Related papers: Functional Approach to Classical Yang-Mills Theori…
We find an explicit form for the Jacobian of arbitrary field-dependent BRST transformations in Yang-Mills theory. For the functional-integral representation of the (gauge-fixed) Yang-Mills vacuum functional, such transformations merely…
A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang-Mills continuum theories with gauge groups $SU(N)$ and $U(1)$ and space-time topologies $\Rl^1\times\Rl^1$ and $\Rl^1\times S^1$. (For the $U(1)$ theory,…
We revisit the dynamical action, developed in earlier studies [1-3], of the gravitational analog of Yang-Mills field, called the diffeomorphism field. We show an inconsistency in the construction of this action and solve it by a…
We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this…
We review the modern classical electrodynamics problems and present the related main fundamental principles characterizing the electrodynamical vacuum-field structure. We analyze the models of the vacuum field medium and charged point…
The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is the first step towards this goal. This…
We explore the relationship between the quantum effective action and the ground state (and excited state) wave functions of a field theory. Applied to the Yang-Mills theory in 2+1 dimensions, we find the leading terms of the effective…
We review a method, suggested many years ago, to numerically measure the relative amplitudes of the true Yang-Mills vacuum wavefunctional in a finite set of lattice-regulated field configurations. The technique is applied in 2+1 dimensions…
We introduce a framework for degenerate classical field theories in the BV formalism, which allows us to discuss many interesting examples of theories which do not admit a Lagrangian description. Further, we study phase spaces and boundary…
We show that every operator in $L^{2}$ has an associated measure on a space of functions and prove that it can be used to find solutions to abstract Cauchy problems, including partial differential equations. We find explicit formulas to…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
A geometrization of the Yang-Mills field, by which an SU(2) gauge theory becomes equivalent to a 3-space geometry - or optical system - is examined. In a first step, ambient space remains Euclidean and current problems on flat space can be…
In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. (The theory is constructive in that, operators acting at different times, actually commute.) We first develop an operator version of the…
A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions,…
Using Hamilton-Jacobi formalism we investigated the massive Yang-Mills theory on both extended and reduced phase-space. The integrability conditions were discussed and the actions were calculated.
We continue ongoing research work on applying the homological algebraic conceptual and technical machinery of Abstract Differential Geometry towards formulating a finitary, causal and quantal version of vacuum Einstein Lorentzian gravity…
Lagrangian of a classical conformal Yang-Mills field in the flat space of even dimension greater than or equal to six involves higher derivatives. We study Lagrangian formulation of the classical conformal Yang-Mills field by using…
We consider the path integral associated to the Moyal formalism for quantum mechanics extended to contain higher differential forms by means of Grassmann odd fields. After revisiting some properties of the functional integral associated to…
This paper consider the functional mechanics as one of modern approaches to a problem of the correspondence between classical mechanics and the statistical physics. Deviations from classical trajectories are calculated and evolution of the…
A gauge-invariant saddle point expansion for the Yang-Mills vacuum transition amplitude on the basis of the squeezed approximation to the vacuum wave functional is outlined. This framework allows the identification of gauge-invariant…