Quantum (Super)Yang-Mills Equations. Global Existence and Mass-Gap.
by
Agostino Prastaro
University of Roma "La Sapienza", Roma - Italy

Quantum (super)Yang-Mills equations are considered in the framework of some noncommutative manifolds (quantum (super)manifolds[1-6]) and for such equations existence theorems of local and global solutions are obtained by using some geometric methods recently introduced by us [2, 4-6]. In particular global properties of solutions are characterized by means of integral bordism groups. A criterion to recognize global solutions with masss-gap is given.
References.
[1] A.Prastaro, (Co)bordisms in PDEs and quantum PDEs, Rep. Math. Phys. 38(3)(1996), 443-455.
[2] A.Prastaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996.
[3] A.Prastaro and Th.M. Rassias, A geometric approach to a noncommutative generalized d'Alembert equation, C. R. Acad. Sci. Paris 330(I)(2000), 545-550.
[4] A.Prastaro, (Co)bordism groups in quantum PDEs, Acta Appl. Math. 64(2000), 111-217.
[5] A.Prastaro, Quantum manifolds and integral (co)bordism groups in quantum partial differential equations, Nonlinear Analysis 47(2001), 2609-2620.
[6] A.Prastaro, (Co)bordism groups in quantum super PDEs, Int. J. Math. Games Th. Algebra, (2003), (to appear).

Date received: February 10, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakr-14.