Spinors, Proper Time and Higher-Spin Fields

TL;DR

This paper develops a Poincare-invariant Lagrangian framework for 4d integer-spin fields using a 5d space with spinor and proper-time coordinates, providing solutions for massless and massive cases.

Contribution

It introduces a novel 5d Lagrangian formulation for integer-spin fields that separates variables and includes explicit solutions for massless and scalar fields.

Findings

Constructed a manifestly Poincare-invariant action.

Derived solutions for massless arbitrary spin fields.

Provided a positive-definite inner product for the theory.

Abstract

We present a Lagrangian formulation for 4d integer-spin relativistic fields in the 5d space spanned by two conjugate Weyl spinors and a Lorentz-invariant proper-time coordinate. We construct a manifestly Poincare-invariant free classical action, find a general solution to equations of motion and a corresponding positive-definite inner product. Our formulation displays a separation of variables: equations of motion represent ODE in a proper time only, while spinor coordinates parameterize the Cauchy hypersurface. We also find momentum eigenstates solutions for massless arbitrary integer-spin fields and a massive scalar field.