Perturbative QED in terms of gauge invariant fields

A formulation of QED using only gauge invariant fields acting on a physical state space is discussed. The fields are the electromagnetic tensor F_μν and a non-local electron field ψ_f depending on a quadruple {f^μ} of auxiliary functions. The f-ambiguity is physically meaningful: the f^μ contain information on the asymptotic configuration of the electromagnetic field accompanying charged particles. Equations of motion are introduced and solved perturbatively, in the sense that expressions for the Wightman functions of the theory are derived. No information on the commutation relations between the basic fields is needed.     

Superstring effects on D=4, N=1 supergravity

We give a lagrangian and supersymmetry transformation rules for the four-dimensional N=1 supergravity sector of superstring theories with their O(α′) corrections, obtained by the dimensional reduction á la Witten of the effective action of the ten-dimensional heterotic superstring. We also give general forms of O(α′ ″) corrections to supersymmetry transformation rules which arise through an axial vector superfield. Since our system is based on the ten-dimensional superstring without any auxiliary fields, our four-dimensional N=1 supergravity is free of auxiliary fields. Our point-field theory lagrangian is supposed to describe the mass-less fields in the untwisted sector of the ten-dimensional heterotic superstring propagating on orbifolds.     

Auxiliary-field anomalies

In general, quantum corrections to matter-supergravity couplings uniquely determine what are acceptable auxiliary fields for N = 1 supergravity, and partially determine those for N = 2. This is because one-loop corrections produce anomalies in not only the local superscale transformations, but also in the local (Poincaré) supersymmetry transformations themselves, except for special cases: in particular, for N = 1 the $\text{n =}\text{1}\text{3}$ minimimal set of auxiliary fields is uniquely chosen.     

The supergroup manifold formulation of the Wess-Zumino multiplet revisited: The supercurrent and the supergravity auxiliary fields

In this paper we provide a consistent first-order group-manifold formulation of the Wess-Zumino system. It is shownhow the well-known auxiliary fields of the ($\text{1}\text{2}$, 0, 0) system arise by supplementing Bianchi identities with the “second-order constraints”; that is, those equations allowing the transition from the first order to the second order of the theory. When the ($\text{1}\text{2}$, 0, 0) multiplet is coupled to N = 1 supergravity and the torsion “second-order constraint” is implemented, we get a non-minimal set of auxiliary fields (scalar, pseudoscalar axial vector and a spinor). We argue this to be the fundamental set of auxiliary fields. The so-called “minimal set” is not coordinate invariant and can be recovered only by adding a non-geometrical constraint.     

On the non-minimal versions of linearized N=1 supergravity

We present the only two other irreducible sets of auxiliary fields (without high spin auxiliary fields) for N=1 supergravity. Each contains 20 + 20 degrees of freedom.     

On Lagrangian formulations for arbitrary bosonic HS fields on Minkowski backgrounds

We review the details of unconstrained Lagrangian formulations for Bose particles propagated on an arbitrary dimensional flat space-time and described by the unitary irreducible integer higher-spin representations of the Poincare group subject to Young tableaux Y(s ₁, ..., s _k ) with k rows. The procedure is based on the construction of scalar auxiliary oscillator realizations for the symplectic sp(2k) algebra which encodes the second-class operator constraints subsystem in the HS symmetry algebra. Application of an universal BRST approach reproduces gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive bosonic fields of any spin with appropriate number of auxiliary fields.     

New approach to nonlinear electrodynamics: Dualities as symmetries of interaction

The duality-symmetric nonlinear electrodynamics in a new formulation with auxiliary tensor fields is considered. The Maxwell field strength appears only in bilinear terms of the corresponding generic Lagrangian, while the self-interaction is represented by a function E depending on the auxiliary fields. Two types of dualities inherent in the nonlinear electrodynamics admit a simple off-shell characterization as symmetry properties of this function. In the standard formulation, the continuous U(1) duality symmetry is nonlinearly realized on the Maxwell field strength. In the new setting, the same symmetry acts as linear U(1) transformations of the auxiliary field variables. The nonlinear U(1) duality condition proves to be equivalent to the U(1) invariance of the self-interaction E. The discrete self-duality (or self-duality by Legendre transformation) amounts to a weaker reflection symmetry of E. For a class of duality-symmetric Lagrangians, an alternative representation with the auxiliary scalar field is introduced and new explicit examples of such systems are found.     

