Bound states of the vector field with a vortex in the Abelian Higgs model

It is pointed out that the vector particle of the 3+1 dimensional Abelian Riggs model can form bound states with a vortex. The modes of the vector field bound by the vortex are effectively represented by a two-dimensional Proca field living on the vortex. We also notice that a heavy-string limit of the vortex yields a bosonic string with internal degrees of freedom given by the two-dimensional Proca field

On perturbative solution of classical Yang-Mills equations with external charges

The method of solving of classical Yang-Mills equations with external charges by means of the perturbative expansion in powers of the external charge $\hat{\varrho}$($\vec{x}$) is considered in the $\hat{A}_{o}$ = 0 gauge. The gauge potentials are calculated in the first three orders for generic $\hat{\varrho}$. It is observed that in general the external color charge generates color magnetic field of the monopole type (i.e., behaving like $r^{-2}$ for r $\to \infty$) in the second order, and that in the third order the color electric field behaves like $r^{-1}$ for r $\to \infty$). This gives infinite energy of such a color charge and motivates an argument that nonvanishing total color charge density (resultant for all kinds of colored quarks) can not be produced in any real expirement

External charges in SU(2) Gauge theory and topology

We observe that the external charges in SU(2) gauge theory can be classified accordingly to their Hopf index. The relationship of this topological classification and the winding number classification of gauge transformations is indicated. The Coulomb solution of the Yang–Mills equations with external charges is obtained with the aid of the gauge transformations characterised by a nonzero winding number

On gauge invariant external sources in Yang-Mills theory

We analyse classical gauge potentials generated by static external sources coupled to gauge invariant, nonlocal operators. For the gauge invariant operators involving fermions we find two sharply distinct cases. In the first one, the external source decouples from Yang–Mills equations what leads to zero gauge potentials. The other one is found to be inconsistent with classical Yang–Mills equations. We consider also nonlocal, gauge invariant operators without fermions. We argue that there exists a possibility that the corresponding classical gauge field configuration is that of the closed magnetic flux tube with quantized energy

Motion of a wave packet in an external Yang-Mills field

Two further examples of motion of a wave packet in external Yang–Mills fields are investigated. We find that because of the interaction with the gauge field the wave packet splits into a number of parts which remain spatially separated in the ħ $\to$ 0 limit. Therefore, these examples confirm our point of view that quantum mechanics of colored particles does not have simple classical limit

Modification of the perturbative QCD towards confinement

Modification of the low momentum behaviour of the perturbative SU(2) gauge theory is proposed. The modification is closely related (although not equivalent) to a nonstandard choice of boundary condition for the Euclidean 2-point gluonic Green function. In the resulting theory already single graphs lead to the confining potential between heavy, static quarks, V(r) = ar$^{2}$ for r $\to \infty

On classical chromodynamics of external charges and fields

Classical mechanics of colored particles in external, classical Yang–Mills fields is discussed from quantum-mechanical point of view. Theory of classical Yang–Mills fields in the presence of external sources is presented

Relativistic quantum mechanics of the Majorana particle

This article is a pedagogical introduction to relativistic quantum mechanics of the free Majorana particle. This relatively simple theory differs from the well-known quantum mechanics of the Dirac particle in several important aspects. First, we present its three equivalent formulations. Next, a so-called axial momentum observable is introduced, and the general solution of the Dirac equation is discussed in terms of eigenfunctions of that operator. We also present pertinent irreducible representations of the Poincaré group. Finally, we show that in the case of massless Majorana particle, the quantum mechanics can be reformulated as a spinorial gauge theory

A new interpretation of fields on MxSU(2)

It is shown that free fields on some manifolds larger than the Minkowski space M(M $\times$ SU(2), M $\times$ SU(2) $\times$ SU(2)) can be regarded as fields describing a composite system of two or three point particles

Limitation of the concept of the clasical colored particle

We argue that a clot of color charged matter placed in an external nonabelian gauge field will not, in general, propagate in any definite direction. Instead, it will tend to disperse all over the space. We also prove that if the position $\vec{x}$(t) and the color, spin vector $\vec{I}$(t) of the classical colored particle are identified with the expectation values of the corresponding quantum operators in the state representing a wave packet, then the classical Wong’s equations give wrong values of $\vec{I}$(t) for large time t