An Abstract Interface to Higher Spin Gauge Field Theory

Abstract

A comprehensive approach to the theory of higher spin gauge fields is proposed. By explicitly separating out details of implementation from general principles, it becomes possible to focus on the bare minimum of requirements that such a theory must satisfy. The abstraction is based on a survey of the progress that has been achieved since relativistic wave equations for higher spin fields were first considered in the nineteen thirties. As a byproduct, a formalism is obtained that is abstract enough to describe a wide class of classical field theories. The formalism, viewed as syntax, can then be semantically mapped to a category of homotopy Lie algebras, thus showing that the theory in some sense exists, at least as an abstract mathematical structure. Still, a concrete physics-like, implementation remains to be constructed. Lacking deep physical insight into the problem, an implementation in terms of generalized vertex operators is set up within which a brute force iterative determination of the first few orders in the interaction can be attempted.

40 pages, typos corrected, references added, subsection added, sections renamed

References in corpus (4)

• Self-Interaction and Gauge Invariance
• Higher Spin Gauge Theories in Various Dimensions
• On the Tensionless Limit of Bosonic Strings, Infinite Symmetries and Higher Spins
• Higher Spin Gauge Theories in Any Dimension

Cited by in corpus (11)

• Gauge invariant Lagrangian construction for massive bosonic higher spin fields in D dimentions
• Parent field theory and unfolding in BRST first-quantized terms
• Quartet unconstrained formulation for massless higher spin fields
• Chiral Higher Spin Theories and Self-Duality
• Investigations into Light-front Quartic Interactions for Massless Fields (I): Non-constructibility of Higher Spin Quartic Amplitudes
• Structure of Higher Spin Gauge Interactions
• A Riccati type PDE for light-front higher helicity vertices
• A local action for fermionic unconstrained higher spin gauge fields in (A)dS space
• Factorization of cubic vertices involving three different higher spin fields
• Mechanical Models for Higher Spin Gauge Fields
• Fermi-Bose cubic couplings in light-cone field theories