Gauge-invariant dressed fermion propagator in massless QED3

The infrared behaviour of the gauge-invariant dressed fermion propagator in massless QED₃ is discussed for three choices of dressing. It is found that only the propagator with the isotropic (in three Euclidean dimensions) choice of dressing is acceptable as the physical fermion propagator. It is explained that the negative anomalous dimension of this physical fermion does not contradict any field-theoretical requirement.     

Aspects of the functional renormalisation group

We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being NPI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson-Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.     

Performance improvements of ultraviolet/infrared dual-band detectors

Results are reported on dual-band detectors based on a GaN/AlGaN structure operating in both the ultraviolet–midinfrared (UV–MIR) and ultraviolet–farinfrared (UV–FIR) regions. The UV detection is due to an interband process, while the MIR/FIR detection is from free carrier absorption in the emitter/contact followed by internal photoemission over the barrier at the GaN/AlGaN interface. The UV detection, which was observed from 300 K to 4.2 K, has a threshold of 360 nm with a peak responsivity of 0.6 mA/W at 300 K. The detector shows a free carrier IR response in the 3–7 μm range up to 120 K, and an impurity response around 54 μm up to 30 K. A response in the range 7–13 μm, which is tentatively assigned to transitions from C impurities and N vacancies in the barrier region, was also observed. It should also be possible to develop a detector operating in the UV–visible–IR regions by choosing the appropriate material system. A dual-band detector design, which allows not only to measure the two components of the photocurrent generated by UV and IR radiation simultaneously but also to optimize the UV and IR responses independently, is proposed.     

No parity anomaly in massless QED3: A BPHZL approach

In this Letter we call into question the perturbatively parity breakdown at 1-loop for the massless QED₃ frequently claimed in the literature. As long as perturbative quantum field theory is concerned, whether a parity anomaly owing to radiative corrections exists or not shall be definitely proved by using a renormalization method independent of any regularization scheme. Such a problem has been investigated in the framework of BPHZL renormalization method, by adopting the Lowenstein–Zimmermann subtraction scheme. The 1-loop parity-odd contribution to the vacuum-polarization tensor is explicitly computed in the framework of the BPHZL renormalization method. It is shown that a Chern–Simons term is generated at that order induced through the infrared subtractions — which violate parity. We show then that, what is called “parity anomaly”, is in fact a parity-odd counterterm needed for restauring parity.     

Gauge-Invariant Spin and Orbital Angular Momentum of Laguerre--Gaussian Laser

We adopt a gauge-invariant definition to calculate the spin and orbital angular momenta of a so-called Ith order Laguerre-Gaussian laser. The results reveal that photons on the axis of the beam may carry an orbital angular momentum of （l - 1）h besides lh per photon. For the spin, we obtain a more reasonable expression proportional to the beam intensity instead of the gradient of the intensity as previously derived. We also discuss how to experimentally discriminate the angular momentum expressions given here and those commonly accepted in the literature.     

A study on relativistic lagrangian field theories with non-topological soliton solutions

We perform a general analysis of the dynamic structure of two classes of relativistic lagrangian field theories exhibiting static spherically symmetric non-topological soliton solutions. The analysis is concerned with (multi-) scalar fields and generalized gauge fields of compact semi-simple Lie groups. The lagrangian densities governing the dynamics of the (multi-) scalar fields are assumed to be general functions of the kinetic terms, whereas the gauge-invariant lagrangians are general functions of the field invariants. These functions are constrained by requirements of regularity, positivity of the energy and vanishing of the vacuum energy, defining what we call “admissible” models. In the scalar case we establish the general conditions which determine exhaustively the families of admissible lagrangian models supporting this kind of finite-energy solutions. We analyze some explicit examples of these different families, which are defined by the asymptotic and central behaviour of the fields of the corresponding particle-like solutions. From the variational analysis of the energy functional, we show that the admissibility constraints and the finiteness of the energy of the scalar solitons are necessary and sufficient conditions for their linear static stability against small charge-preserving perturbations. Furthermore, we perform a general spectral analysis of the dynamic evolution of the small perturbations around the statically stable solitons, establishing their dynamic stability. Next, we consider the case of many-components scalar fields, showing that the resolution of the particle-like field problem in this case reduces to that of the one-component case. The study of these scalar models is a necessary step in the analysis of the gauge fields. In this latter case, we add the requirement of parity invariance to the admissibility constraints. We determine the general conditions defining the families of admissible gauge-invariant models exhibiting finite-energy electrostatic spherically symmetric solutions which, unlike the (multi-) scalar case, are not always stable. The variational analysis of the energy functional leads now to supplementary restrictions to be imposed on the lagrangian densities in order to ensure the linear stability of the solitons. We establish a correspondence between any admissible soliton-supporting (multi-) scalar model and a family of admissible generalized gauge models supporting finite-energy electrostatic point-like solutions. Conversely, for each admissible soliton-supporting gauge-invariant model there is an associated unique admissible (multi-) scalar model with soliton solutions. This shows the exhaustive character of the admissibility and stability conditions in determining the class of soliton-supporting generalized gauge models. The usual Born-Infeld electrodynamic theory and its non-abelian extensions are shown to be (very particular) examples of one of these families.     

