Vector Gauge Research Articles

Electric field-based quantization of the gauge invariant Proca theory

We consider the gauge invariant version of the Proca theory, where besides the real vector field there is also the real scalar field. We quantize the theory such that the commutator of the scalar field operator and the electric field operator is given by a predefined three-dimensional vector field, say $\cal E$ up to a global prefactor. This happens when the field operators of the gauge invariant Proca theory satisfy the proper gauge constraint. In particular, we show that $\cal E$ given by the classical Coulomb field leads to the Coulomb gauge constraint making the vector field operator divergenceless. We also show that physically unreadable gauge constraints can have a strikingly simple $\cal E$-representation in our formalism. This leads to the discussion of Debye, Yukawa, etc. gauges. In general terms, we explore the mapping between classical vector fields and gauge constraints imposed on the operators of the studied theory.

Drell-Yan production in third-generation gauge vector leptoquark models at NLO+PS in QCD

Motivated by the long-standing hints of lepton-flavour non-universality in the b → cℓν and b → sℓ+ℓ− channels, we study Drell-Yan ditau production at the Large Hadron Collider (LHC). In the context of models with third-generation gauge vector leptoquarks (LQs), we calculate the complete mathcal{O} (αs) corrections to the pp → τ+τ− process, achieving next-to-leading order (NLO) plus parton shower (NLO+PS) accuracy using the POWHEG method. We provide a dedicated Monte Carlo code that evaluates the NLO QCD corrections on-the-fly in the event generation and use it to study the numerical impact of NLO+PS corrections on the kinematic distributions that enter the existing experimental searches for non-resonant ditau final states. Based on our phenomenological analysis we derive NLO accurate constraints on the masses and couplings of third-generation gauge vector LQs using the latest LHC ditau search results corresponding to an integrated luminosity of around 140 fb−1 of proton-proton collisions at sqrt{s} = 13 TeV. The presented NLO+PS generator allows for an improved signal modelling, making it an essential tool for future ATLAS and CMS searches for vector LQs in τ+τ− final states at LHC Run III and beyond.

Novel effects of the W-boson mass shift in the 3-3-1 model

The recent precision measurement of the W-boson mass reveals an exciting hint for the new physics as of the 3-3-1 model. We indicate that the 3-3-1 model contains distinct sources by itself that may cause the W-mass deviation, as measured, such as the tree-level Z-Z' mixing, the tree-level W-Y and Z-Z'-X mixings, as well as the non-degenerate gauge vector (X, Y) and new Higgs doublets. We point out that the gauge vector doublet negligibly contributes to this mass shift, whereas the rest of the effects with tree-level mixings governed by Z-Z' and new Higgs doublets are significant. A discussion of scalar sextet contributions is also given.

Gauge field localization in branes: coupling to a scalar function and coupling to torsion in teleparallel gravity scenario

This paper is aimed at investigating the behavior of gauge vector and tensor fields on thick brane in f(T) gravity. This thick brane is not capable of providing a normalizable zero mode for both gauge and Kalb Ramond fields. To overcome this problem, we propose two distinct types of gauge-invariant couplings. In the first coupling, the fields are minimally coupled to the scalar field responsible for generating the thick brane. In the second coupling, we use the geometric coupling in which the fields are non-minimally coupled to torsion. Another issue that we investigate is resonant modes, which allow us to understand the massive spectrum of fields. Indeed we note that an internal structure appears for the Kalb–Ramond massive solutions and both couplings show resonant modes of the massive spectrum.

Merging of Dirac points through uniaxial modulation on an optical lattice

We analyze the scenario of modulating the potential strength of bound atoms in an optical honeycomb lattice patterned by an electric field to emulate uniaxial strain. This modulation can be achieved by a combination of the strength of the patterned electric field and gauge vector effects using the Floquet approach. We show that such a modulation allows one to follow through a topological transition between a semi-metal and a band insulator, when two non-equivalent K points merge as a function of the electric field strength. We explicitly compute the wavefunctions for the moving K points and the Chern numbers up to the transition. Anisotropic effective masses and the insulating gap are described close to the semimetal-insulator transition.

Lifshitz gauge duality

Motivated by variety of realizations of the compact Lifshitz model, I predict and explore properties of its three phases, study its phase transitions and derive its fractonic gauge dual. The resulting U(1) vector gauge theory efficiently and robustly encodes the restricted mobility of its dipole conserving charged matter and the corresponding topological vortex defects. The gauge theory provides a transparent formulation of the three phases of the Lifshitz model and gives a field theoretic formulation of the associated two-stage Higgs transitions.

