Fractional Bosonic Strings

TL;DR

This paper introduces a fractional calculus extension of bosonic string theory, modifying the Polyakov action, deriving equations of motion, analyzing symmetries, and establishing a Hamiltonian framework with a fractional light-cone gauge.

Contribution

It presents the first fractional generalization of bosonic string theory, extending classical actions and equations to fractional calculus, and explores the resulting symmetries and Hamiltonian structure.

Findings

Derived fractional equations of motion for the string

Analyzed symmetries and gauge fixing in the fractional framework

Established a Hamiltonian formulation with fractional light-cone gauge

Abstract

The aim of this paper is to present a simple generalization of bosonic string theory in the framework of the theory of fractional variational problems. Specifically, we present a fractional extension of the Polyakov action, for which we compute the general form of the equations of motion and discuss the connection between the new fractional action and a generalization the Nambu-Goto action. Consequently, we analyse the symmetries of the modified Polyakov action and try to fix the gauge, following the classical procedures. Then we solve the equations of motion in a simplified setting. Finally, we present an Hamiltonian description of the classical fractional bosonic string and introduce the fractional light-cone gauge. It is important to remark that, throughout the whole paper, we thoroughly discuss how to recover the known results as an "integer" limit of the presented model.