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 analyze 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 a 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.
Fractional bosonic strings / Diaz, Victor Alfonzo; Giusti, Andrea. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 59:3(2018), pp. 033509.1-033509.13. [10.1063/1.5021776]
Fractional bosonic strings
Diaz, Victor Alfonzo;Giusti, Andrea
2018
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 analyze 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 a 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.