General Dynamical Equations for Free Particles and?Their Galilean Invariance

Dynamical equations describing evolution of state functions in space-time of a given metric are important components of physical theories of particles. A method based on a group of the metric is used to obtain an infinite set of general dynamical equations for a scalar and analytical function representing free and spinless particles. It is shown that this set of equations is the same for any group of the metric that consists of an invariant Abelian subgroup of translations in time and space. For Galilean space-time, such group is the extended Galilei group. Using this group, it is proved that the infinite set of equations has only one subset of Galilean invariant dynamical equations, and that the equations of this subset are Schr?dinger-like equations.     

The Color Gauge Invariance and a Possible Origin of Mass in QCD

The general scale parameter, having the dimensions of mass squared, is dynamically generated in the QCD gluon sector. It is introduced through the difference between the regularized full gluon self-energy and its value at some finite point. It violates transversality of the full gluon self-energy. The Slavnov-Taylor identity for the full gluon propagator, when it is given by the corresponding equation of motion, is also violated by it. So in order to maintain both transversality and the identity it should be disregarded from the very beginning, i.e., put formally zero everywhere. However, we have shown how to preserve the above-mentioned identity at non-zero mass squared parameter. This allows one to establish the structure of the full gluon propagator when it is explicitly present. Its contribution does not survive in the perturbation theory regime, when the gluon momentum goes to infinity. At the same time, its contribution dominates the structure of the full gluon propagator when the gluon momentum goes to zero. We have also proposed a method how to restore transversality of the relevant gluon propagator in a gauge invariant way, while keeping the mass squared parameter “alive”.     

On the Gauge Invariance of The Transition Probability of A Charged Particle in Electromagnetic Field

This paper suggests a principle to find a unitary operator U which transforms non-hysical quantity,zero-potential Hamiltonian H0,into true physical quantity UH0U for a charged particle in classical electromagnetic field,and puts forward a unified form of constructing gauge-independent transition probabilitites in this case.Different methods correspond to different unitary operators which satisfy the above-mentioned principle.     

Superconformal Invariance and the Geography¶of Four-Manifolds

The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide nontrivial information about four-manifold topology. In particular, in the example of gauge group SU(2) with one doublet hypermultiplet, we derive a theorem relating classical topological invariants such as the Euler character and signature to sum rules for Seiberg–Witten invariants. A short account of this paper can be found in [1]. Received: 19 December 1998 / Accepted: 7 March 1999     

Qweak, N → Δ, and physics beyond the standard model

The data-taking phase of the Qweak experiment ended in May of 2012 at the Thomas Jefferson National Accelerator Facility. Qweak aims to measure the weak charge of the proton, Q _W ^p , via parity-violating elastic electron-proton scattering. The expected value of Q _W ^p is fortuitously suppressed, which leads to an increased sensitivity to physics beyond the Standard Model.     

Lorentz Invariance and Brownian Motion of Test Particles with Constant Classical Velocity in Electromagnetic Vacuum

We show that the velocity and position dispersions of a test particle with a nonzero constant classical velocity undergoing Brownian motion caused by electromagnetic vacuum fluctuations in a space with plane boundaries can be obgained from those of the static case by Lorentz transformation. We explicitly derive the Lorentz transformations relating the dispersions of the two cases and then apply them to the case of the Brownian motion of a test particle with a constant classical velocity parallel to the boundary between two conducting planes. Our results show that the influence of a nonzero initial velocity is negligible for nonrelativistic test particles.     

Magnetic moment of the Δ++ baryon in QCD string approach

The magnetic moment of the Δ⁺⁺ baryon is computed within a new approach based on the QCD string Hamiltonian. The string tension σ is the only dimensionful quantity forming the magnetic moment of both the nucleon and the Δ⁺⁺ baryon; however, color Coulomb and spin-spin interactions cancel each other in the nucleon magnetic moment, while, in Δ⁺⁺, they add up coherently. The result π_Δ++ is in good agreement with experimental data.     

Exact Calculations of Vertex ^-sγb and ,^-sZb in the Unitary Gauge

In this paper, we present the exact calculations for the vertex ^-sγb and ^sZb in the unitary gauge. We find that （a） the divergent- and μ-dependent terms are left in the effective vertex function Г^γμ（p, k） for b → sγ transition even after we sum up the contributions from four related Feynman diagrams; （b） for an on-shell photon, such terms do not contribute et al.; （c） for off-shell photon, these terms will be canceled when the contributions from both vertex ^sγb and ^sZb are taken into account simultaneously, and therefore the finite and gauge-independent function Zo（xt） = Co（xt） ＋ Do（xt）/4, which governs the semi-leptonic decay b → sl^- l^＋, is derived in the unitary gauge.     

