Gauge invariant gluon spin operator for spinless nonlinear wave solutions

We consider nonlinear wave type solutions with intrinsic mass scale parameter and zero spin in a pure SU(2) quantum chromodynamics (QCD). A new stationary solution which can be treated as a system of static Wu–Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered nonlinear wave type solutions have common features: presence of the mass scale parameter, nonvanishing projection of the color fields along the propagation direction and zero spin. The last property requires revision of the gauge invariant definition of the spin density operator which is supposed to produce spin one states for the massless vector gluon field. We construct a gauge invariant definition of the classical gluon spin density operator which is unique and Lorentz frame independent.

On finite energy monopole solutions in Weinberg–Salam model

We study the problem of existence of finite energy monopole solutions in the Weinberg–Salam model starting with the most general ansatz for static axially-symmetric electroweak magnetic fields. The ansatz includes an explicit construction of field configurations with various topologies described by the monopole and Hopf charges. We introduce a unique [Formula: see text] gauge invariant definition for the electromagnetic field. It has been proved that the magnetic charge of any finite energy monopole solution must be screened at far distance. This implies nonexistence of finite energy monopole solutions with a nonzero total magnetic charge. In the case of a special axially-symmetric Dashen–Hasslacher–Neveu ansatz, we revise the structure of the sphaleron solution and show that sphaleron represents a nontrivial system of monopole and antimonopole with their centers located in one point. This is different from the known interpretation of the sphaleron as a monopole–antimonopole pair like Nambu’s “dumb-bell.” In general, the axially-symmetric magnetic field may admit a helical structure. We conjecture that such a solution exists and estimate an upper bound for its energy, [Formula: see text].

The Interior Euler-Lagrange Operator in Field Theory

The paper is devoted to the interior Euler-Lagrange operator in field theory, representing an important tool for constructing the variational sequence. We give a new invariant definition of this operator by means of a natural decomposition of spaces of differential forms, appearing in the sequence, which defines its basic properties. Our definition extends the well-known cases of the Euler-Lagrange class (Euler-Lagrange form) and the Helmholtz class (Helmholtz form). This linear operator has the property of a projector, and its kernel consists of contact forms. The result generalizes an analogous theorem valid for variational sequences over 1-dimensional manifolds and completes the known heuristic expressions by explicit characterizations and proofs.

Professions as Science-Based Occupations

How professions should be defined and separated from other occupations has constituted an enduring theoretical and empirical problem in studies of the professions. In this article, the definitions of the so-called list approaches, involving enumerations of social attributes, are scrutinized. Weak-nesses are highlighted and analysed. It is argued that an alternative approach to the issue of definition, commencing from the epistemic or cognitive dimensions of professions, may be more fruitful. One such possibility is presented by setting out from realist philosophy of science. The links between science and profession are explored by addressing, primarily, the relation between the concepts of mechanism and intervention. A new, ‘invariant’ definition is proposed. In conclusion, a few consequences for future empirical studies of the professions are outlined.

A Recursive Fuzzy System for Efficient Digital Image Stabilization

A novel digital image stabilization technique is proposed in this paper. It is based on a fuzzy Kalman compensation of the global motion vector (GMV), which is estimated in the log-polar plane. The GMV is extracted using four local motion vectors (LMVs) computed on respective subimages in the logpolar plane. The fuzzy Kalman system consists of a fuzzy system with the Kalman filter's discrete time-invariant definition. Due to this inherited recursiveness, the output results into smoothed image sequences. The proposed stabilization system aims to compensate any oscillations of the frame absolute positions, based on the motion estimation in the log-polar domain, filtered by the fuzzy Kalman system, and thus the advantages of both the fuzzy Kalman system and the log-polar transformation are exploited. The described technique produces optimal results in terms of the output quality and the level of compensation.

INVARIANT DEFINITION OF REST MASS AND DYNAMICS OF PARTICLES IN 4D FROM BULK GEODESICS IN BRANE-WORLD AND NON-COMPACT KALUZA–KLEIN THEORIES

In the Randall–Sundrum brane-world scenario and other non-compact Kaluza–Klein theories, the motion of test particles is higher-dimensional in nature. In other words, all test particles travel on five-dimensional geodesics but observers, who are bounded to spacetime, have access only to the 4D part of the trajectory. Conventionally, the dynamics of test particles as observed in 4D is discussed on the basis of the splitting of the geodesic equation in 5D. However, this procedure is not unique and therefore leads to some problems. The most serious one is the ambiguity in the definition of rest mass in 4D, which is crucial for the discussion of the dynamics. We propose the Hamilton–Jacobi formalism, instead of the geodesic one, to study the dynamics in 4D. On the basis of this formalism we provide an unambiguous expression for the rest mass and its variation along the motion as observed in 4D. It is independent of the coordinates and any parameterization used along the motion. Moreover, we are able to show a comprehensive picture of the various physical scenarios allowed in 4D, without having to deal with the subtle details of the splitting formalism. Moreover we study the extra non-gravitational forces perceived by an observer in 4D who describes the geodesic motion of a bulk test particle in 5D. Firstly, we show that the so-called fifth force fails to account for the variation of rest mass along the particle's worldline. Secondly, we offer here a new definition that correctly takes into account the change of mass observed in 4D.

Reply by the authors to F. J. Esparza and E. Gómez‐Treviño

Despite the time that has passed since the original short discussion, I think some useful points can be made regarding the note by Esparza and Gómez‐Treviño. First, the authors are quite correct to point out that (3) of their note is not a rotation invariant definition of phase as was claimed in the original discussion. This slip most likely carried into later texts unchallenged. The fact is, however, that (3) is rotation invariant for a 2‐D earth. It was in this context that the change was made to the definition in Vozoff (1971).