Isolation and quantization of the two degrees of freedom of the electromagnetic potential for any gauge

The true dynamical degrees of freedom (TDDF) of the electromagnetic potential are found for any gauge. They are the components of the Fourier transform of the electromagnetic potential on a two-dimensional spacelike plane orthogonal to the lightlike momentum vector for k² = 0 and vanish for k² ≠ 0. Gauge invariance is related to the (two-parameter) indeterminacy of this spacelike plane and the arbitrariness of the component of the electromagnetic potential along the momentum vector. By direct quantization of the TDDF for any gauge (compatible with the equations of motion), some of the well-known problems of the usual treatments are avoided. For instance, the constraint div E = 0 is a c-number (agrees with the commutation relations) without choosing a gauge, there appears no need for an indefinite metric in the space of state amplitudes, the commutators for creation and annihilation operators of every component of the electromagnetic potential (timelike, longitudinal, and transverse) have the same sign, and the energy of the electromagnetic field is positive for any gauge. When gauges are chosen, the results of the literature are recovered. In our treatment, gauge fixation and quantization commute.     

Lorentz-non-invariant counter-terms in QCD in a general axial gauge

It is shown in the context of a pure Yang-Mills theory that the solution of the Slavnov-Taylor identities in a general axial gauge admits counter-terms which may or may not be Lorentz invariant. It follows from the background field method that these counter-terms must be gauge invariant. The Lorentz-non-invariant counter-terms appear already at the one-loop level and depend both on the gauge parameter α and the non-covariant vector n_ω.     

Singular and regular gauges in soft–collinear effective theory: The introduction of the new Wilson line T

Gauge invariance in soft–collinear effective theory (SCET) is discussed in regular (covariant) and singular (light-cone) gauges. It is argued that SCET, as it stands, is not capable to define in a gauge invariant way certain non-perturbative matrix elements that are an integral part of many factorization theorems. Those matrix elements involve two quark or gluon fields separated not only in light-cone direction but also in the transverse one. This observation limits the range of applicability of SCET. To remedy this we argue that one needs to introduce a new Wilson line as part of SCET formalism, that we call T. This Wilson line depends only on the transverse component of the gluon field. As such it is a new feature to the SCET formalism and it guarantees gauge invariance of the non-perturbative matrix elements in both classes of gauges.     

Helmholtz Theorem and the V-Gauge in the Problem of Superluminal and Instantaneous Signals in Classical Electrodynamics

In this work we substantiate the applying of the Helmholtz vector decomposition theorem (H-theorem) to vector fields in classical electrodynamics. Using the H-theorem, within the framework of the two-parameter Lorentz-like gauge (so called v-gauge), we show that two kinds of magnetic vector potentials exist: one of them (solenoidal) can act exclusively with the velocity of light c and the other one (irrotational) with an arbitrary finite velocity v (including a velocity more than c). We show also that the irrotational component of the electric field has a physical meaning and can propagate exclusively instantaneously.     

Derivation of an effective Lagrangian from a generalized scalar curvature

A spinor Lagrangian invariant under global coordinate, local Lorentz and local chiral SU(n) × SU(n) gauge transformations is presented. The invariance requirement necessitates the introduction of boson fields, and a theory for these fields is then developed by relating them to generalizations of the vector connections in general relativity and utilizing an expanded scalar curvature as a boson Lagrangian. In implementing this plan, the local Lorentz group is found to greatly facilitate the correlation of the boson fields occurring in the spinor Lagrangian with the generalized vector connections.The independent boson fields of the theory are assumed to be the inhomogeneously transforming irreducible parts of the connections. It turns out that no homogeneously transforming parts are necessary to reproduce the chiral Lagrangian usually used as a basis for phenomenological field theories. The Lagrangian in question appears when the gravitational interaction is turned off. It includes pseudoscalar, spinor, vector, and axial vector fields, and the vector fields carry mass in spite of the fact that the theory is locally gauge invariant.     

The component gauges in supergravity

We present N = 1 supergravity in superspace gauges where the relation to component supergravity is immediate. Among the new results are the inverse vielbein to all orders in φ, some important components of the connection, a Lorentz transformation between our two “component gauges”, the component transformations for a spinor multiplet and some results concerning the axial current for various matter systems coupled to supergravity.     

