2017/10/31 by Victor Alfonzo Diaz, Andrea Giusti
Mathematics · Physics and Astronomy · #Action (physics) #Black Holes and Theoretical Physics #Bosonic string theory #Connection (principal bundle) #Equations of motion #Fractional Differential Equations Solutions #Fractional calculus #Generalization #Hamiltonian (control theory) #Homogeneous space #Pulsars and Gravitational Waves Research #hep-th #math-ph #math.MP #msc:26A33 #msc:81T30
paper · pdf · doi:10.1063/1.5021776
published as J. Math. Phys. 59, 033509 (2018) · 21 pages, no figures
openalex created_date 2017/11/10 · openalex publication_date 2018/03/01 · arxiv created 2018/03/22 · arxiv updated 2018/03/26 · openalex updated_date 2026/08/05
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.