Universal Formalism Research Articles

Generalized lagrangian equations of nonlliner reaction—diffusion

The principle of virtual dissipation for irreversible processes in open systems given a new formulation where variations are unconstrained everywhere including the boundary. As a complementary development a new chemical thermodynamics of open systems initiated earlier is given a simplified derivation and new results are presented. A new evaluation of entropy production for fully nonlinear reaction-diffusion along with the variational principle provide field and lagrangian equations of evolution far from local equilibrium with inertia and gravity forces. The earlier inconvenient use of the entropy produced as an auxillary state variable is eliminated. It is shown that the description by lagrangian equations is complete and rigorous and constitutes a universal formalism derived from first principles. It does not require prior knowledge of coitinuum field equations and leads directly to a large variety of finite element methods. Applications to internal relaxation with quantum kinetics are also indicated.

Canonical expansions of commutators and field products on the cone and at short distances in the universal algebra formalism

The algebraic structure of canonical Wilson expansions is investigated by the mathematical formalism of universal algebras, which enables one to investigate the structure of multiplication operations for quantum fields. In other approaches these operations are regarded as primary structureless concepts. It is shown that if the existence of equal-time commutators is assumed one can express the operation of multiplication of two fields in terms of singular factors that are not multiplications and in terms of two independent, in general, nonassoeiative nonsingular multiplication operations. The method can be directly generalized to the case of singularities that are not compatible with the existence of equal-time commutators.