Energy and Magnetic Moment of a Quantum Charged Particle in Time-Dependent Magnetic and Electric Fields of Circular and Plane Solenoids

We consider a quantum spinless nonrelativistic charged particle moving in the xy plane under the action of a time-dependent magnetic field, described by means of the linear vector potential A=B(t)−y(1+α),x(1−α)/2, with two fixed values of the gauge parameter α: α=0 (the circular gauge) and α=1 (the Landau gauge). While the magnetic field is the same in all the cases, the systems with different values of the gauge parameter are not equivalent for nonstationary magnetic fields due to different structures of induced electric fields, whose lines of force are circles for α=0 and straight lines for α=1. We derive general formulas for the time-dependent mean values of the energy and magnetic moment, as well as for their variances, for an arbitrary function B(t). They are expressed in terms of solutions to the classical equation of motion ε¨+ωα2(t)ε=0, with ω1=2ω0. Explicit results are found in the cases of the sudden jump of magnetic field, the parametric resonance, the adiabatic evolution, and for several specific functions B(t), when solutions can be expressed in terms of elementary or hypergeometric functions. These examples show that the evolution of the mentioned mean values can be rather different for the two gauges, if the evolution is not adiabatic. It appears that the adiabatic approximation fails when the magnetic field goes to zero. Moreover, the sudden jump approximation can fail in this case as well. The case of a slowly varying field changing its sign seems especially interesting. In all the cases, fluctuations of the magnetic moment are very strong, frequently exceeding the square of the mean value.

Quadratic gravity and restricted Weyl symmetry

In this paper, we investigate the relationship between quadratic gravity and a restricted Weyl symmetry where a gauge parameter [Formula: see text] of Weyl transformation satisfies a constraint [Formula: see text] in a curved spacetime. First, we briefly review a model with a restricted gauge symmetry on the basis of QED, where a [Formula: see text] gauge parameter [Formula: see text] obeys a similar constraint [Formula: see text] in a flat Minkowski spacetime, and explain that the restricted gauge symmetry removes one on-shell mode of gauge field, which together with the Feynman gauge leaves only two transverse polarizations as physical states. Next, it is shown that the restricted Weyl symmetry also eliminates one component of a dipole field in quadratic gravity around a flat Minkowski background, leaving only a single scalar state. Finally, we show that the restricted Weyl symmetry cannot remove any dynamical degrees of freedom in static background metrics by using the zero-energy theorem of quadratic gravity. This fact also holds for the Euclidean background metrics without imposing the static condition.

Track gauge monitoring scope optimization on small urban railway systems

Urban transport plays a key role in the sustainable development of large cities. Urban railway systems, as eco-friendly mass transport systems, are becoming the basis of urban traffic development. Maintaining a high-quality service with continuously increasing traffic demand places an additional burden on public transport operators. Track geometry control has a major impact on availability and maintenance costs of public transport. Good management of rail infrastructure involves continuous monitoring of track geometry (track gauge, cant, twist, horizontal and vertical irregularities) where surveying should be done up to several times a year. Measuring of track geometry in chosen track cross-sections can be done automatically with relatively expensive equipment, or manually which is cheaper but takes longer. Therefore, the question arose as to whether it is possible on small urban railway networks to reduce monitoring scope by increasing of sampling distance, and if so, what should be recommended sampling distance. This paper presents, on the example of the City of Osijek tramway system, how changes in sampling distance effects on track gauge parameter. The results of the conducted analyses are presented and discussed. The recommendations on track gauge monitoring scope optimization on small urban networks are made.

Renormalization and mixing of the Gluino-Glue operator on the lattice

We study the mixing of the Gluino-Glue operator in $$\mathcal{N}=1$$ N = 1 Supersymmetric Yang–Mills theory (SYM), both in dimensional regularization and on the lattice. We calculate its renormalization, which is not merely multiplicative, due to the fact that this operator can mix with non-gauge invariant operators of equal or, on the lattice, lower dimension. These operators carry the same quantum numbers under Lorentz transformations and global gauge transformations, and they have the same ghost number. We compute the one-loop quantum correction for the relevant two-point and three-point Green’s functions of the Gluino-Glue operator. This allows us to determine renormalization factors of the operator in the $${\overline{\mathrm{MS}}}$$ MS ¯ scheme, as well as the mixing coefficients for the other operators. To this end our computations are performed using dimensional and lattice regularizations. We employ a standard discretization where gluinos are defined on lattice sites and gluons reside on the links of the lattice; the discretization is based on Wilson’s formulation of non-supersymmetric gauge theories with clover improvement. The number of colors, $$N_c$$ N c , the gauge parameter, $$\beta $$ β , and the clover coefficient, $$c_{\mathrm{SW}}$$ c SW , are left as free parameters.

