Gonihedric String Equation

TL;DR

This paper explores the properties and continuum formulation of the gonihedric string, proposing a generalized Dirac equation with infinite-dimensional wave functions to describe its spectrum and string tension.

Contribution

It introduces a novel generalization of the Dirac equation with infinite-dimensional matrices to model the gonihedric string's properties.

Findings

Spectrum includes particles and antiparticles with increasing half-integer spins.

Explicit formulas for mass spectrum enable calculation of string tension.

Demonstrates the string-like nature of the theory.

Abstract

We discuss the basic properties of the gonihedric string and the problem of its formulation in continuum. We propose a generalization of the Dirac equation and of the corresponding gamma matrices in order to describe the gonihedric string. The wave function and the Dirac matrices are infinite-dimensional. The spectrum of the theory consists of particles and antiparticles of increasing half-integer spin lying on quasilinear trajectories of different slope. Explicit formulas for the mass spectrum allow to compute the string tension and thus demonstrate the string character of the theory.