Superior properties of SmBCO coated conductors at high magnetic fields and elevated temperatures

In addition to the well investigated YBa₂Cu₃O_7?δ (Y-123, YBCO) compound, many other rare earth-123 compounds are candidate materials for the production of coated conductors. Sm-123 seems to be an excellent alternative because of its higher transition temperature (T_c) and higher critical current densities (J_c) in external magnetic fields. Because of the fast decrease of J_c in YBCO at elevated temperatures, especially around the boiling point of liquid nitrogen, the slightly higher T_c can be an important advantage. Recently, significant progress has been made in the production of long length Sm-123 based coated conductors. We report here on transport measurements on these conductors in the liquid nitrogen temperature range. The critical current densities were determined as a function of the applied field and the crystallographic orientation under maximum Lorentz force configuration. A shift of the c-axis (～7°) from the tape normal was found. The conductor properties were compared to those of commercially available YBCO coated conductors. The critical current densities as well as the irreversibility fields are higher in the SmBCO tapes, thus demonstrating the superior properties of the Sm-123 compound.     

Lorentz anomaly in arbitrary dimensions

It is shown that the Lorentz invariance is broken in gauge theories of chiral Weyl fermions in flat space-time via one-loop quantum corrections. Abelian gauge fields contribute to this anomaly in even dimensions larger than or equal to four and non-Abelian gauge fields do in even dimensions larger than or equal to six. The anomaly is proportional toD/2–1 power to the charge, whereD is a number of space-time dimensions.     

Transformation properties under broken symmetry

A general condition is derived which allows a local field (in an arbitrary field theory) to belong simultaneously to a fixed representation of the Lorentz group and a given representation of a broken symmetry group. Specializing to local currents one obtains the conditions of Gross and Jackiw for a complete current algebra, the condition of Bég et al. for the dimension of a current component to be independent of its Lorentz index, and the condition necessary for covariant derivatives in broken chiral theories to be covariant. Also, one is able to understand observation of Kimel on the failure of complete current algebra in gauge field models with mass-breaking terms, those by Takahashi and others on the impossibility of assigning a dimension to Duffin-Kemmer scalar and Klein-Gordon vector fields, and some other specific results. The above condition allows a critical examination of operator product expansions. The point of the paper is in its generality; it makes possible a unified view of a large number of specific results and observations.     

Global existence of coupled Yang-Mills and scalar fields in 2 + 1 dimensional space-time

We present results on the Cauchy problem for coupled classical Yang-Mills and scalar fields in n + 1 dimensional space-time both in the temporal and in the Lorentz gauge. We prove the existence of local solutions for any n, and the existence of global solutions for n = 1, 2 in the temporal gauge and for n = 1 in the Lorentz gauge. The last result also holds for massive Yang-Mill fields.     

An operatorially solved model of massless two-dimensional quantum chromodynamics

An operator solution is constructed in (1,1) dimensions to the massless quantum chromodynamics of n fermion quarks and n² ? 1 vector boson gluons with local colour SU(n) symmetry. The interacting quark field is a confined SU(n) Thirring field with zero Abelian coupling. The colour gluons are dependent Lie fields obeying the gluon-free fermionic current identity. Explicit local infinitesimal operator colour transformations (with an arbitrary coordinate-independent Lorentz vector coefficient defining the gauge) are given and the requirement of proper colour covariance linked to the vanishing of the coloured quark source currents and hence to the absence of coloured quark-composite states. The status of Noether's theorem is also clarified.     

The matrix element of the transverse component of the bilocal vector current and its parton interpretation

In this paper we study the matrix element of the transverse component of the bilocal vector current in the context of deep inelastic scattering. The BJL limit of high energy amplitudes together with light-front current algebra imply the same parton interpretation for its matrix element as that of the plus component. On the other hand, the transverse component depends explicitly on the gluon field operator in QCD, appears as “twist three” and hence its matrix element has no manifest parton interpretation. In this paper we perform calculations in light-front time-ordering perturbative QCD for a dressed quark target to order α_s and demonstrate that the matrix element of the transverse component of the bilocal vector current has the same parton interpretation as that of the plus component.     

