Gonihedric String Equation II

TL;DR

This paper proposes a generalized Dirac form for the gonihedric string equation, deriving a new equation with symmetric solutions, non-Jacobian form, and explicit mass spectrum formulas indicating nonzero string tension.

Contribution

Introduces a novel generalized Dirac equation for gonihedric strings with symmetric solutions and non-Jacobian form, expanding theoretical understanding of string equations.

Findings

Derived explicit mass spectrum formulas with nonzero string tension.

Found a new symmetric solution to Majorana commutation relations.

Discussed dual transformations of the Dirac equation and its generalizations.

Abstract

Arguing that the equation for the gonihedric string should have a generalized Dirac form, we found a new equation which corresponds to a symmetric solution of the Majorana commutation relations and has non-Jacobian form. The corresponding generalized gamma-matrices are anticommuting. Explicit formulas for the mass spectrum lead to nonzero string tension $M^{2}_{j} \geq M^{2}(j+1)^{2}$. We discuss also new dual transformation of the Dirac equation and of the proposed generalizations.