Note on Dirac–Kähler massless fields

Abstract

We obtain the canonical and symmetrical Belinfante energy-momentum tensors of Dirac−Kähler's fields. It is shown that the traces of the energy-momentum tensors are not equal to zero. We find the canonical and Belinfante dilatation currents which are not conserved, but a new conserved dilatation current is obtained. It is pointed out that the conformal symmetry is broken. The canonical quantization is performed and the propagator of the massless fields in the first-order formalism is found.

A discrete model of the Dirac-Kähler equation

“…where r = 1, 2, 3. It is known (see [14,18]) that in the classical (continuous) theory there are three massless analogs of Equation (4.3). Now we describe discrete counterparts In the case m 1 = 0 and m 2 = 0 we obtain −δ c 1 ω = 0,…”

“…We prove the same in the discrete case. Recently much attention has been directed to the study of the massless Dirac-Kähler field [14,16,18]. From the physics point of view the Dirac-Kähler system has three massless limits [14].…”

“…Recently much attention has been directed to the study of the massless Dirac-Kähler field [14,16,18]. From the physics point of view the Dirac-Kähler system has three massless limits [14]. In [16,18], it has shown that the Kalb-Ramond field (notoph) equations and the electromagnetic equations are partial cases of the Dirac-Kähler massless equation.…”

“…Let us consider the case m 2 = 0 and m 1 = 0. In the continuous theory this is the so-called electromagnetic massless limit of the Dirac-Kähler equation [14,18]. A discrete analog for this case has the form…”

Field Theory of Massive and Massless Vector Particles in the Duffin–kemmer–petiau Formalism

“…One can find early references on DKP equations in [6]. The matrix form of RWE is also convenient for the formulation of higher derivative field equations [7], [8], [9], [10], fields with multi-spin [11], [12], [13], [14], [15], [16], Einstein gravity equations [17], fields in curved space-time [18], [19], [20] and quantum chromodynamics [21]. There is a vast number of papers devoted to DKP equations, and, therefore, we mention only some part of them.…”