Constant Background Field Research Articles

An O(a) modified lattice set-up of the Schrödinger functional in SU(3) gauge theory

The set-up of the QCD Schrodinger functional (SF) on the lattice with staggered quarks requires an even number of points L/a in the spatial directions, while the Euclidean time extent of the lattice, T/a, must be odd. Identifying a unique renormalisation scale, L = T, is then only possible up to O(a) lattice artefacts. In this article we study such lattices in the pure SU(3) gauge theory, where we can also compare to the standard set-up. We consider the SF coupling as obtained from the variation of an SU(3) Abelian and spatially constant background field. The O(a) lattice artefacts can be cancelled by the existing O(a) boundary counterterm. However, its coefficient, ct, differs at the tree-level from its standard value, so that one first needs to re-determine the induced background gauge field. The perturbative one-loop correction to the coupling allows to determine ct to one-loop order. A few numerical simulations serve to demonstrate that residual cutoff effects in the step scaling function are small in both cases, T = L ± a and comparable to the standard case with T = L.

An uncombed inversion of multiwavelength observations reproducing the net circular polarization in a sunspot’s penumbra

Context. The penumbra of sunspots has a complex magnetic field topology whose three-dimensional organization remains unclear after more than a century of investigation.Aims. I derive a geometrical model of the penumbral magnetic field topology from an uncombed inversion setup designed to reproduce the net circular polarization (NCP) of simultaneous spectra in near-infrared (IR; 1.56 μ m) and visible (VIS; 630 nm) spectral lines.Methods. I inverted the co-spatial spectra of five photospheric lines with a model that mimicked vertically interlaced magnetic fields with two distinct components, labeled background field and flow channels because of their characteristic properties (flow velocity, field inclination). The flow channels were modeled as a perturbation of the constant background field with a Gaussian shape using the SIRGAUS code. The location and extension of the Gaussian perturbation in the optical depth scale retrieved by the inversion code were then converted to a geometrical height scale. By estimating the geometrical size of the flow channels, I investigated the relative amount of magnetic flux in the flow channels and the background field atmosphere.Results. The uncombed model is able to reproduce the NCP well on the limb side of the spot and less successfully on the center side; the VIS lines are better reproduced than the near-IR lines. I find that the Evershed flow happens along nearly horizontal field lines close to the solar surface given by optical depth unity. The magnetic flux that is related to the flow channels constitutes about 20−50% of the total magnetic flux in the penumbra. Conclusions. The gradients that can be produced by a Gaussian perturbation are too small for a perfect reproduction of the NCP in the IR lines with their small formation height range, where a step function seems to be required. Two peculiarities of the observed NCP, a sign change in the NCP of the VIS lines on the center side and a ring structure around the umbra with opposite signs of the NCP in the Ti i line at 630.37 nm and the Fe i line at 1565.2 nm, deserve closer attention in future modeling attempts. The large fraction of magnetic flux related to the flow channel component could suffice to replenish the penumbral radiative losses in the flux tube picture.

NEW RELATIONS BETWEEN SPINOR AND SCALAR ONE-LOOP EFFECTIVE LAGRANGIANS IN CONSTANT BACKGROUND FIELDS

Simple new relations are presented between the one-loop effective Lagrangians of spinor and scalar particles in constant curvature background fields, both electromagnetic and gravitational. These relations go beyond the well-known cases for self-dual background fields.

Holographic flavor transport in arbitrary constant background fields

We use gauge-gravity duality to compute a new transport coefficient associated with a number Nf of massive = 2 supersymmetric hypermultiplet fields propagating through an = 4 SU(Nc) super-Yang-Mills theory plasma in the limits of large Nc and large 't Hooft coupling, with Nf << Nc. We introduce a baryon number density as well as arbitrary constant electric and magnetic fields, generalizing previous calculations by including a magnetic field with a component parallel to the electric field. We can thus compute all components of the conductivity tensor associated with transport of baryon number charge, including a component never before calculated in gauge-gravity duality. We also compute the contribution that the flavor degrees of freedom make to the stress-energy tensor, which exhibits divergences associated with the rates of energy and momentum loss of the flavor degrees of freedom. We discuss two currents that are free from these divergences, one of which becomes anomalous when the magnetic field has a component parallel to the electric field and hence may be related to recent study of charge transport in the presence of anomalies.