Superstrings and the auxiliary field structure of supergravity

We construct the complete superfield of vertex operators corresponding to the four-dimensional N = 1 supergravity multiplet associated with the heterotic superstring. The supergravity fields are shown to consist of a graviton, gravitino, and two auxiliary fields and to form a new minimal supermultiplet. The role of R-invariance in new minimal supergravity is discussed.     

String-like topological excitations of the electromagnetic field

In order to analyze the topological properties of an arbitrary configuration of the electromagnetic field, its strength F_μν is expressed in terms of new auxiliary fields which replace the gauge potential A_μ. These new fields have only physical singularities even in the presence of monopoles (no Dirac strings) and exhibit a new local O(1, 1) symmetry which replaces the gauge invariance. Boundary conditions on these fields may induce localized string-like singularities or topological defects which act as sources of magnetic field. A typical defect which emerges is a sort of tadpole formed by a non-quantized monopole attached to one or more magnetic strings of finite length. For topological reasons the total magnetic charge is quantized.     

Calculation of gauge couplings and compact circumferences from self-consistent dimensional reduction

We consider a system of gravity plus free massless matter fields in 4 + N dimensions, and look for solutions in which N dimensions form a compact curved manifold, with the energy-momentum tensor responsible for the curvature produced by quantum fluctuations in the matter fields. For manifolds of sufficient symmetry (including spheres, CP^N, and manifolds of simple Lie groups) the metric depends on only a single multiplicative parameter ?², and the field equations reduce to an algebraic equation for ?, involving the potential of the matter fields in the metric of the manifold. With a large number of species of matter fields, the manifold will be larger than the Planck length, and the potential can be calculated using just one-loop graphs. In odd dimensions these are finite, and give a potential of form C_N/?⁴. Also there are induced Yang-Mills and Einstein-Hilbert terms in the effective 4-dimensional action, proportional to additional numerical coefficients, D_N and E_N. General formulas are given for the gauge coupling g² in terms of C_N and D_N, and the ratio ?²/8πG in terms of C_N and E_N. Numerical values for C_N, D_N, and E_N are obtained for scalar and spinor fields on spheres of odd dimensionality N. It is found that the potential, g² and ?²/8πG can all be positive but only when the compact manifold has N = 3 + 4 k dimensions. (The positivity of the potential is needed for stability of the sphere against uniform dilations or contractions). In this case, solutions exist either for spinor fields alone or for suitable mixes of spinor and scalar fields provided the ratio of the number of scalar fields to the number of fermion fields is not too large. Numerical values of the O(N + 1) gauge couplings and 8φG/?² are calculated for illustrative values of the numbers of spinor fields. It turns out that large numbers of matter fields are needed to make these parameters reasonably small.     

Hodge theory used to produce finite self-energy models of the electron

The relationship between electromagnetic fields and topology is discussed. Hodge theory is generalized to classify static fields in static wormhole models. This generalization is used to show models of the electron exist which have finite self-energy. These models always have 1/R ² electric fields and self-energies of 4πq ²/R ₀, whereR ₀ is the inner radius of the wormhole.     

Infrared stability of global symmetries

We study the infrared stability of global symmetries. It is shown that small orthogonal groups O(N) (N < 4) are infrared attractive, while their direct products are unstable. We also discuss the stability of simple supersymmetric models and the role of auxiliary fields.     

Chromomagnetic screening at high temperature

Chromomagnetic fields are studied using linear response theory. We show that the spurious pole at |k|≈g ² T of the static transverse gluon propagator at finite temperature is cancelled, when the full magnetic permeability function is calculated toO(g ²). Consequently the chromomagnetic fields induced by static external perturbations behave regularly and, to this order, similarly to magnetic fields in QED. We further discuss the relevance of this cancellation for perturbative calculations.     

Dipole contribution of Fe3+ ions in 12k positions to the anisotropy energy constant of the BaFe12O19 hexaferrite

The anisotropy of local fields on ⁵⁷Fe nuclei of Fe³⁺ ions located in the 12k positions of the BaFe₁₂O₁₉ ferrite is studied at low temperatures. The contributions of the anisotropy of the dipole and hyperfine fields to the anisotropy of local fields are separated. The contribution of Fe³⁺ ions in the 12k positions to the anisotropy energy constant K ₁ is calculated in the case of the interionic magnetic dipole-dipole interaction. This contribution comprises more than one-half the experimental K ₁ value.     