Which gauges are ghost-free?

A sufficient condition for the decoupling of Faddeev-Popov ghosts is nonabelian gauge theories is given. For a wide range of gauge functions only transverse gluons propagate thus enlarging the class of “physical” gauges used in recent QCD calculations.     

Factorization and hence reggeization in Yang-Mills theories

We show how to calculate high-energy gauge meson exchange reactions in general, spontaneously broken Yang-Mills theories. We exploit a class of non-covariant gauges in which the scattering amplitudes take on a factorized form in leading order in ln s. Such factorization can only be consistent with Lorentz invariance if the amplitudes have a power law, or Regge behaviour. We evaluate the trajectory functions by a one-loop calculation and verify that the gauge mesons lie on the trajectories.     

A treatise on the interaction of molecular systems with short-pulsed highly-intense external fields

In this review, we consider two gauges: one, the field-free gauge, is formed by the field-free electronic eigenstates and the other, the field-dressed gauge, is formed by the field-dressed electronic basis set. The field-free gauge is used, of course, in the case of time-independent systems but then it is also the more common one to be used in the case of molecular systems exposed to external fields. This gauge is conceptually simple and therefore numerically friendly — two features which make it versatile for numerical application. The field-dressed gauge is, eventually, more involved but yields deeper insight which might lead to a better understanding of the complicated interaction between a molecular system and external fields. In addition, these features can be exploited to develop efficient and reliable approximations that may save CPU (computer processing unit) time in numerical applications. These two gauges are the main topics of the present review.     

Lorentz gauge and Gribov ambiguity in the compact lattice U(1) theory

The Gribov ambiguity problem is studied for compact U(1) lattice theory within the Lorentz gauge. In the Coulomb phase, it is shown that apart from double Dirac sheets Gribov copies originate mainly from zero-momentum modes of the gauge fields. The removal of the zero-momentum modes is necessary for reaching the absolute maximum of the Lorentz gauge functional.     

Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We show how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form.     

Some remarks on the geometry of superspace supergravity

In this note, we first give a quick presentation of the supergeometry underlying supergravity theories, using an intrinsic differential geometric language. For this, we adopt the point of view of Cartan geometries, and rely as well on the work of John Lott, who has found a unified geometrical interpretation of the torsion constraints for many supergravity theories, based on the use of H-structures. In this framework, the constraints amount to requiring first-order integrability of H-structures, for a specific supergroup H.The supergroup H used by Lott is not the usual diagonal representation of the Lorentz group on superspace, but an extension of the latter. This extension appears to be natural and it can be related to the super-Poincaré group. We also observe that the constraints arising from the requirement of first-order integrability have basically the same form, in any spacetime dimension.Looking at supergravity from an affine viewpoint (i.e. as a gauge theory for the super-Poincaré group), we show that requiring first-order integrability amounts to requiring the equivalence, up to gauge transformations, between infinitesimal gauge supertranslations acting on the supervielbein and infinitesimal superdiffeomorphisms acting on the supervielbein.The latter action is performed through a covariant Lie derivative, whose expression involves naturally the supertorsion tensor. We use this expression to show that the term added to the spin connection, in the supercovariant derivative of d=11 supergravity, has a natural superspace origin. In particular, the 4-form field strength is related to a specific component of the supertorsion tensor.We conclude by some general remarks concerning Killing spinors in geometry and supergravity, discussing their possible interpretations, as Killing vector fields on a specific supermanifold on one hand, and as parallel spinors for an appropriate connection on the other hand. We show that this last interpretation is very natural from the point of view of Klein and Cartan geometries.     

The structure of the new superspace

The new superspace of Wess and Zumino is generalized to the unconstrainedN-extendedD-dimensional case, it amounts actually to a reparametrization of the old superspace. Recurrence relations for the transformation law and for the covariant derivatives of the superfields defined in the new superspace are obtained. The definition of the component fields as local Lorentz covariant fields has the consequence that the gauge covariant expressions obtained for the vielbein and the connection of the new superspace don't contain the terms dropped out in the Wess-Zumino gauge of supergravity.