BPS Monopoles in Moduli Space under SU(2) Gauge Potential

Solving Dirac equation for a BPS monopole moving in the field of another BPS monopole in moduli space, it has been shown that spin momentum of the interacting monopole behaves as an extra energy source. The possibilities of splitting of the energy levels of the system have been explored.     

On the strong and weak effects in the s-wave monopole-fermion interactions

Neglecting the masses of light fermions at small distances and corrections due to higher angular momentum excitations and heavy fermions, we show that strong and weak effects do not forbid the monopole catalysis of proton decay. We develop a simple bag-like model of a proton with a monopole sitting at its center and estimate the proton lifetime. We show that the monopole catalysis is not allowed in a variant of the SU(5) grand unified theory, so this process is not characteristic to all GUTs.     

Some remarks on selfconsistency and core polarization phenomena in nuclei

Isoscalar and isovector monopole polarizability are studied and shown to suggest naturally the idea of operator renormalization. The link with Hartree-Fock selfconsistency is established and an algebraic characterization and extension of the theory proposed.     

On the supersymmetric solitons and monopoles

The basic results in a new trend in supersymmetry and soliton theory are presented. It is shown that the soliton expectation value of the energy operator is the mass of the soliton without quantum corrections. A new supersymmetric monopole model in three dimensions is constructed by generalization of the supersymmetric sine-Gordon model in one space dimension.     

A new model for ideal gases. Decay to the Maxwellian distribution

In this work, a new model in kinetic gas theory for deriving the Maxwellian velocity distribution (MVD) is proposed. We construct an operator that governs the discrete time evolution of the velocity distribution. This operator, which conserves the momentum and the energy of the ideal gas, has the MVD as a fixed point. Moreover, for any initial out-of-equilibrium velocity distribution, it is shown that the gas decays to the equilibrium distribution, that is, to the MVD.     

Spectrum of Schrödinger field in a noncommutative magnetic monopole

The energy spectrum of a nonrelativistic particle on a noncommutative sphere in the presence of a magnetic monopole field is calculated. The system is treated in the field theory language, in which the one-particle sector of a charged Schrödinger field coupled to a noncommutative U(1) gauge field is identified. It is shown that the Hamiltonian is essentially the angular momentum squared of the particle, but with a nontrivial scaling factor appearing, in agreement with the first-quantized canonical treatment of the problem. Monopole quantization is recovered and identified as the quantization of a commutative Seiberg–Witten mapped monopole field.     

Quantum mechanics of space and time

A formulation of relativistic quantum mechanics is presented independent of the theory of Hilbert space and also independent of the hypothesis of spacetime manifold. A hierarchy is established in the nondistributive lattice of physical ensembles, and it is shown that the projections relating different members of the hierarchy form a semigroup. It is shown how to develop a statistical theory based on the definition of a statistical operator. Involutions defined on the matrix representations of the semigroup are interpreted in terms ofCPT conjugations. The theory of particles of spin one-half and systems with higher spin is developed from first principles. Methods are also developed for defining energy, momentum, orbital angular momentum, and weighted spacetime coordinates without reference to a manifold.     

Spin force and torque in non-relativistic Dirac oscillator on a sphere

The spin force operator on a non-relativistic Dirac oscillator (in the non-relativistic limit the Dirac oscillator is a spin one-half 3D harmonic oscillator with strong spin–orbit interaction) is derived using the Heisenberg equations of motion and is seen to be formally similar to the force by the electromagnetic field on a moving charged particle. When confined to a sphere of radius R, it is shown that the Hamiltonian of this non-relativistic oscillator can be expressed as a mere kinetic energy operator with an anomalous part. As a result, the power by the spin force and torque operators in this case are seen to vanish. The spin force operator on the sphere is calculated explicitly and its torque is shown to be equal to the rate of change of the kinetic orbital angular momentum operator, again with an anomalous part. This, along with the conservation of the total angular momentum, suggests that the spin force exerts a spin-dependent torque on the kinetic orbital angular momentum operator in order to conserve total angular momentum. The presence of an anomalous spin part in the kinetic orbital angular momentum operator gives rise to an oscillatory behavior similar to the Zitterbewegung. It is suggested that the underlying physics that gives rise to the spin force and the Zitterbewegung is one and the same in NRDO and in systems that manifest spin Hall effect.     