3D and 1D micromagnetic calculation for hard/soft bilayers with in-plane easy axes

Macroscopic hysteresis loops and microscopic magnetic moment distributions have been determined by three-dimensional (3D) as well as one-dimensional (1D) micromagnetic models for exchange-coupled Nd₂Fe₁₄B/α–Fe bilayers and carefully compared with each other. It is found that the results obtained from the two methods are consistent with each other, where the nucleation and coercive fields decrease monotonically as the soft layer thickness L^s increases whilst the largest maximum energy products (roughly 600 kJ/m³) occur at L^s=5 nm. Moreover, the calculated angular distributions in the thickness direction for the magnetic moments are similar. Nevertheless, the calculated critical fields and energy products by 3D OOMMF are systematically smaller than those given by the 1D model, mainly due to the local demagnetization fields, which are taken into account in the 3D calculation and ignored in the 1D calculation. It is demonstrated by the 3D calculation that the large demagnetization fields in the corners of the soft layers reduce the nucleation fields and thus facilitate the magnetic reversal. Such an effect enhances as L^s increases. When L^s=20 nm, the differences between the coercivity is as large as 30%, while the nucleation fields obtained by the two methods have opposite signs.     

Spontaneous breaking of supersymmetry and gauge invariance in supergravity

Using the new minimal auxiliary fields of N = 1 supergravity it is found possible to construct a model of local supersymmetry which spontaneously breaks both supersymmetry and gauge invariance. The status of the cosmological constant resulting from this breaking is discussed.     

Anisotropic pressure in dense neutron matter under the presence of a strong magnetic field

Dense neutron matter with recently developed BSk19 and BSk21 Skyrme effective forces is considered in magnetic fields up to ¹⁰²⁰ G at zero temperature. The breaking of the rotational symmetry by the magnetic field leads to the differentiation between the pressures along and perpendicular to the field direction which becomes significant in the fields H>Hth∼¹⁰¹⁸ G. The longitudinal pressure vanishes in the critical field ¹⁰¹⁸<Hc?¹⁰¹⁹ G, resulting in the longitudinal instability of neutron matter. For the Skyrme force fitted to the stiffer underlying equation of state (BSk21 vs. BSk19) the threshold Hth and critical Hc magnetic fields become larger. The longitudinal and transverse pressures as well as the anisotropic equation of state of neutron matter are determined under the conditions relevant for the cores of magnetars.     

Determination of the effective g-value of n-InAs by four-wave mixing spectroscopy

Spin resonant four-wave mixing of the radiation of two single frequency CO₂ lasers is observed in n-InAs. By this method the effective g-value of the material is determined in magnetic fields up to 6.5 T. The temperature of the sample is 1.5 K; the carrier concentration is 1.5 × 10¹⁶/cm³. The observed g-values lie between 14.7 at 0.5 T and 13.7 at 6.3 T and extrapolate to 15.0 at B = 0. We observed symmetric lineshapes at high magnetic fields with linewidths of the order of 1.3 kG corresponding to 0.9 cm^-1. At low magnetic fields the lines show an asymmetric shape with a steep decrease at the high field side of the resonance.     

Effective Field Theory for Fermi Systems in a Large N Expansion

A system of fermions with short-range interactions at finite density is studied using the framework of effective field theory. The effective action formalism for fermions with auxiliary fields leads to a loop expansion in which particle-hole bubbles are resummed to all orders. For spin-independent interactions, the loop expansion is equivalent to a systematic expansion in 1/N, where N is the spin-isospin degeneracy g. Numerical results at next-to-leading order are presented and the connection to the Bose limit of this system is elucidated.     

On Einstein four-manifolds

In this paper we obtain obstructions to the existence of Einstein metrics satisfying auxiliary sectional curvature bounds. In particular, we give sufficient conditions for a compact-oriented Einstein four-manifold M to be isometric to either the sphere S⁴ or the complex projective space CP². Also, we improve the Hitchin–Thorpe’s inequality which relates the Euler characteristic of M and its signature.