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By comparision with numerical results in the maximal Abelian projection of lattice Yang-Mills theory, it is argued that the nonperturbative dynamics of Yang Mills theory can be described by a set of fields that take their values in the coset space SU(2)/U(1). The Yang-Mills connection is parameterized in a special way to separate the dependence on the coset… (More)

As a contribution to the ongoing discussion of trajectories of spinless particles in spaces with torsion we show that the geometry of such spaces can be induced by embedding their curves in a euclidean space without torsion. Technically speaking, we define the tangent (velocity) space of the embedded space imposing non-holonomic constraints upon the tangent… (More)

A novel time domain solver of Maxwell’s equations in passive (dispersive and absorbing) media is proposed. The method is based on the path integral formalism of quantum theory and entails the use of (i) the Hamiltonian formalism and (ii) pseudospectral methods (the fast Fourier transform, in particular) of solving differential equations. In contrast to… (More)

A method of path integral construction without gauge fixing in the holomorphic representation is proposed for finite-dimensional gauge models. This path integral determines a manifestly gauge-invariant kernel of the evolution operator. 1. It is well known that a gauge symmetry leads to constraints on dynamical variables in the theory [1]. Therefore, the… (More)

The physical phase space in gauge systems is studied. Effects caused by a nonEuclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac gauge invariant states is used to derive a necessary modification of the Hamiltonian path integral in gauge theories of the… (More)

To verify the conjecture that Yang-Mills theory in the infrared limit is equivalent to a spin system whose excitations are knot solitons, a numerical algorithm based on the inverse Monte Carlo method is proposed. To investigate the stability of the effective spin field action, numerical studies of the renormalization group flow for the coupling constants… (More)

We develop a mathematically well-defined path integral formalism for general symplectic manifolds. We argue that in order to make a path integral quantization covariant under general coordinate transformations on the phase space and involve a genuine functional measure that is both finite and countably additive, the phase space manifold should be equipped… (More)

We study the problem of the existence of a local quantum scalar field theory in a general affine metric space that in the semiclassical approximation would lead to the autoparallel motion of wave packets, thus providing a deviation of the spinless particle trajectory from the geodesics in the presence of torsion. The problem is shown to be equivalent to the… (More)

A low energy bound in a class of chiral solitonic field theories related the infrared physics of the SU(N) Yang-Mills theory is established. 1. The model. Consider N−1 smooth fields na = na(x) in spacetime taking their values in the Lie algebra of SU(N). The fields are chosen to be commutative [na, nb] = 0 and orthonormal (na, nb) = δab with respect the… (More)

A system with anholonomic constraints where the trajectories of physical degrees of freedom are autoparallels on a manifold equipped with a general Cartan connection is discussed. A variational principle for the autoparallel trajectories is derived from the d’Alambert-Lagrange principle for anholonomic constrained systems. A geometrical… (More)