Vector Gauge Research Articles

Raman coupling in atomic Bose-Einstein condensed with phase-locked laser system

We present a simple, versatile and reliable phase-locked laser system. The system consists of an external cavity diode laser, Ti: Sapphire laser, fast detector, phase frequency detector (PFD) and loop filters. The beat signal of the laser is detected with a detector. From the PFD, we can obtain an error signal. The loop filter converts the output of the PFD into a control voltage and thus drives piezoelectric ceramic transducer (PZT) and current of diode laser. After locking, the bandwidth of the beat signal is reduced form MHz to Hz. So the line-width of the diode laser is almost close to that of Ti: Sapphire laser. The locking range is from sub-MHz to 10 GHz. So it is used for the ground hyperfine state transition of 87Rb. Through the use of the phase-locked loop system, we can drive the transition of 87Rb atoms between two ground hyperfine states F=2 and 1. The system is used to demonstrate Raman transition between two states through changing the detuning of the beat signal. From this, we can obtain Rabi frequency = 10 kHz. So, this system can be used to induce an effective vector gauge potential for 87Rb Bose-Einstein condensed and realize the spin-orbit coupling.

The Explanation for the Origin of the Higgs Scalar and for the Yukawa Couplings by the <i>Spin-Charge-Family</i> Theory

The spin-charge-family theory is a kind of the Kaluza-Klein theories, but with two kinds of the spin connection fields, which are the gauge fields of the two kinds of spins. The SO(13,1) representation of one kind of spins manifests in d = (3 + 1) all the properties of family members as assumed by the standard model; the second kind of spins explains the appearance of families. The gauge fields of the first kind, carrying the space index m = (0,...,3), manifest in d = (3 + 1) all the vector gauge fields assumed by the standard model. The gauge fields of both kinds of spins, which carry the space index (7, 8) gaining at the electroweak break nonzero vacuum expectation values, manifest in d = (3 + 1) as scalar fields with the properties of the Higgs scalar of the standard model with respect to the weak and the hyper charge ( and , respectively), while they carry additional quantum numbers in adjoint representations, offering correspondingly the explanation for the scalar Higgs and the Yukawa couplings, predicting the fourth family and the existence of several scalar fields. The paper 1) explains why in this theory the gauge fields are with the scalar index s = (5,6,7,8) doublets with respect to the weak and the hyper charge, while they are with respect to all the other charges in the adjoint representations; 2) demonstrates that the spin connection fields manifest as the Kaluza-Klein vector gauge fields, which arise from the vielbeins; and 3) explains the role of the vielbeins and of both kinds of the spin connection fields.

On the use of projection operators in electrodynamics

In classical electrodynamics all the measurable quantities can be derived from the gauge invariant Faraday tensor . Nevertheless, it is often advantageous to work with gauge dependent variables. In [, ] and [], and in the present paper too, the transformation of the vector potential in the Lorenz gauge to that in the Coulomb gauge is considered. This transformation can be done by applying a projection operator that extracts the transverse part of spatial vectors. In many circumstances the proper projection operator is replaced by a simplified transverse one. It is widely held that such a replacement does not affect the result in the radiation zone. In this paper the action of the proper and simplified transverse projections will be compared by making use of specific examples of a moving point charge. It will be demonstrated that whenever the interminable spatial motion of the source is unbounded with respect to the reference frame of the observer the replacement of the proper projection operator by the simplified transverse one yields, even in the radiation zone, an erroneous result with error which is of the same order as the proper Coulomb gauge vector potential itself.

On brane symmetries

The geometric approach to branes is reformulated in terms of gauge vector fields interacting with massless tensor multiplets in gravitational backgrounds

The Aharonov–Bohm effect and its stationary scattering states from the flat circular annulus U(1) holonomy

In this paper we study the stationary scattering problem of the Aharonov–Bohm (AB) effect. To achieve this goal we construct a Hamiltonian from the most general representations of the Heisenberg algebra. Such representations are defined on a non-simply-connected manifold which we set as the flat circular annulus. By means of the von Neumann's self-adjoint extensions formalism, the scattering data are then provided. No solenoid is considered in this paper. The corresponding Hamiltonian is based on a topological quantum degree of freedom inherent in such representations. This variable stands for the magnetic vector gauge potential at quantum level. Our outcomes confirm the topological nature of this effect.