Charged Particles in Monopole Background on Fuzzy Sphere

In this note we study the quantum mechanics of a charged particle on fuzzy sphere and in the presence of magnetic monopoles. We discuss the proper inclusion of the electromagnetic interaction in the Hamiltonian through the covariant form of the momentum operator. We consider two different kinds of monopoles. The first one is associated with projective modules and obtained from the corresponding projector. The second one we obtain by solving directly the noncommutative Maxwell equations over the fuzzy sphere. Among these, are the monopole connections for which the Hamiltonian operator can be diagonalized in an algebraic way.      

The Quantum Commutator Algebra of a Perfect Fluid

A perfect fluid is quantized by the canonical method. The constraints are found and this allows the Dirac brackets to be calculated. Replacing the Dirac brackets with quantum commutators formally quantizes the system. There is a momentum operator in the denominator of some coordinate quantum commutators. It is shown that it is possible to multiply throughout by this momentum operator. Factor ordering differences can result in a viscosity term. The resulting quantum commutator algebra is unusual.     

The nut solution as a gravitational dyon

Linearized theory suggests that the NUT solution of Einstein's equations corresponds to a source with both mass and dual mass i.e. to a gravitational dyon. This is born out by the striking identity between the Killing operators of the NUT solution and the ‘total angular momentum’ operators of the monopole. On this basis, Misner's periodic time condition is shown to be the analogue of the Dirac quantization, and results from the requirement that the generators integrate to a global Lie group. It is also shown that there are no bound states for a Klein-Gordon field in NUT space provided the field vanishes in the conventional way at the horizon. For this purpose a generalized ‘tortoise coordinate’ is introduced.     

Charge exchange scattering of charged gauge bosons by 't Hooft-Polyakov monopole

We have studied the scattering of a low energy charged gauge boson by a 't Hooft-Polyakov monopole in a spontaneously broken SU(2) gauge theory. It is found that a charge exchange scattering occurs in the sector of zero total angular momentum. The charge exchange scattering has a nonvanishing finite amplitude when the size of the monopole becomes very small. Implications of our results are discussed.     

Wave equation for a magnetic monopole

We show that there is room, in the Dirac equation, for a massless monopole. The basic idea is that the Dirac equation admits a second electromagnetic minimal coupling associated to the chiral gauge , which is only valid for a massless particle, but satisfies all the symmetry laws of a monopole. In the problem of the diffusion on a central electric field, we find the Poincaré integral and the Dirac relationeg/=n/2. The latter is deduced as a consequence of the fact (which is shown in this paper) thateg/c is the projection of the total angular momentum on the symmetry axis of the system formed by the monopole and the electric charge. Another important property is that a monopole and an antimonopole have opposite helicities (as for the neutrino), but do not have opposite charges: this precludes a vacuum magnetic polarization which would be analogous to the electric one, but allows us to imagine an aether made up of monopole-antimonopole pairs. The theory is then generalized on the basis of a nonlinear equation which is the most general invariant equation under the chiral gauge law. This equation admits solutions corresponding to massive monopoles, among which there are bradyons (i.e., ordinary massive particles) and tachyons. This equation is shown to be closely related to previous works initiated by Hermann Weyl, on Dirac's theory in the framework of general relativity. In conclusion, it is suggested that massless monopoles are perhaps excited states of the neutrino and that they may be produced in some weak interactions. Consequences on the solar activity are considered.     

