On kinematical constraints in Regge calculus

Abstract

In the (3+1)D Hamiltonian Regge calculus (one of the coordinates, t, is continuous) conjugate variables (defined on the triangles of the discrete 3D section ) are finite connections and antisymmetric area bivectors. The latter, however, are not independent, since triangles may have common edges. This circumstance can be taken into account with the help of the set of kinematical bilinear constraints on bivectors (which are required to hold by the definition of a Regge manifold). Some of these contain derivatives with respect to t, so taking them into account with the help of Lagrange multipliers would result in the appearance of extra dynamical variables (namely, the Lagrange multipliers themselves will prove to be conjugate momenta; this circumstance would be especially disturbing in quantum theory, where it would modify the dynamical content of the theory) not having analogues in the continuum theory. It is shown that kinematical constraints with derivatives are consequences of the equations of motion for the Regge action supplemented by the rest of these constraints without derivatives, and can be omitted; so the additional dynamical variables do not appear.