Exceptional field theory. III.E8(8)

We develop exceptional field theory for E$_{8(8)}$, defined on a (3+248)-dimensional generalized spacetime with extended coordinates in the adjoint representation of E$_{8(8)}$. The fields transform under E$_{8(8)}$ generalized diffeomorphisms and are subject to covariant section constraints. The bosonic fields include an `internal' dreibein and an E$_{8(8)}$-valued `zweihundertachtundvierzigbein' (248-bein). Crucially, the theory also features gauge vectors for the E$_{8(8)}$ E-bracket governing the generalized diffeomorphism algebra and covariantly constrained gauge vectors for a separate but constrained E$_{8(8)}$ gauge symmetry. The complete bosonic theory, with a novel Chern-Simons term for the gauge vectors, is uniquely determined by gauge invariance under internal and external generalized diffeomorphisms. The theory consistently comprises components of the dual graviton encoded in the 248-bein. Upon picking particular solutions of the constraints the theory reduces to D=11 or type IIB supergravity, for which the dual graviton becomes pure gauge. This resolves the dual graviton problem, as we discuss in detail.

Minimal [formula omitted] supergravity models of inflation coupled to matter

The supersymmetric extension of “Starobinsky” R+αR2 models of inflation is particularly simple in the “new minimal” formalism of supergravity, where the inflaton has no scalar superpartners. This paper is devoted to matter couplings in such supergravity models. We show how in the new minimal formalism matter coupling presents certain features absent in other formalisms. In particular, for the large class of matter couplings considered in this paper, matter must possess an R-symmetry, which is gauged by the vector field which becomes dynamical in the “new minimal” completion of the R+αR2 theory. Thus, in the dual formulation of the theory, where the gauge vector is part of a massive vector multiplet, the inflaton is the superpartner of the massive vector of a nonlinearly realized R-symmetry. The F-term potential of this theory is of no-scale type, while the inflaton potential is given by the D-term of the gauged R-symmetry. The absolute minimum of the potential is always exactly supersymmetric, so in this class of models if realistic vacua exist, they must be always metastable. We also briefly comment on possible generalizations of the examples discussed here and we exhibit some features of higher-curvature supergravity coupled to matter in the “old minimal” formalism.

Hidden sector dark matter models for the Galactic Center gamma-ray excess

The gamma-ray excess observed from the Galactic Center can be interpreted as dark matter particles annihilating into Standard Model fermions with a cross section near that expected for a thermal relic. Although many particle physics models have been shown to be able to account for this signal, the fact that this particle has not yet been observed in direct detection experiments somewhat restricts the nature of its interactions. One way to suppress the dark matter's elastic scattering cross section with nuclei is to consider models in which the dark matter is part of a hidden sector. In such models, the dark matter can annihilate into other hidden sector particles, which then decay into Standard Model fermions through a small degree of mixing with the photon, Z, or Higgs bosons. After discussing the gamma-ray signal from hidden sector dark matter in general terms, we consider two concrete realizations: a hidden photon model in which the dark matter annihilates into a pair of vector gauge bosons that decay through kinetic mixing with the photon, and a scenario within the generalized NMSSM in which the dark matter is a singlino-like neutralino that annihilates into a pair of singlet Higgs bosons, which decay through their mixing with the Higgs bosons of the MSSM.

On gradient field theories: gradient magnetostatics and gradient elasticity

In this work, the fundamentals of gradient field theories are presented and reviewed. In particular, the theories of gradient magnetostatics and gradient elasticity are investigated and compared. For gradient magnetostatics, non-singular expressions for the magnetic vector gauge potential, the Biot–Savart law, the Lorentz force and the mutual interaction energy of two electric current loops are derived and discussed. For gradient elasticity, non-singular forms of all dislocation key formulas (Burgers equation, Mura equation, Peach–Koehler stress equation, Peach–Koehler force equation, and mutual interaction energy of two dislocation loops) are presented. In addition, similarities between an electric current loop and a dislocation loop are pointed out. The obtained fields for both gradient theories are non-singular due to a straightforward and self-consistent regularization.

Constraints on gauge field production during inflation

In order to gain new insights into the gauge field couplings in the early universe, we consider the constraints on gauge field production during inflation imposed by requiring that their effect on the CMB anisotropies are subdominant. In particular,we calculate systematically the bispectrum of the primordial curvature perturbation induced by the presence of vector gauge fields during inflation. Using a model independent parametrization in terms of magnetic non-linearity parameters, we calculate for the first time the contribution to the bispectrum from the cross correlation between the inflaton and the magnetic field defined by the gauge field. We then demonstrate that in a very general class of models, the bispectrum induced by the cross correlation between the inflaton and the magnetic field can be dominating compared with the non-Gaussianity induced by magnetic fields when the cross correlation between the magnetic field and the inflaton is ignored.