On projection (in)dependence of the dual superconductor mechanism of confinement

We study the temperature dependence of the monopole condensate in different Abelian projections of the SU(2) gauge theory on the lattice. Using the Fröhlich-Marchetti monopole creation operator, we show numerically that the monopole condensate depends on the choice of the Abelian projection.     

On a projection in dependence on monopole condensate in the lattice SU(2) gauge theory

We study the temperature dependence of the monopole condensate in different Abelian projections of the SU(2) lattice gauge theory in the thermodynamic limit. Using the Fröhlich-Marchetti monopole creation operator, we show numerically that the monopole condensate depends strongly on the choice of the Abelian projection. Contrary to the claims in the literature, we observe that, in the Abelian-Polyakov gauge and in the field strength gauge, the monopole condensate does not vanish at the critical temperature in the large-volume limit. Therefore, the monopole condensate in these gauges is not an order parameter of the confinement-deconfinement phase transition.     

Energy Momentum Distributions of Texture and?Monopole Metrics in General Relativity

The aim of this study is to investigate the energy-momentum distributions of texture and monopole topological defects metrics in general relativity (GR). For this aim Einstein, Bergmann-Thomson, Landau-Lifshitz (LL), M?ller and Papapetrou energy-momentum densities have been used in general relativity theory. We obtained that (i) for the texture metric only Einstein and Bergmann-Thomson energy densities give the same results but the others energy and momentum densities do not provide the same results in GR; (ii) for the monopole metric, while Einstein, Bergmann-Thomson and Papapetrou energy and momentum densities are giving the same energy-momentum results, M?ller and Landau-Lifshitz densities do not give the same energy results with the other definitions in GR.     

The physics of vortex superconductivity. II

The effect of charge on a vortex world-sheet is examined. The relationship between world-sheet charge, winding number, and the flow of momentum along the vortex is illuminated. Full solutions for bosonic field and current profiles are obtained numerically. Both the string energy per unit length and tension are calculated. As an application stationary circular string solutions are studied. We find that except possibly for extreme cases rings stabilized by winding number alone do not exist. The role of angular momentum in stabilizing a ring is then discussed, emphasizing its model independent nature, and it is shown that in this case stationary spinning ring solutions, called vortons, are easily found. In a cosmological setting this can lead to a massive overdensity of vortons equivalent to a monopole problem.     

On the algebra of symmetries of Laplace and Dirac operators

We consider a generalization of the classical Laplace operator, which includes the Laplace–Dunkl operator defined in terms of the differential-difference operators associated with finite reflection groups called Dunkl operators. For this Laplace-like operator, we determine a set of symmetries commuting with it, in the form of generalized angular momentum operators, and we present the algebraic relations for the symmetry algebra. In this context, the generalized Dirac operator is then defined as a square root of our Laplace-like operator. We explicitly determine a family of graded operators which commute or anticommute with our Dirac-like operator depending on their degree. The algebra generated by these symmetry operators is shown to be a generalization of the standard angular momentum algebra and the recently defined higher-rank Bannai–Ito algebra.     

电磁学与电动力学中的磁单极-I

本文及后继三篇文章在电磁学和电动力学框架内分别介绍磁单极的若干奇特性质.针对由一个磁单极和一个点电荷构成的体系,首先证明这个体系的电磁场角动量具有极简洁的表达式并讨论可能的电荷量子化,然后显式地演示体系角动量的转化与守恒.     

On the theory of recursion operator

The general structure and properties of recursion operators for Hamiltonian systems with a finite number and with a continuum of degrees of freedom are considered. Weak and strong recursion operators are introduced. The conditions which determine weak and strong recursion operators are found.In the theory of nonlinear waves a method for the calculation of the recursion operator, which is based on the use of expansion into a power series over the fields and the momentum representation, is proposed. Within the framework of this method a recursion operator is easily calculated via the Hamiltonian of a given equation. It is shown that only the one-dimensional nonlinear evolution equations can posses a regular recursion operator. In particular, the Kadomtsev-Petviashvili equation has no regular recursion operator.