Abstract
We develop a general framework which we believe may provide some insights into the structure of interacting `high spin` field theories. A finite or infinite set of classical spin fields is described by means of a field defined on an enlarged spacetime manifold. The free action and its gauge symmetries are gathered into a nilpotent differential operator on this manifold. In particular, the choice of Grassmann-valued extra coordinates leads to theories involving only a finite set of fields, the possible contents (spin multiplicities, degree of reducibility, etc.) of which are classified according to the representations of a unitary algebra. The interacting theory is characterized by a functional of the field on the enlarged manifold. We show that there is among these functionals a natural graded Lie algebra structure allowing one to rewrite the gauge invariance condition of the action in a concise form which is a nonlinear generalization of the nilpotency condition of the free theory. We obtain the general solution of this `classical master equation`{sup ,} which can be built recurrently starting form the cubic vertex, and we study its symmetries. Our formalism lends itself to a systematic introduction of additional conditions, such as locality, polynomiality, etc. We write
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Citation Formats
Fougere, F.
Algebraic construction of interacting higher spin field theories; Construction algebrique de theories de champs de spin eleve en interaction.
France: N. p.,
1991.
Web.
Fougere, F.
Algebraic construction of interacting higher spin field theories; Construction algebrique de theories de champs de spin eleve en interaction.
France.
Fougere, F.
1991.
"Algebraic construction of interacting higher spin field theories; Construction algebrique de theories de champs de spin eleve en interaction."
France.
@misc{etde_10127913,
title = {Algebraic construction of interacting higher spin field theories; Construction algebrique de theories de champs de spin eleve en interaction}
author = {Fougere, F}
abstractNote = {We develop a general framework which we believe may provide some insights into the structure of interacting `high spin` field theories. A finite or infinite set of classical spin fields is described by means of a field defined on an enlarged spacetime manifold. The free action and its gauge symmetries are gathered into a nilpotent differential operator on this manifold. In particular, the choice of Grassmann-valued extra coordinates leads to theories involving only a finite set of fields, the possible contents (spin multiplicities, degree of reducibility, etc.) of which are classified according to the representations of a unitary algebra. The interacting theory is characterized by a functional of the field on the enlarged manifold. We show that there is among these functionals a natural graded Lie algebra structure allowing one to rewrite the gauge invariance condition of the action in a concise form which is a nonlinear generalization of the nilpotency condition of the free theory. We obtain the general solution of this `classical master equation`{sup ,} which can be built recurrently starting form the cubic vertex, and we study its symmetries. Our formalism lends itself to a systematic introduction of additional conditions, such as locality, polynomiality, etc. We write down the general form of the solutions exhibiting a scale invariance. The case of a spin 1 field yields, as a unique solution, Yang-Mills theory. In view of quantization, we show that the solution of the classical master equation straightforwardly provides a solution of the (quantum) Batalin-Vilkoviski master equation. One may then obtain a gauge fixed action in the usual way.}
place = {France}
year = {1991}
month = {Oct}
}
title = {Algebraic construction of interacting higher spin field theories; Construction algebrique de theories de champs de spin eleve en interaction}
author = {Fougere, F}
abstractNote = {We develop a general framework which we believe may provide some insights into the structure of interacting `high spin` field theories. A finite or infinite set of classical spin fields is described by means of a field defined on an enlarged spacetime manifold. The free action and its gauge symmetries are gathered into a nilpotent differential operator on this manifold. In particular, the choice of Grassmann-valued extra coordinates leads to theories involving only a finite set of fields, the possible contents (spin multiplicities, degree of reducibility, etc.) of which are classified according to the representations of a unitary algebra. The interacting theory is characterized by a functional of the field on the enlarged manifold. We show that there is among these functionals a natural graded Lie algebra structure allowing one to rewrite the gauge invariance condition of the action in a concise form which is a nonlinear generalization of the nilpotency condition of the free theory. We obtain the general solution of this `classical master equation`{sup ,} which can be built recurrently starting form the cubic vertex, and we study its symmetries. Our formalism lends itself to a systematic introduction of additional conditions, such as locality, polynomiality, etc. We write down the general form of the solutions exhibiting a scale invariance. The case of a spin 1 field yields, as a unique solution, Yang-Mills theory. In view of quantization, we show that the solution of the classical master equation straightforwardly provides a solution of the (quantum) Batalin-Vilkoviski master equation. One may then obtain a gauge fixed action in the usual way.}
place = {France}
year = {1991}
month = {Oct}
}