We introduce a method that generates invariant functions from perturbative classical field theories depending on external parameters. Applying our methods to several field theories such as abelian BF , Chern-Simons and 2-dimensional Yang-Mills theory, we obtain, respectively, the linking number for embedded submanifolds in compact varieties, the Gauss’ and the second Milnor’s invariant for link...

A manifestly gauge-invariant hamiltonian formulation [1] of classical electrodynamics has been shown to be relativistic invariant by the construction of the generators of the Poincare Lie algebra. The original formulation in terms of reduced distribution functions for the particles is applied here to the case of two charges interacting through the classical electrodynamical field. A reduced des...

A new non-perturbative approach to quantum field theory is proposed. Instead of performing a path integral over configurations of classical fields, D-theory works with discrete quantized variables. Classical spin fields are replaced by quantum spins, and classical gauge fields are replaced by quantum links. The classical fields of a d-dimensional quantum field theory reappear as low-energy effe...

It is known that classical electromagnetic radiation at a frequency in resonance with energy splittings of atoms in a dielectric medium can be described using the classical sine-Gordon theory. In this paper we quantize the electromagnetic field and compute quantum corrections to the classical results by using known results from the sine-Gordon quantum field theory.

In this paper, transfinite element method is used to analyze the two dimensional thermoelasticity problems. A comparison is made between the thermoelastic analysis results of the classical theory and theories with one or two relaxation times (i.e. L-S and G-L theories), for the half space problem. Governing equations are transformed to Laplace domain and then, node variables are calculated by t...

A new non-perturbative approach to quantum field theory is proposed. Instead of performing a path integral over configurations of classical fields, D-theory works with discrete quantized variables. Classical spin fields are replaced by quantum spins, and classical gauge fields are replaced by quantum links. The classical fields of a d-dimensional quantum field theory reappear as low-energy effe...

The spherically and cylindrically symmetric solutions of the SU (3) Yang-Mills theory are obtained. The corresponding gauge potential has the confining properties. It is supposed that: a) the spherically symmetric solution is a field distribution of the classical " quark " and in this sense it is similar to the Coulomb potential; b) the cylindrically symmetric solution describes a classical fie...