Topologically massive Yang-Mills: A Hamilton-Jacobi constraint analysis

Abstract

We analyse the constraint structure of the topologically massive Yang-Mills theory in instant-form and null-plane dynamics via the Hamilton-Jacobi formalism. The complete set of hamiltonians that generates the dynamics of the system is obtained from the Frobenius' integrability conditions, as well as its characteristic equations. As generators of canonical transformations, the hamiltonians are naturally linked to the generator of Lagrangian gauge transformations. C 2014 AIP Publishing LLC.

Involutive constrained systems and Hamilton-Jacobi formalism

“…The functions H ′ α are the very generators of the dynamical evolution (14), acting as hamiltonian functions. Therefore, the HJ formalism describes singular systems as several independent variables systems.…”

“…Lagrangian and hamiltonian dynamics find place as direct mathematical consequences of the HJ theory. With the suggestive name of "the complete figure" of the variational calculus, the HJ formalism was extended to treat singular systems by Güler [9], followed by generalizations for higher order derivative lagrangians [10], Berezin systems [11], linear actions [12] and applications, specially in the gravitational field [13] and topologically massive theories [14]. In the HJ formalism, canonical constraints form a set of PDEs of the first-order, and the dynamical evolution is generated by a complete set of independent hamiltonian functions, resulting in a system with several independent variables.…”

Polysymplectic formulation for topologically massive Yang–Mills field theory

“…where the δ stands for the identity for the generators of the internal group, and by considering relation (18), π…”

“…Based on the two previous examples, we will consider now the Lagrangian for the three dimensional topologically massive Yang-Mills field theory given by [18]…”

“…At the classical level, equations of motion for the topologically massive Yang-Mills theory has been studied from different perspectives, including the standard Dirac-Hamiltonian [17] and the Hamilton-Jacobi [18] approaches. In this article we analyze this topologically massive theory from the modern viewpoint of the polysymplectic framework for field theories (see [19,20,21,22,23,24,25] for generalities and the geometric description, and [24,26,27,28] for some specific examples).…”