Constraints on the leading-twist pion distribution amplitude from a QCD light-cone sum rule with chiral current

We study our non-perturbative formalism to describe scalar gauge-invariant metric fluctuations by extending the Ponce de León metric.     

Infrared vibrational spectra of l-histidinium dihydrogen orthophosphate orthophosphoric acid (LHP)

The entire vibrational spectrum of a single crystal of l-histidinium dihydrogen orthophosphate orthophosphoric acid (LHP) was studied by infrared (IR) spectroscopy from 10 up to 4000 cm⁻¹. The polarized infrared (IR) reflectivity spectra were measured between 7 and 250 K, in the frequency range 10–600 cm⁻¹. From the IR spectral analysis, the phonon modes were classified within their symmetry species, and their longitudinal (LO) and transversal (TO) optical frequencies were calculated. A tentative assignment of the various internal modes observed in the transmissivity spectrum of LHP, between 300 and 4000 cm⁻¹, is proposed. The present study did not reveal any low-temperature structural phase transition.     

IR Spectrum of C8H2: Integrated Band Intensities and Some Observational Implications

Polyynes are of astrophysical interest since they appear to be involved in organic chemistry in very different mediums. In Titan's atmosphere, the lightest polyyne, C₄H₂, was detected by Voyager. Recently C₄H₂ and C₆H₂ have been discovered in a protoplanetary nebula, suggesting polyynes as a possible chemical pathway to PAH (polycyclic aromatic hydrocarbons). Moreover, several experimental simulations and modeling imply their production from the photochemistry of methane and their involvement in the formation of organic aerosols. After the study of C₄H₂ and C₆H₂ spectra in the UV and IR wavelength range, we report here the first spectrum of gaseous C₈H₂ in the range 400–4000 cm⁻¹ at room temperature and low resolution. The task was hardly achieved because of the high instability of this molecule with temperature and pressure. To avoid exothermic polymerization, the compound as mixed with a solvent. We have performed a separate spectroscopic study of the solvent to determine C₈H₂ partial pressure within the mixture. This allowed us to calculate C₈H₂ integrated band intensities. In the studied wavelength range, C₈H₂ presents three main bands similar to those of C₆H₂ in terms of vibrational type, position, and relative intensity. To study the possible identification of these polyynes by spatial observatories (Cassini–Huygens, ISO), we have also measured the C₆H₂ and C₈H₂ infrared spectra in the range 400–1500 cm⁻¹ at 0.35 cm⁻¹ resolution.     

A note on failure of the ladder approximation to QCD

In this Letter we show that the claim made in [V. Gogohia, Phys. Lett. B 611 (2005) 129] that the ladder approximation to QCD is internally inconsistent is incorrect. The incorrect conclusion in [V. Gogohia, Phys. Lett. B 611 (2005) 129] is based on the incorrect use of a QED-type Ward–Takahashi relation, which does not hold in the ladder approximation to QCD. We give a proof for this fact.     

Globally conformal invariant gauge field theory with rational correlation functions

Operator product expansions (OPE) for the product of a scalar field with its conjugate are presented as infinite sums of bilocal fields V_κ(x₁,x₂) of dimension (κ,κ). For a globally conformal invariant (GCI) theory we write down the OPE of V_κ into a series of twist (dimension minus rank) 2κ symmetric traceless tensor fields with coefficients computed from the (rational) 4-point function of the scalar field.

We argue that the theory of a GCI hermitian scalar field of dimension 4 in D=4 Minkowski space such that the 3-point functions of a pair of 's and a scalar field of dimension 2 or 4 vanish can be interpreted as the theory of local observables of a conformally invariant fixed point in a gauge theory with Lagrangian density .     

Schwinger mechanism for gluon-pair production in the presence of arbitrary time-dependent chromo-electric field

We study the Schwinger mechanism for gluon-pair production in the presence of an arbitrary time-dependent chromo-electric background field E ^a (t) with arbitrary color index a=1,2,…,8 in SU(3) by directly evaluating the path integral. We obtain an exact expression for the probability of non-perturbative gluon-pair production per unit time per unit volume and per unit transverse momentum, , from arbitrary E ^a (t). We show that the tadpole (or single-gluon) effective action does not contribute to the non-perturbative gluon-pair production rate, . We find that the exact result for non-perturbative gluon-pair production is independent of all the time derivatives , where n=1,2,…,∞, and that it has the same functional dependence on the two Casimir invariants, [E ^a (t)E ^a (t)] and [d _abc E ^a (t)E ^b (t)E ^c (t)]², as the constant chromo-electric field E ^a result with the replacement: E ^a →E ^a (t). This result relies crucially on the validity of the shift conjecture, which has not yet been established. This result may be relevant to the study of the production of a non-perturbative quark–gluon plasma at RHIC and LHC.     

