Algebraic renormalization of antisymmetric tensor matter fields

Topological gauge theories with antisymmetric tensor matter fields

A new type of topological matter interactions involving second–rank antisymmetric tensor matter fields with an underlying NT ≧ 1 topological supersymmetry are proposed. The construction of the 4–dimensional, NT = 1 Donaldson–Witten theory, the NT = 1 super–BF model and the NT = 2 topological B–model with tensor matter are explicitly worked out.

Quantization of chiral antisymmetric tensor fields

Chiral antisymmetric tensor fields can have chiral couplings to quarks and leptons. Their kinetic terms do not mix different representations of the Lorentz symmetry. A mass term is forbidden by symmetry. We demonstrate that the interacting theory for such fields can be consistently quantized. The Hamiltonian is hermitean and bounded from below. In contrast, the Hamiltonian for the free fields i...

Antisymmetric Tensor Gauge Fields on S4

Antisymmetric tensor generalizations of affine vector fields.

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely r...

Stochastic Quantization of Non-Abelian Antisymmetric Tensor Fields

A Stochastic Quantization Method (in short, SQM)l) was first introduced by Parisi and Wu) as the third quantization method of gauge theories. Their statement is as follows: In this scheme there is no need to fix the gauge degrees of freedom, i.e., no need to introduce any artificial auxiliary fields (ghost and multiplier fields). It is the main advantage of the SQM. It is essentially governed b...