Table of Contents
ISRN High Energy Physics
Volume 2012, Article ID 674985, 25 pages
Research Article

Basics Polyakov’s Quantum Surface Theory on the Formalism of Functional Integrals and Applications

Departamento de Matemática Aplicada, Instituto de Matemática, Universidade Federal Fluminense, Rua Mario Santos Braga, 24220-140 Niterói, RJ, Brazil

Received 28 August 2012; Accepted 1 October 2012

Academic Editors: C. Ahn and M. Alishahiha

Copyright © 2012 Luiz C. L. Botelho. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose an alternative view to the covariant Polyakov’s string path integral. In our new approach we clarified the role of the Liouville model on string theory for Q.C.D. and Dual Models. In the appendices, we present additional material, difficult to find in the specialized path integral literature on the detailed evaluation of the (Q.C.D.) fermion determinant, the path integral proof of the Atiyah-Singer index theorem on Riemannian Manifolds, and the role of the expansion on Polyakov’s String path integral, all containing important new results, insights on theses topics.