Nonrelativistic fermionic energy gap in the nonabelian gauge systems

We demonstrate that the nonrelativistic fermions open the energy gap when the SU([Formula: see text]) gauge bosons, mediating the interaction between fermions, acquire the mass. Surprisingly, even though there is the SU([Formula: see text]) gauge symmetry, there is always one fermionic energy gap which is not degenerate to the rest of the [Formula: see text] fermions for [Formula: see text] in the fundamental representation.

Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket

We introduce the concept of a variational tricomplex, which is applicable both to variational and nonvariational gauge systems. Assigning this tricomplex with an appropriate symplectic structure and a Cauchy foliation, we establish a general correspondence between the Lagrangian and Hamiltonian pictures of one and the same (not necessarily variational) dynamics. In practical terms, this correspondence allows one to construct the generating functional of a weak Poisson structure starting from that of a Lagrange structure. As a byproduct, a covariant procedure is proposed for deriving the classical BRST charge of the BFV formalism by a given BV master action. The general approach is illustrated by the examples of Maxwell’s electrodynamics and chiral bosons in two dimensions.