General massless field equations for higher spin in dimension 4

We present a classical field theory of interacting loops, whose low energy limit is D=4, N=1 supergravity. In Fourier modes, the theory is obtained by gauging the infinite dimensional algebra KM (SuperPoincaré) ⊕ Virasoro, where KM indicates the Kac-Moody extension. Taylor expanding the superloop vielbein in the “internal” coordinates yields towers of D=4 fields with arbitrarily high spins. The superloop diffeomorphisms relate all the higher spin fields. The field equations are obtained by requiring the closure of the generalized supersymmetries. Two different mechanisms give rise to masses for the higher modes: (i) a Kaluza-Klein type mass generation from “internal” loop coordinates, (ii) a non-vanishing background value for the zero mode of the Virasoro gauge field.

Download Full-text

Invariance of the Massless Field Equations under Changes of the Metric

General Relativity and Gravitation ◽

10.1023/a:1018802624345 ◽

1998 ◽

Vol 30 (3) ◽

pp. 379-387 ◽

Cited By ~ 4

Author(s):

G. F. Torres del Castillo ◽

J. A. Mondragón-Sánchez

Keyword(s):

Field Equations ◽

Massless Field

Download Full-text

Uniﬁcation of massless ﬁeld equations solutions for any spin

EPL (Europhysics Letters) ◽

10.1209/0295-5075/ac4621 ◽

2021 ◽

Author(s):

Sergio Hojman ◽

Felipe Asenjo

Keyword(s):

Wave Equation ◽

Exact Solutions ◽

Potential Functions ◽

Field Equations ◽

Fermionic Field ◽

Massless Field ◽

Coupled Equations ◽

Klein Gordon ◽

Fermionic Fields ◽

Derivatives Of

Abstract A uniﬁcation in terms of exact solutions for massless Klein–Gordon, Dirac, Maxwell, Rarita– Schwinger, Einstein, and bosonic and fermionic ﬁelds of any spin is presented. The method is based on writing all of the relevant dynamical ﬁelds in terms of products and derivatives of pre–potential functions, which satisfy d’Alambert equation. The coupled equations satisﬁed by the pre–potentials are non-linear. Remarkably, there are particular solutions of (gradient) orthogonal pre–potentials that satisfy the usual wave equation which may be used to construct exact non–trivial solutions to Klein–Gordon, Dirac, Maxwell, Rarita–Schwinger, (linearized and full) Einstein and any spin bosonic and fermionic ﬁeld equations, thus giving rise to an uniﬁcation of the solutions of all massless ﬁeld equations for any spin. Some solutions written in terms of orthogonal pre–potentials are presented. Relations of this method to previously developed ones, as well as to other subjects in physics are pointed out.

Download Full-text