Hard thermal loops, to quadratic order, in the background of a spatial ’t Hooft loop

We compute the simplest hard thermal loops for a spatial 't Hooft loop in the deconfined phase of a SU(N) gauge theory. We expand to quadratic order about a constant background field A_0 = Q/g, where Q is a diagonal, color matrix and g is the gauge coupling constant. We analyze the problem in sufficient generality that the techniques developed can be applied to compute transport properties in a "semi"-Quark Gluon Plasma. Notably, computations are done using the double line notation at finite N. The quark self-energy is a Q-dependent thermal mass squared, of order g^2T^2, where T is the temperature, times the same hard thermal loop as at Q=0. The gluon self-energy involves two pieces: a Q-dependent Debye mass squared, of order g^2T^2, times the same hard thermal loop as for Q=0, plus a new hard thermal loop, of order g^2T^3, due to the color electric field generated by a spatial 't Hooft loop.

Reducing pulse distortion in fast-light pulse propagation through an erbium-doped fiber amplifier using a mutually incoherent background field

It was reported earlier that it is possible to obtain large pulse advancement with minimum pulse distortion in fast-light propagation through an erbium-doped fiber amplifier by placing the pulse on top of a mutually coherent constant background field. Here we show that comparable distortion reduction can be obtained through use of a mutually incoherent background field, a procedure that could be much more readily implemented under many circumstances. We also show that further improvement can be obtained by means of adjusting the pulse power, and for a pulse-power of 100μW the distortion decreases about 56% from 0.56 with no background while the fractional advancement decreases only about 3% from 0.16.

Simulating the all-order hopping expansion II: Wilson fermions

We investigate the extension of the Prokof'ev–Svistunov worm algorithm to Wilson lattice fermions in an external scalar field. We effectively simulate by Monte Carlo the graphs contributing to the hopping expansion of the two-point function on a finite lattice to arbitrary order. Tests are conducted for a constant background field i.e. free fermions at some mass. For the method introduced here this is expected to be a representative case. Its advantage is that we know the exact answers and can thus make stringent tests on the numerics. The approach is formulated in both two and three space–time dimensions. In D = 2 Wilson fermions enjoy special positivity properties and the simulation is similarly efficient as in the Ising model. In D = 3 the method also works at sufficiently large mass, but there is a hard sign problem in the present formulation hindering us to take the continuum limit.

TWO-LOOP VACUUM DIAGRAMS IN BACKGROUND FIELD AND THE HEISENBERG–EULER EFFECTIVE ACTION

We show that in arbitrary even dimensions, the two-loop scalar QED Heisenberg–Euler effective action can be reduced to simple one-loop quantities, using just algebraic manipulations, when the constant background field satisfies F2 = -f2𝟙, which in four dimensions coincides with the condition for self-duality, or definite helicity. This result relies on new recursion relations between two-loop and one-loop diagrams, with background field propagators. It also yields an explicit form of the renormalized two-loop effective action in a general constant background field in two dimensions.

Casimir dependence of transverse distribution of pairs produced from a strong constant chromoelectric background field

The transverse distribution of gluon and quark-antiquark pairs produced from a strong constant chromo-electric field depends on two gauge invariant quantities, $C_1=E^aE^a$ and $C_2=[d_{abc}E^aE^bE^c]^2$, as shown earlier in [G.C. Nayak and P. van Nieuwenhuizen, Phys. Rev. D 71, 125001 (2005)] for gluons and in [G.C. Nayak, Phys. Rev. D 72, 125010 (2005)] for quarks. Here, we discuss the explicit dependence of the distribution on the second Casimir invariant, C_2, and show the dependence is at most a 15% effect.

Non-perturbative renormalization group calculation of the scalar self-energy

We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow equations for the n-point functions which are also differential equations with respect to a constant background field. This makes them, a priori, difficult to solve. However, we demonstrate in this paper that, within a simple approximation which turns out to be quite accurate, the solution of these flow equations is not more complicated than that of the flow equations obtained in the derivative expansion. Thus, with a numerical effort comparable to that involved in the derivative expansion, we can get the full momentum dependence of the n-point functions. The method is applied, in its leading order, to the calculation of the self-energy in a 3-dimensional scalar field theory, at criticality. Accurate results are obtained over the entire range of momenta.

