Antisymmetric tensor fields in 4D: actions, symmetries and first order Duffin–Kemmer–Petiau formulations

Abstract Analyzing the representations of the Lorentz group, we give a systematic count and construction of all the possible Lagrangians describing an antisymmetric rank two tensor field. The count yields two scalars, which provide the ingredients of the gauge invariant Kalb–Ramond model, equivalent to the sigma model and familiar from super gravity and string theory, and of the conformally invariant Avdeev–Chizhov model, which describes self-dual tensors. The count also includes a pseudoscalar with symmetric coupling, and an additional pseudoscalar, an antisymmetrized form of the Avdeev–Chizhov Lagrangian. This quantity was first derived in an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> superalgebraic model of the weak interactions. It is also conformally invariant, and naturally implements the Landau CP symmetry. Then, by extending the DKP ten component formalism, we recover the model Lagrangians as first order systems. To complete the analysis, we classify all local Lorentz invariant potentials (mass terms and quartic couplings) for charged antisymmetric tensor fields coupled to a Yang-Mills field.