Self-interacting asymmetric dark matter coupled to a light massive dark photon

Dark matter (DM) with sizeable self-interactions mediated by a light species offers a compelling explanation of the observed galactic substructure; furthermore, the direct coupling between DM and a light particle contributes to the DM annihilation in the early universe. If the DM abundance is due to a dark particle-antiparticle asymmetry, the DM annihilation cross-section can be arbitrarily large, and the coupling of DM to the light species can be significant. We consider the case of asymmetric DM interacting via a light (but not necessarily massless) Abelian gauge vector boson, a dark photon. In the massless dark photon limit, gauge invariance mandates that DM be multicomponent, consisting of positive and negative dark ions of different species which partially bind in neutral dark atoms. We argue that a similar conclusion holds for light dark photons; in particular, we establish that the multi-component and atomic character of DM persists in much of the parameter space where the dark photon is sufficiently light to mediate sizeable DM self-interactions. We discuss the cosmological sequence of events in this scenario, including the dark asymmetry generation, the freeze-out of annihilations, the dark recombination and the phase transition which gives mass to the dark photon. We estimate the effect of self-interactions in DM haloes, taking into account this cosmological history. We place constraints based on the observed ellipticity of large haloes, and identify the regimes where DM self-scattering can affect the dynamics of smaller haloes, bringing theory in better agreement with observations. Moreover, we estimate the cosmological abundance of dark photons in various regimes, and derive pertinent bounds.

A confining model for charmonium and new gauge-invariant field equations

We discuss a confining model for charmonium in which the attractive force are derived from a new type of gauge field equation with a generalized $SU_3$ gauge symmetry. The new gauge transformations involve non-integrable phase factors with vector gauge functions $\om^a_{\mu}(x)$. These transformations reduce to the usual $SU_3$ gauge transformations in the special case $\om^a_\mu(x) = \p_\mu \xi^a(x)$. Such a generalized gauge symmetry leads to the fourth-order equations for new gauge fields and to the linear confining potentials. The fourth-order field equation implies that the corresponding massless gauge boson has non-definite energy. However, the new gauge boson is permanently confined in a quark system by the linear potential. We use the empirical potentials of the Cornell group for charmonium to obtain the coupling strength $f^2/(4\pi) \approx 0.19$ for the strong interaction. Such a confining model of quark dynamics could be compatible with perturbation. The model can be applied to other quark-antiquark systems.

Scalar gauge fields

In this paper we give a variation of the gauge procedure which employs a scalar gauge field, $B (x)$, in addition to the usual vector gauge field, $A_\mu (x)$. We study this variant of the usual gauge procedure in the context of a complex scalar, matter field $\phi (x)$ with a U(1) symmetry. We will focus most on the case when $\phi$ develops a vacuum expectation value via spontaneous symmetry breaking. We find that under these conditions the scalar gauge field mixes with the Goldstone boson that arises from the breaking of a global symmetry. Some other interesting features of this scalar gauge model are: (i) The new gauge procedure gives rise to terms which violate C and CP symmetries. This may have have applications in cosmology or for CP violation in particle physics; (ii) the existence of mass terms in the Lagrangian which respect the new extended gauge symmetry. Thus one can have gauge field mass terms even in the absence of the usual Higgs mechanism; (iii) the emergence of a sine-Gordon potential for the scalar gauge field; (iv) a natural, axion-like suppression of the interaction strength of the scalar gauge boson.

Local observables in a landscape of infrared gauge modes

Cosmological local observables are at best statistically determined by the fundamental theory describing inflation. When the scalar inflaton is coupled uniformly to a collection of subdominant massless gauge vectors, rotational invariance is obeyed locally. However, the statistical isotropy of fluctuations is spontaneously broken by gauge modes whose wavelength exceeds our causal horizon. This leads to a landscape picture where primordial correlators depend on the position of the observer. We compute the stochastic corrections to the curvature power spectrum, show the existence of a new local observable (the shape of the quadrupole), and constrain the theory using Planck limits.

Fractional fermion charges induced by axial-vector and vector gauge potentials and parity anomaly in planar graphenelike structures

We show that fermion charge fractionalization can take place in a recently proposed chiral gauge model for graphene even in the absence of Kekul\'e distortion in the graphene honeycomb lattice. In this model, electrons couple in a chiral way to a pseudomagnetic field with a vortex profile in such a way that it can be used to describe the influences of topological defects, such as disclinations, on the electronic states. We also extend the model by adding the coupling of fermions to an external magnetic field and show that the fermion charge can be fractionalized by means of only gauge potentials. It is shown that the chiral fermion charge can also have fractional value. We also relate the fractionalization of the fermion charge to the parity anomaly in an extended quantum electrodynamics, which involves vector and axial-vector gauge fields.

