Necessity of Integral Formalism

Thermofield Dynamics and Path-Integral Formalism

Thermofield Dynamics (TFD), a real time formalism for thermal quantum field theory, is formulated in terms of a path-integral approach following the Weinberg procedure. In order to assure precise rules for the development, we use a representation of Lie-algebras such that the TFD algebraic ingredients are derived, including the tilde conjugation rules. The association with the canonical formali...

Parton Degrees of Freedom from the Path-Integral Formalism

We formulate the hadronic tensor Wμν of deep inelastic scattering in the path-integral formalism. It is found that there are 3 gauge invariant and topologically distinct contributions which correspond to the valence, cloud and sea partons. The phenomenological consequences of this classification in terms of the small x behavior, Gottfried sum rule violation, and evolution are emphasized. The op...

Predator-prey quasicycles from a path-integral formalism.

The existence of beyond mean-field quasicycle oscillations in a simple spatial model of predator-prey interactions is derived from a path-integral formalism. The results agree substantially with those obtained from analysis of similar models using system size expansions of the master equation. In all of these analyses, the discrete nature of predator-prey populations and finite-size effects lea...

A boundary integral formalism for stochastic ray tracing in billiards.

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to ...

Dynamic Programming and a New Formalism in the Theory of Integral Equations.