Spectral properties of local gauge invariant composite operators in the SU(2) Yang–Mills–Higgs model

The spectral properties of a set of local gauge (BRST) invariant composite operators are investigated in the SU(2) Yang–Mills–Higgs model with a single Higgs field in the fundamental representation, quantized in the ’t Hooft $$R_{\xi }$$ R ξ -gauge. These operators can be thought of as a BRST invariant version of the elementary fields of the theory, the Higgs and gauge fields, with which they share a gauge independent pole mass. The two-point correlation functions of both BRST invariant composite operators and elementary fields, as well as their spectral functions, are investigated at one-loop order. It is shown that the spectral functions of the elementary fields suffer from a strong unphysical dependence from the gauge parameter $$\xi $$ ξ , and can even exhibit positivity violating behaviour. In contrast, the BRST invariant local operators exhibit a well defined positive spectral density.

Precise calculation of the decay rate of false vacuum with multi-field bounce

We study the decay rate of a false vacuum in gauge theory at the one-loop level. We pay particular attention to the case where the bounce consists of an arbitrary number of scalar fields. With a multi-field bounce, which has a curved trajectory in the field space, the mixing among the gauge fields and the scalar fields evolves along the path of the bounce in the field space and the one-loop calculation of the vacuum decay rate becomes complicated. We consider the one-loop contribution to the decay rate with an arbitrary choice of the gauge parameter, and obtain a gauge invariant expression of the vacuum decay rate. We also give proper treatments of gauge zero modes and renormalization.

Six-dimensional ultraviolet completion of the ℂℙ(N) σ model at two loops

We extend the recent one-loop analysis of the ultraviolet completion of the [Formula: see text] nonlinear [Formula: see text] model in six dimensions to two-loop order in the [Formula: see text] scheme for an arbitrary covariant gauge. In particular we compute the anomalous dimensions of the fields and [Formula: see text]-functions of the four coupling constants. We note that like Quantum Electrodynamics (QED) in four dimensions the matter field anomalous dimension only depends on the gauge parameter at one loop. As a nontrivial check we verify that the critical exponents derived from these renormalization group functions at the Wilson–Fisher fixed point are consistent with the [Formula: see text] expansion of the respective large [Formula: see text] exponents of the underlying universal theory. Using the Ward–Takahashi identity we deduce the three-loop [Formula: see text] renormalization group functions for the six-dimensional ultraviolet completeness of scalar QED.

Full . Full O(α) electroweak radiative corrections to e^+ e^-→ZH with beam polarizations at the ILCO(α) electroweak radiative corrections to e^+ e^-→ZH with beam polarizations at the ILC

We present full electroweak radiative corrections to with the initial beam polarizations at the International Linear Collider (ILC). The calculation is checked numerically by using three consistency tests that are ultraviolet finiteness, infrared finiteness, and gauge parameter independence. In phenomenological results, we study the impact of the electroweak corrections to total cross section as well as its distributions. In addition, we discuss the possibility of searching for an additional Higgs in arbitrary beyond the Standard Model (BSM) through ZH production at the ILC.

Optimization Design of PDC Bit Gauge Using CFD-DPM and Central Composite Design

Polycrystalline Diamond Compact (PDC) bit has been widely used in natural gas/oil drilling industry for its advantages such as no rotating parts, highly rate of penetration (ROP) and durability. In recent decades, the comprehensive property of PDC bit has been improved rapidly due to the scientists’ efforts. Hydraulic design of PDC bit is very important because the retention of the cuttings may dramatically decrease ROP. Most current researches focus on how blade profile and nozzle parameters affect hydraulic performance of PDC bit, but, the understanding of gauge geometrical parameters (mainly refer to gauge width, gauge length and gauge spiral angle) effects on hydraulic performance of PDC bit is still incomplete. In this paper, a simulation method and an optimization method were applied to find the best gauge parameter for 8.5 inch PDC bit. In the proposed approach, the approximate range of above three parameters were confirmed first based on previous studies. Then, the central composite design (CCD) was used to design numerical simulation scheme and the discrete particle modeling (DPM) was used to track the cuttings and the velocity of particles and fluid were evaluated to study the hydraulic performance of drill bit under different gauge geometrical parameters. Finally, the optimal geometrical parameter of gauge could be obtained according to the simulation results. Overall, the proposed approach can be used to design PDC bit gauge structure to improve the cuttings’ velocity away from bottomhole, which will result in huge improvement of ROP.