Retarded Fields of Null Particles and the Memory Effect

We consider the retarded solution to the scalar, electromagnetic, and linearized gravitational field equations in Minkowski spacetime, with source given by a particle moving on a null geodesic. In the scalar case and in the Lorenz gauge in the electromagnetic and gravitational cases, the retarded integral over the infinite past of the source does not converge as a distribution, so we cut off the null source suitably at a finite time ${t}_{0}$ and then consider two different limits: (i) the limit as the observation point goes to null infinity at fixed ${t}_{0}$, from which the ``$1/r$'' part of the fields can be extracted and (ii) the limit ${t}_{0}\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$ at fixed ``observation point.'' The limit (i) gives rise to a ``velocity kick'' on distant test particles in the scalar and electromagnetic cases, and it gives rise to a ``memory effect'' (i.e., a permanent change in relative separation of two test particles) in the linearized gravitational case, in agreement with previous analyses. As already noted, the second limit does not exist in the scalar case or for the Lorenz gauge vector potential and Lorenz gauge metric perturbation in the electromagnetic and linearized gravitational cases. However, in the electromagnetic case, we obtain a well-defined distributional limit for the electromagnetic field strength, and in the linearized gravitational case, we obtain a well-defined distributional limit for the linearized Riemann tensor. In the gravitational case, this limit agrees with the Aichelberg-Sexl solution. There is no memory effect associated with this limiting solution. This strongly suggests that the memory effect---including nonlinear memory effect of Christodoulou---should not be interpreted as arising simply from the passage of (effective) null stress energy to null infinity but rather as arising from a ``burst of radiation'' associated with the creation of the null stress energy [as in case (i) above] or, more generally, with radiation present in the spacetime that was not ``produced'' by the null stress energy.

Statistics of anisotropies in inflation with spectator vector fields

We study the statistics of the primordial power spectrum in models where massless gauge vectors are coupled to the inflaton, paying special attention to observational implications of having fundamental or effective horizons embedded in a bath of infrared fluctuations. As quantum infrared modes cross the horizon, they classicalize and build a background vector field. We find that the vector experiences a statistical precession phenomenon. Implications for primordial correlators and the interpretation thereof are considered. Firstly, we show how in general two, not only one, additional observables, a quadrupole amplitude and an intrinsic shape parameter, are necessary to fully describe the correction to the curvature power spectrum, and develop a unique parametrization for them. Secondly, we show that the observed anisotropic amplitude and the associated preferred direction depend on the volume of the patch being probed. We calculate non-zero priors for the expected deviations between detections based on microwave background data (which probes the entire Hubble patch) and large scale structure (which only probes a fraction of it).

Localization of gauge fields in a tachyonic de Sitter thick braneworld

In this work we show that universal gauge vector fields can be localized on the recently proposed 5D thick tachyonic braneworld which involves a de Sitter cosmological background induced on the 3-brane. Namely, by performing a suitable decomposition of the vector field, the resulting 4D effective action corresponds to a massive gauge field, while the profile along the extra dimension obeys a Schroedinger-like equation with a Poeschl-Teller potential. It turns out that the massless zero mode of the gauge field is bound to the expanding 3-brane and allows us to recover the standard 4D electromagnetic phenomena of our world. Moreover, this zero mode is separated from the continuum of Kaluza-Klein (KK) modes by a mass gap determined by the scale of the expansion parameter. We also were able to analytically solve the corresponding Schroedinger-like equation for arbitrary mass, showing that KK massive modes asymptotically behave like plane waves as expected.

Exceptional field theory. II.E7(7)

We introduce exceptional field theory for the group E_{7(7)}, based on a (4+56)-dimensional spacetime subject to a covariant section condition. The `internal' generalized diffeomorphisms of the coordinates in the fundamental representation of E_{7(7)} are governed by a covariant `E-bracket', which is gauged by 56 vector fields. We construct the complete and unique set of field equations that is gauge invariant under generalized diffeomorphisms in the internal and external coordinates. Among them feature the non-abelian twisted self-duality equations for the 56 gauge vectors. We discuss the explicit solutions of the section condition describing the embedding of the full, untruncated 11-dimensional and type IIB supergravity, respectively. As a new feature compared to the previously constructed E_{6(6)} formulation, some components among the 56 gauge vectors descend from the 11-dimensional dual graviton but nevertheless allow for a consistent coupling by virtue of a covariantly constrained compensating 2-form gauge field.

Dark Forces at KLOE/KLOE-2

Searches for dark matter particles in the GeV mass range and for dark forces are strongly motivated by the numerous striking astrophysical observations recently re- ported by many experiments. Flavor factories, like the Frascati Φ-factory DAΦNE, are particularly suited to search for the light gauge vector boson, called U boson, which is thought to mediate an unknown interaction between hypothetical dark matter particles. By using the KLOE detector, limits on U boson coupling factor e 2 of the order of 10 −5 ÷ 10 −7 have been set through the study of the φ Dalitz decay, the Higgsstrahlung process and Uγ events. New experiments with the upgraded KLOE detector and the increased luminosity of DAΦNE are expected to improve the already set upper limits by a factor of two or better.