by introducing the Lagrangian multiplier fields. We shall start with the following Lagrangian :