Yang-Mills and Dirac fields in a bag, existence and uniqueness theorems

Yang-Mills and Dirac fields in a bag, constraints and reduction

“…The reduced phase space is shown to be the union o} symplectic [1]. The aim of this paper is to study the structureof tHe space of solutions.…”

Yang-Mills and Dirac Fields with Inhomogeneous Boundary Conditions

“…Minimally interaeting Yang-Mills and Dirae filelds with homogeneous bag boundary eonditions have been studied in [1] and [2]. In this p~per we extend the results on the finite time existenee and uniqueness of solutions for inhotnogeneous boundary data.…”

“…The existence and uniqueness result of [2] . This implies that the choice of boundary eonditions (1.17) is eonsistent, provided eondition (1.14) is satisfied.…”

“…In [2] we used the theory of Lipsehitz perturbat1ions of strongly continuous semigroups to obtain the existenee and uniqueness theorems for the evolution equations under the homogeneous boundary eonditions nE=O, nA=O , teurlA=O , rw=o , rDw=o.…”

“…The proof of part b) of Theorem 2, stating that the eonstraint equation is preserved under the classical dynamics is given in [2]. The atgument literally applies to the ease of inhomogeneous boundary eonditions.…”