Abstract
We formulate the conditions for the generalized fields in the space with additional commuting Weyl spinor coordinates which define the infinite half-integer spin representation of the four-dimensional Poincaré group. Using this formulation we develop the BRST approach and derive the Lagrangian for the half-integer infinite spin fields.
Highlights
Various aspects of massless infinite spin irreducible representations of the Poincare group [1,2,3] attract much attention last time
Many of interesting points related to the Lagrangian formulation for massless infinite spin fields still deserve further study
In the recent paper [27] the BRST construction was used to derive the Lagrangian for the infinite integer spin fields (1.1) with additional spinorial coordinate. This approach is some generalization of the BRST construction which was used for finding the Lagrangians of the free fields of different types in flat and AdS spaces
Summary
Various aspects of massless infinite spin irreducible representations of the Poincare group [1,2,3] attract much attention last time (see, e.g., [4]– [38]). Which depends on the space-time coordinates xm and additional commuting Weyl spinor ξα, ξα = (ξα)∗ The conditions that such field describes the infinite spin representation are written in the form. In the recent paper [27] the BRST construction was used to derive the Lagrangian for the infinite integer spin fields (1.1) with additional spinorial coordinate This approach is some generalization of the BRST construction which was used for finding the Lagrangians of the free fields of different types in flat and AdS spaces We construct the Hermitian BRST charge and the corresponding equation of motion which reproduce the conditions for the component fields Taking into account this BRST charge, we derive the space-time Lagrangian for fermionic infinite spin field. Appendix C is devoted to construction of the solution to the equations (1.9) on the base of the twistor formalism and description of the irreducible representation of the infinite half-integer spin filed
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