“Dynamical” interactions and gauge invariance

Abstract

In order to avoid known, long-standing problems with higher-spin interactions, the electromagnetic field is introduced "dynamically" by using a nonsingular, Lorentztype transformation, acting as adjoint representation on the Poincaré algebra of the free theory. In doing so, Lorentz transformation and local gauge transformation are placed on the same foundations, leading to the phase transition as a consequence of the gauge transformation. The procedure is exemplified in the case of plane waves for the Dirac-type equation and the Rarita-Schwinger equation.published as Physical Review D84 (2011) 065022 † Deceased.Understanding the higher-spin interactions 1 is a long-standing problem. However, in spite of its 70 years history, the main goal -the construction of a consistent higher-spin theory, even for the electromagnetic interaction which ought to be the simplest case -has not been achieved yet.The theory of higher-spin interactions has never belonged to the "mainstream" theories. The field has been cultivated by groups of enthusiasts. On the other hand, the theory of higher-spin interactions is needed for solving many mainstream problems. It is related to the Standard Model (SM) in several ways. By introducing the massive spin-one gauge bosons into the theory one also introduces higher-spin problems into the Standard Model. Difficulties appear for instance in scattering processes with the charged gauge bosons W ± in the initial or final state, or in constructing three-vertex gauge boson self-interactions. A consistent higher-spin interaction theory is also needed in chromodynamics. Quantum Chromodynamics (QCD) does not yet allow one to describe low-energy hadronic processes in terms of underlying quark-gluon dynamics. Because of this one has to use a more phenomenological approach in terms of hadronic fields. However, one of the basic problems here is the treatment of hadrons with higher spins [2].Also for theories beyond the SM one needs a better understanding of ordinary higherspin field theory. String theory for instance is free of many higher-spin problems and due to this it is believed that it can consistently describe quantum gravity. A reason behind this consistent behaviour is that string theories contain an infinite tower of all spin states. But at the same time serious troubles exist in the physical interpretation of the string theories. The existence of a consistent higher-spin interaction theory would help in better understanding the physics behind the string theory. It is believed that if a breakthrough in understanding the basic problems of the ordinary higher-spin field theory happens, it might become a fashionable topic [3].The investigations of higher-spin fields started in the 1930s of the last century with papers by Dirac [4], Wigner [5], Fierz and Pauli [6], and were followed by the works of Rarita and Schwinger [7], Bargmann and Wigner [8], and others [9,10,11,12,13,14,15]. The difficulties in higher-spin physics revealed themselves when one tried to couple higherspin fields to an electromagn...

Consistence between $\pi N{\rm{\Delta }}$ spin-3/2 gauge couplings and electromagnetic gauge invariance

“…This makes the interacting theory not Lorentz covariant, since we get superluminal solutions to the field equations, even at the classical level [7]. Consistency at the classical level has been achieved by introducing the electromagnetic interactions nonminimally through exploiting properties of the Poincare group [11][12][13]. The abovementioned quantum inconsistencies have been reported for the RS field minimally coupled to the electromagnetic field in the presence of a nonvanishing magnetic field [5] and for the coupling to a spinor and the derivative of a scalar field in the presence of a nonvanishing gradient [8].…”

“…rendering (12) no longer valid. Then, using the trimmed propagator is not possible in the radiative case.…”

Gauge and Lorentz Transformation Placed on the Same Foundation

“…As an example of higher spin, the spin-3/2 case is considered in detail in Ref. [33]. As it turns out, the Rarita-Schwinger spin-3/2 equation on the presence of a "dynamical" interaction is algebraically consistent and causal.…”

Inconsistency of the ‘spin-3/2 gauge invariant’ interaction of Rarita–Schwinger fields

“…Something analogous happen when the RS field is coupled to Dirac and pseudoscalar fields via the 'conventional' coupling in the presence of a critical gradient of the pseudoscalar [7]. At the classical level, in the case of EM coupling, the inconsistency can be avoided if certain nonminimal couplings are used instead [8].…”