Magnetization plateau in the S=1/2 XXZ spin chain with period 3 magnetic field

We investigate the S=1/2 XXZ spin chain with period 3 magnetic field term. The magnetization plateau-nonplateau transition at m=±1/6 is expected to be of the Berezinski–Kosterlitz–Thouless type from the bosonization argument. By examining the level crossing of low-lying excitations numerically, we precisely determine the plateau phase diagram.     

Is electromagnetic gauge invariance spontaneously violated in superconductors?

We aim to give a pedagogical introduction to those elementary aspects of superconductivity which are not treated in the classic textbooks. In particular, we emphasize that global U (1) phase rotation symmetry, and not gauge symmetry, is spontaneously violated, and show that the BCS wave function is, contrary to claims in the literature, fully gauge invariant. We discuss the nature of the order parameter, the physical origin of the many degenerate states, and the relation between formulations of superconductivity with fixed particle numbers vs. well-defined phases. We motivate and to some extend derive the effective field theory at low temperatures, explore symmetries and conservation laws, and justify the classical nature of the theory. Most importantly, we show that the entire phenomenology of superconductivity essentially follows from the single assumption of a charged order parameter field. This phenomenology includes Anderson’s characteristic equations of superfluidity, electric and magnetic screening, the Bernoulli Hall effect, the balance of the Lorentz force, as well as the quantum effects, in which Planck’s constant manifests itself through the compactness of the U (1) phase field. The latter effects include flux quantization, phase slippage, and the Josephson effect.     

Spontaneously broken quark helicity symmetry

We discuss the origin of chiral-symmetry breaking in the light-cone representation of QCD. In particular, we show how quark helicity symmetry is spontaneously broken in SU (N) gauge theory with massless quarks if that theory has a condensate of fermion light-cone zero modes. The symmetry breaking appears as induced interactions in an effective light-cone Hamiltonian equation based on a trivial vacuum. The induced interaction is crucial for generating a splitting between pseudoscalar and vector meson masses, which we illustrate with spectrum calculations in some 1 + 1-dimensional reduced models of gauge theory.     

Characteristic polynomials of random Hermitian matrices and Duistermaat–Heckman localisation on non-compact Kähler manifolds

We reconsider the problem of calculating a general spectral correlation function containing an arbitrary number of products and ratios of characteristic polynomials for a N×N random matrix taken from the Gaussian Unitary Ensemble (GUE). Deviating from the standard “supersymmetry” approach, we integrate out Grassmann variables at the early stage and circumvent the use of the Hubbard–Stratonovich transformation in the “bosonic” sector. The method, suggested recently by J.V. Fyodorov [Nucl. Phys. B 621 [PM] (2002) 643], is shown to be capable of calculation when reinforced with a generalisation of the Itzykson–Zuber integral to a non-compact integration manifold. We arrive to such a generalisation by discussing the Duistermaat–Heckman localisation principle for integrals over non-compact homogeneous Kähler manifolds. In the limit of large-N the asymptotic expression for the correlation function reproduces the result outlined earlier by A.V. Andreev and B.D. Simons [Phys. Rev. Lett. 75 (1995) 2304].     

A Composite Scheme for Gas Dynamics in Lagrangian Coordinates

One cycle of a composite finite difference scheme is defined as several time steps of an oscillatory scheme such as Lax–Wendroff followed by one step of a diffusive scheme such as Lax–Friedrichs. We apply this idea to gas dynamics in Lagrangian coordinates. We show numerical results in two dimensions for Noh's infinite strength shock problem and the Sedov blast wave problem, and for several one-dimensional problems including a Riemann problem with a contact discontinuity. For Noh's problem the composite scheme produces a better result than that obtained with a more conventional Lagrangian code.     

High-Order Scheme for a Nonlinear Maxwell System Modelling Kerr Effect

This paper is devoted to the derivation of an efficient numerical scheme for the Kerr–Maxwell system. We begin by studying the 1-D Riemann problem. We obtain a result of existence and uniqueness for large data. Then we develop a high-order Roe solver and exhibit solutions in 1-D and 2-D simulations.     

Effect of spin-flip scattering on electrical transport in magnetic tunnel junctions

By means of the nonequilibrium Green function technique, the effect of spin-flip scatterings on the spin-dependent electrical transport in ferromagnet–insulator–ferromagnet (FM–I–FM) tunnel junctions is investigated. It is shown that Jullière's formula for the tunnel conductance must be modified when including the contribution from the spin-flip scatterings. It is found that the spin-flip scatterings could lead to an angular shift of the tunnel conductance, giving rise to the junction resistance not being the largest when the orientations of magnetizations in the two FM electrodes are antiparallel, which may offer an alternative explanation for such a phenomenon observed previously in experiments in some FM–I–FM junctions. The spin-flip assisted tunneling is also observed.