Production of electron-positron pairs and photon emission by an electron in an axial-vector background field

The possibility of radiative effects induced by fermion interaction with a constant axial-vector background field is studied within an extended standard model. The production of electron-positron pairs by photons and photon emission by electrons and positrons are examined. The rates of these processes are calculated within the Furry picture. It is shown that the rates obtained in this way depend strongly on the polarization states of the particles involved. As a result, ultrarelativistic particles predominantly occupy specific spin states—namely, charged particles occur in states where the sign of the helicity is coincident with the sign of the effective potential, while photons have polarization of sign opposite to the sign of the effective potential. This leads to spatial asymmetries, which may give rise to observable phenomena in astrophysical and cosmological investigations.

Design and Test of a Compound Persistent-Pulsed Magnet for Fast Field Cycling NMR

In order to investigate the possibility of using superconducting magnets for fast field cycling (FFC) NMR relaxometry, a NbTi magnet able to achieve high field variation rates in a constant background field has been designed and tested. The design layout consists in an outer superconducting magnet working in persistent mode and an inner superconducting magnet working in pulsed mode. The layout of the inner magnet has been optimized taking into account field strength, field homogeneity, stray field and inductive coupling with outer magnet. A demonstration pulsed magnet has been tested in a background field, achieving the main desired working features.

INTERACTING RELATIVISTIC PARTICLE: TIME–SPACE NONCOMMUTATIVITY AND SYMMETRIES

We discuss the symmetry properties of the reparametrization invariant model of an interacting relativistic particle where the electromagnetic field is taken as the constant background field. The direct coupling between the relativistic particle and the electromagnetic gauge potential is a special case of the above with a specific set of subtleties involved in it. For the above model, we demonstrate the existence of a time–space noncommutativity (NC) in the space–time structure from the symmetry considerations alone. We further show that the NC and commutativity properties of this model are different aspects of a unique continuous gauge symmetry that is derived from the nonstandard gauge-type symmetry transformations by requiring their consistency with (i) the equations of motion, and (ii) the expressions for the canonical momenta, derived from the Lagrangians. We provide a detailed discussion on the noncommutative deformation of the Poincaré algebra.

Homogeneous versus spiral phases of hole-doped antiferromagnets: A systematic effective field theory investigation

Using the low-energy effective field theory for magnons and holes---the condensed matter analog of baryon chiral perturbation theory for pions and nucleons in QCD---we study different phases of doped antiferromagnets. We systematically investigate configurations of the staggered magnetization that provide a constant background field for doped holes. The most general configuration of this type is either constant itself or represents a spiral in the staggered magnetization. Depending on the values of the low-energy parameters, a homogeneous phase, a spiral phase, or an inhomogeneous phase is energetically favored. The reduction of the staggered magnetization upon doping is also investigated.

Large-order perturbation theory and de Sitter/anti–de Sitter effective actions

We analyze the large-order behavior of the perturbative weak-field expansion of the effective Lagrangian density of a massive scalar in de Sitter and anti--de Sitter space, and show that this perturbative information is not sufficient to describe the nonperturbative behavior of these theories, in contrast to the analogous situation for the Euler-Heisenberg effective Lagrangian density for charged scalars in constant electric and magnetic background fields. For example, in even-dimensional de Sitter space there is particle production, but the effective Lagrangian density is nevertheless real, even though its weak-field expansion is a divergent nonalternating series whose formal imaginary part corresponds to the correct particle production rate. This apparent puzzle is resolved by considering the full nonperturbative structure of the relevant Feynman propagators, and cannot be resolved solely from the perturbative expansion.

