Weyl’s Gauge Argument

The standard $\mathbb{U}(1)$ “gauge principle” or “gauge argument” produces an exact potential A=dλ and a vanishing field F=d ² λ=0. Weyl (in Z. Phys. 56:330–352, 1929; Rice Inst. Pam. 16:280–295, 1929) has his own gauge argument, which is sketchy, archaic and hard to follow; but at least it produces an inexact potential A and a nonvanishing field F=dA≠0. I attempt a reconstruction.     

Gauge invariant quark Green’s functions with polygonal Wilson lines

Properties of gauge invariant two-point quark Green’s functions, defined with polygonal Wilson lines, are studied. The Green’s functions can be classified according to the number of straight line segments their polygonal lines contain. Functional relations are established between the Green’s functions with different numbers of segments on the polygonal lines. An integrodifferential equation is obtained for the Green’s function with one straight line segment, in which the kernels are represented by a series of Wilson loop vacuum averages along polygonal contours with an increasing number of segments and functional derivatives on them. The equation is exactly solved in the case of two-dimensional QCD in the large-N _c limit. The spectral properties of the Green’s function are displayed.     

Supersymmetric U（1） Gange Field Theory with Massive Gauge Field

A new mechanism to introduce the mass of U(1) gauge field in supersymmetric U(1) gauge theory is discussed.The model has the strict local U(1) gauge symmetry and supersymmetry.Because we introduce two vector superfields simultaneously,the model contains a massive U(1) gauge field as well as a massless U(1) gauge field.     

Gauge boson masses and lepton mixing inO(4)⊗U(1) gauge model

The Cabibbo angle is introduced as a mixing angle of the gauge bosonsW ^± andX ^± in anO(4)?U(1) gauge model. Masses of gauge bosons are calculated to beM _W=82 (input), \(M_z = \sqrt 2 M_W s\gamma = 130\) (γ is mixing angle, sin² γ=0.21),M _x=666, andM _Y=660, in units GeV. TheW _μ ^± andZ _μ ⁰ couple to the familiar charged and neutral currents, respectively. The effective neutrino oscillation angle is found to be the Cabibbo angle.     

Effective Action for Noncommutative U（1） Gauge Theory with Higher Dimensional Terms

In this paper we apply the assumption of our recent work in noncommutative scalar models to the noncommutative U（1） gauge theories. This assumption is that the noneommutative effects start to be visible continuously from a scale ANC and that below this scale the theory is a commutative one. Based on this assumption and using background field method and loop calculations, an effective action is derived for noncommutative U（1） gauge theory. It will be shown that the corresponding low energy effective theory is asymptotically free and that under this condition the noncommutative quadratic IR divergences will not appear. The effective theory contains higher dimensional terms, which become more important at high energies. These terms predict an elastic photon-photon scattering due to the noncommutativity of space. The coefficients of these higher dimensional terms also satisfy a positivity constraint indicating that in this theory the related diseases of superluminal signal propagating and bad analytic properties of S-matrix do not exist. In the last section, we will apply our method to the noncommutative extra dimension theories.     

Schrödinger’s Equation with Gauge Coupling Derived from a Continuity Equation

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ? S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out.     

Decomposition of Noncommutative U（1） Gauge Potential

We investigate the decomposition of noncommutative gauge potential Ai, and find that it has inner structure, namely, Ai can be decomposed in two parts, bi and αi, where bi satisfies gauge transformations while αi satisfies adjoint transformations, so dose the Seiberg-Witten mapping of noncommutative U（1） gauge potential. By means of Seiberg-Witten mapping, we construct a mapping of unit vector field between noncommutative space and ordinary space, and find the noncommutative U（1） gauge potential and its gauge field tensor can be expressed in terms of the unit vector field. When the unit vector field has no singularity point, noncommutative gauge potential and gauge field tensor will equal ordinary gauge potential and gauge field tensor     

A model with flavor-dependent gauged U(1)_(B-L_1)×U(1)_(B-L_2-L_3) symmetry

We propose a new model with flavor-dependent gauged U(1)_(B-L_1)×U(1)_(B-L_2-L_3) symmetry in addition to the flavor-blind symmetry in the Standard Model. The model contains three right-handed neutrinos to cancel gauge anomalies and several Higgs bosons to construct the measured fermion masses. We show the generic features of the model and explore its phenomenology. In particular, we discuss the current bounds on the extra gauge bosons from the K and B meson mixings as well as the LEP and LHC data, and focus on their contributions to the lepton flavor violating processes of ?_(i+1) →?_iγ(i=1,2).     