Decays of the Higgs Bosons Н, H,A, and H± into a Photon and a Gauge Boson

Russian Physics Journal - Within the framework of the Minimal Supersymmetrtic Standard Model, we have investigated the decay channels of Higgs bosons into a photon and a gauge boson: H(h; A)...     

Calculation of the Förster Resonance Energy Transfer Parameters in Nanospheres Containing CdSe/ZnS Quantum Dots and Diarylethene

Journal of Applied Spectroscopy - An analysis is presented for theoretical model studies of photochromic systems with reversible fluorescence modulation derived from polymer nanospheres containing...     

Form Invariance and Lie Symmetries of the Rotational Relativistic Birkhoff System

For a rotational relativistic Birkhoff system,the relation between the form invariance and the Lie symmetries are given Under infinitesimal transformations of groups.If the infinitesimal transformation generators ξ0 and ξμ satisfy the conditions of the form invariance,and the determining equation of Lie symmetries holds,the form invariance leads to a Lie symmetry of the system.Furthermore,if the infinitesimal transformations generators ξ0 and ξμ satisfy the conditions of the form invariance and the determining equation of Lie symmetry holds,and if there is a gauge function G satisfying the structure equation of Lie symmetry,then the form invariance will lead to the Lie symmetrical conserved quantity of the system.An example is given to illustrate the application of the results.     

Gauge invariance and the virial theorem for the quantized Schrödinger field

A gauge invariant canonical generator for the scale transformation of the quantized Schrödinger field is proposed on the basis of the gauge invariance of the virial theorem.     

Energy-Momentum of a Cosmological Brane Model and the Gauge Hierarchy

We analyze in this paper the general covariant energy-momentum tensor of the gravitational system in general five-dimensional cosmological brane-world models. Then through calculating this energy-momentum for the cosmological generalization of the Randall-Sundrum model, which includes the original RS model as the static limit, we are able to show that the weakness of the gravitation on the “visible” brane is a general feature of this model. This is the origin of the gauge hierarchy from a gravitational point of view. Our results are also consistent with the fact that a gravitational system has vanishing total energy.     

Cartan’s Spiral Staircase in Physics and, in Particular, in the Gauge Theory of Dislocations

In 1922, Cartan introduced in differential geometry, besides the Riemannian curvature, the new concept of torsion. He visualized a homogeneous and isotropic distribution of torsion in three dimensions (3d) by the “helical staircase”, which he constructed by starting from a 3d Euclidean space and by defining a new connection via helical motions. We describe this geometric procedure in detail and define the corresponding connection and the torsion. The interdisciplinary nature of this subject is already evident from Cartan’s discussion, since he argued—but never proved—that the helical staircase should correspond to a continuum with constant pressure and constant internal torque. We discuss where in physics the helical staircase is realized: (i) In the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d theories of gravity, namely (a) in 3d Einstein-Cartan gravity—this is Cartan’s case of constant pressure and constant intrinsic torque—and (b) in 3d Poincaré gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the gauge field theory of dislocations of Lazar et al., as we prove for the first time by arranging a suitable distribution of screw dislocations. Our main emphasis is on the discussion of dislocation field theory.     

The Universal Gerbe,Dixmier–Douady Class,and Gauge Theory

We clarify the relation between the Dixmier–Douady class on the space of self-adjoint Fredholm operators (universal B-field) and the curvature of determinant bundles over infinite-dimensional Grassmannians. In particular, in the case of Dirac type operators on a three dimensional compact manifold we obtain a simple and explicit expression for both forms.     

Resonance structure in the γγ invariant mass spectrum in pC, dC, and dCu interactions

Along with ?? ⁰ and ?? mesons, a resonance structure in the invariant mass spectrum of two photons atM _??? = 360 ± 7 ± 9 MeV is observed in dC interactions at momentum 2.75 GeV/c per nucleon. This resonance structure is not observed in pC collisions at the beam momentum 5.5 GeV/c. The result obtained in the reaction dC is confirmed by the second experiment carried out on the deuteron beam at momentum 3.83 GeV/c per nucleon with a copper target. Some other checks of the observed effect are presented.