``Background field integration-by-parts'' and the connection between one-loop and two-loop Heisenberg-Euler effective actions

We develop integration-by-parts rules for Feynman diagrams involving massive scalar propagators in a constant background electromagnetic field, and use these to show that there is a simple diagrammatic interpretation of mass renormalization in the two-loop scalar QED Heisenberg-Euler effective action for a general constant background field. This explains why the square of a one-loop term appears in the renormalized two-loop Heisenberg-Euler effective action. No integrals need be evaluated, and the explicit form of the background field propagators is not needed. This dramatically simplifies the computation of the renormalized two-loop effective action for scalar QED, and generalizes a previous result obtained for self-dual background fields.

Self-similar transport processes in a two-dimensional realization of multiscale magnetic field turbulence

We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect of turbulence on the microscopic particle dynamics. Our main goal is to analyse the dispersion of ideal test particles faced to diverse conditions in the turbulent domain. Depending on the amplitude of the background field and the input test particle velocity, we observe distinct transport regimes ranging from subdiffusion of guiding centres in the limit of Hamiltonian dynamics to random walks on a percolating fractal array and, further, to nearly diffusive behaviour of the mean-square particle displacement versus time. In all cases, we find a complex microscopic structure of the particle motion revealing long-time rests and trapping phenomena, sporadically interrupted by the phases of active cross-field propagation reminiscent of Levy-walk statistics. These complex features persist even when the particle dispersion is diffusive. An interpretation of the results obtained is proposed in connection with the fractional kinetics paradigm extending the microscopic properties of transport far beyond the conventional picture of a Brownian random motion. A calculation of the transport exponent for random walks on a fractal lattice is advocated from topological arguments. An intriguing indication of the topological approach is a gap in the transport exponent separating Hamiltonian-like and fractal random walk-like dynamics, supported through the simulation.

A new method to solve the non-perturbative renormalization group equations

We propose a method to solve the non-perturbative renormalization group equations for the n-point functions. In leading order, it consists in solving the equations obtained by closing the infinite hierarchy of equations for the n-point functions. This is achieved: (i) by exploiting the decoupling of modes and the analyticity of the n-point functions at small momenta: this allows us to neglect some momentum dependence of the vertices entering the flow equations; (ii) by relating vertices at zero momenta to derivatives of lower order vertices with respect to a constant background field. Although the approximation is not controlled by a small parameter, its accuracy can be systematically improved. When it is applied to the O(N) model, its leading order is exact in the large-N limit; in this case, one recovers known results in a simple and direct way, i.e., without introducing an auxiliary field.

Soft-gluon production due to a gluon loop in a constant chromoelectric background field

We obtain an exact result for the soft gluon production and its p_T distribution due to a gluon loop in a constant chromo-electric background field E^a with arbitrary color. Unlike Schwinger's result for e^+e^- pair production in QED which depends only on one gauge invariant quantity, the Electric field E, we find that the p_T distribution of the gluons depend on two gauge invariant quantities, E^aE^a and [d_{abc}E^aE^bE^c]^2.

Finite-difference Euler Deconvolution Algorithm Applied to the Interpretation of Magnetic Data from Northern Bulgaria

Here, we propose a new, finite-difference algorithm for Euler deconvolution, based on the Euler’s homogeneity equation accounting for a constant background field which allows simultaneous depth and shape estimation. The algorithm uses as input data the measured anomalous field and its first-order derivatives, in contrast to methods based on the input of higher order field derivatives. The test of the algorithm on a model of interfering fields of elementary sources with different field fall-off rates, resulting in background close to a linear one, shows that it can give a good estimation of both the depth to the sources singular points and their respective structural indices. A set of tests was carried out on column-like models with shapes ranging from the elementary model of a dipole to that of a point pole, and of models of arbitrary shape with two singular points in between. It showed that when the ratio of the distance between the observation plane and the source’s top and the length of the body allows classification of it as a dipole or a point pole, the value of the estimated structural index is close to the integer value, typical for the respective elementary source. In such cases the estimated depth value refers to that of the special internal point of the respective type of source. This can facilitate in certain situations the interpretation of non-integer structural indices and their associated depth estimates obtained with the new Euler deconvolution algorithm. Inversion of a set of magnetic data from northern Bulgaria, caused by basaltic bodies of different shape, with the proposed method confirmed that the most intense anomalies are caused by column-like bodies outcropping on the surface and with considerable depth extent.