Relation of Poisson’s ratio on average with Young’s modulus. Auxetics on average

A linear relation between the Poisson’s ratio averaged along the transverse directions and Young’s modulus of the tensed cubic crystal is established. It is found that the coefficients of the linear relation in the dimensionless form depend on two dimensionless elastic parameters combined from three compliance coefficients. By virtue of this fact, the form of angular regions of the crystal orientation with negative Poisson’s ratio on average varies as the magnitude of one dimensionless coefficient and the sign of the other one. We find the critical value of the dimensionless parameter at which there is the topological change in the structure of the angular regions occurs is established.     

SU(2) ×U(1) Gauge theory of bosonic and fermionic fields inS 3 ×R space-time

The tetradic Lorentz-gauge invariant formulation of the SU(2) × U(1) theory in S³ × R space-time is presented and the general gauge covariant Dirac-Klein-Gordon-Maxwell-Yang-Mills equations are derived. A direct comparison of these equations to those of the SU(2) × U(1) gauge theory on Minkowskian background points out major differences effectively induced by the minimally coupling to S³ × R gravity.     

U(1)×U(1) quaternionic metrics from harmonic superspace

We construct, using harmonic superspace and the quaternionic quotient approach, a quaternionic-Kähler extension of the most general two centres hyper-Kähler metric. It possesses U(1)×U(1) isometry, contains as special cases the quaternionic-Kähler extensions of the Taub-NUT and Eguchi–Hanson metrics and exhibits an extra one-parameter freedom which disappears in the hyper-Kähler limit. Some emphasis is put on the relation between this class of quaternionic-Kähler metrics and self-dual Weyl solutions of the coupled Einstein–Maxwell equations. The relation between our explicit results and the recent general ansatz of Calderbank and Pedersen for quaternionic-Kähler metrics with U(1)×U(1) isometries is traced in detail.     

A Note on Fick’s Law with Phase Transitions

Journal of Statistical Physics - We characterize the non equilibrium stationary states in two classes of systems where phase transitions are present. We prove that the interface in the limit is a...     

Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter

The present study deals with a spatially homogeneous and anisotropic Bianchi type-I (B-I) cosmological models representing massive strings in normal gauge for Lyra’s manifold by applying the variation law for generalized Hubble’s parameter that yields a constant value of deceleration parameter. The variation law for Hubble’s parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential-law type. Using these two forms, Einstein’s modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier, P.S.: Phys. Rev. D 28, 2414 (1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component s¹ ₁\sigma^{1}_{~1} of the shear tensor s^j _i\sigma^{j}_{~i}. This condition leads to A=(BC) ^m , where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the both decelerating and accelerating universes. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.     

A New Class of Inhomogeneous Cosmological Models with Electromagnetic Field in Normal Gauge for Lyra’s Manifold

A new class of exact solutions of Einstein’s modified field equations in inhomogeneous space-time for perfect fluid distribution with electromagnetic field is obtained in the context of normal gauge for Lyra’s manifold. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F ₁₂ is a non-vanishing component of the electromagnetic field tensor. It has been found that the displacement vector β(t) behaves like the cosmological constant Λ in the normal gauge treatment and the solutions are consistent with the recent observations of Type Ia supernovae. Physical and geometric aspects of the models are also discussed in the presence of magnetic field.     

Phase diagram of planar U(1)×U(1) superconductor: Condensation of vortices with fractional flux and a superfluid state

We discuss a phase diagram of two-dimensional U(1)×U(1) superconductor in the field theoretic formalizm of [Phys. Rev. Lett. 89 (2002) 067001]. In particular we discuss that when penetration length is short the system exhibit a quasi-neutral quasi-superfluid state which is a state when quasi-long range order sets in only in phase difference while individually the phases are disordered.     

Constrained Correlation Dynamics of SU(N) Gauge Theories in Canonical Form (Ⅱ) Gauge Constrained Conditions

In this paper, gauge constrained conditions and quantization of SU(N) gauge theories are analysed by means of Dirac's formalism. In the framework of algebraic dynamics, gauge invariance, Gauss law and Ward identities are discussed. With use of the version of conservation law in correlation dynamics, the conserved Gauss law and Ward identities related to residual gauge invariance can be transformed into initial value problems.     

It?’s Lemma with Quantum Calculus (q-Calculus): Some Implications

q-derivatives are part of so called quantum calculus. In this paper we investigate how such derivatives can possibly be used in It?’s lemma. This leads us to consider how such derivatives can be used in a social science setting. We conclude that in a It? Lemma setting we cannot use a macroscopic version of the Heisenberg uncertainty principle with q-derivatives.