Exploring HVV amplitudes with CP violation using decomposition and the on-shell scattering amplitude method* *Supported by the National Natural Science Foundation of China ( 11847168), the Fundamental Research Funds for the Central Universities of China (GK202003018) and the Natural Science Foundation of Shannxi Province, China (2019JM-431, 2019JQ-739)

violation may play an important role in baryogenesis in the early universe and should be examined comprehensively at colliders. We study the properties of vertexes between Higgs and gauge boson pairs by defining a violation phase angle ξ, which indicates the mixture of -even and -odd Higgs states in in new physics. A series of amplitudes, , and , with a phase angle are studied systematically to explicitly explain why violation can only be probed independently in the process. We obtain a novel amplitude decomposition relation that illustrates that if two preconditions (multilinear momentum dependent vertexes, and the current of is formally proportional to a photon's polarization vector) are satisfied, a higher-point amplitude can be decomposed into a summation of a series of lower-point amplitudes. As a practical example, the amplitude of the and processes can be decomposed into a summation of many amplitudes. We calculate these amplitudes in the framework of the on-shell scattering amplitude method, considering both massless and massive vector gauge bosons with the violation phase angle. The above two approaches provide consistent results and clearly reveal the violation ξ dependence in the amplitudes.

Quantum electrodynamics in the null-plane causal perturbation theory. II.

We develop a complete formulation of quantum gauge invariance in light-front dynamics for interacting theories with massless vector gauge fields in the framework of null-plane causal perturbation theory. We apply the general results to quantum electrodynamics, showing that the so-called "gauge terms" present in the photon commutation distribution when quantized under the null-plane gauge condition have no contribution in the calculation of the physical S-operator matrix elements at any order. We use this result to prove the normalizability of the theory, and to calculate the electron's self-energy at second order.

Constraints on ultralight axions, vector gauge bosons, and unparticles from geodetic and frame-dragging measurements

The geodetic and frame-dragging effects are the direct consequences of the spacetime curvature near Earth which can be probed from the Gravity probe B (GP-B) satellite. The satellite result matches quite well with Einstein’s general relativistic result. The gyroscope of the satellite which measures the spacetime curvature near Earth contains lots of electrons and nucleons. Ultralight axions, vector gauge bosons, and unparticles can interact with these electrons and nucleons through different spin-dependent and spin-independent operators and change the drift rate of the gyroscope. Some of these ultralight particles can either behave as a long range force between some dark sector or Earth and the gyroscope or they can behave as a background oscillating dark matter fields or both. These ultralight particles can contribute an additional precession of the gyroscopes, limited to be no larger than the uncertainty in the GP-B measurements. Compared with the experimental results, we obtain bounds on different operator couplings.

Sphere on a plane: Two-dimensional scattering from a finite curved region

Non-relativistic particles that are effectively confined to two dimensions can in general move on curved surfaces, allowing dynamical phenomena beyond what can be described with scalar potentials or even vector gauge fields. Here we consider a simple case of piecewise uniform curvature: a particle moves on a plane with a spherical extrusion. Depending on the latitude at which the sphere joins the plane, the extrusion can range from an infinitesimal bump to a nearly full sphere that just touches the plane. Free classical motion on this surface of piecewise uniform curvature follows geodesics that are independent of velocity, while quantum mechanical scattering depends on energy. We compare classical, semi-classical, and fully quantum problems, which are all exactly solvable, and show how semi-classical analysis explains the complex quantum differential cross section in terms of interference between two classical trajectories: the sphere on a plane acts as a kind of double slit.

Conformal metric-affine gravities

We revisit the gauge symmetry related to integrable projective transformations in metric-affine formalism, identifying the gauge field of the Weyl (conformal) symmetry as a dynamical component of the affine connection. In particular, we show how to include the local scaling symmetry as a gauge symmetry of a large class of geometric gravity theories, introducing a compensator dilaton field that naturally gives rise to a Stückelberg sector where a spontaneous breaking mechanism of the conformal symmetry is at work to generate a mass scale for the gauge field. For Ricci-based gravities that include, among others, General Relativity, f(R) and f(R, R μν R μν) theories and the EiBI model, we prove that the on-shell gauge vector associated to the scaling symmetry can be identified with the torsion vector, thus recovering and generalizing conformal invariant theories in the Riemann-Cartan formalism, already present in the literature.

Scalar and vector gauges unification in de Sitter ambient space formalism

We consider the massless minimally coupled scalar field in the de Sitter ambient space formalism as a gauge potential or connection field. We construct the scalar gauge theory by helping an arbitrary constant five-vector field Bα analogous to the standard gauge theory. The Lagrangian density of the interaction between the scalar and spinor fields is presented in this framework. The Yukawa potential can be extracted from this Lagrangian density at the null curvature limit by an appropriate choice of a constant five-vector field. It is shown that the de Sitter ambient space formalism permits us to unify the scalar and vector gauge fields. By choosing a matrix form for the constant five-vector field Bα, the unification of scalar and vector gauge fields in the spectral action of noncommutative geometry can be rewritten. We discuss that if the scalar gauge field is considered as a conformal sector of the background metric field, it may be interpreted as the connection field between the different de Sitter hyperboloids in the quantum geometry from the classical point of view.

Fundamental forces and their dynamics

In this essay, we wish to propose a general principle: the equation of motion or dynamics of a fundamental force should not be prescribed but instead be entirely driven by geometry of the appropriate spacetime manifold, and the equation is then obtained by employing only the geometric property without appeal to an action. The motivation for this pronouncement comes from the fact that the equation of motion of general relativity follows from the geometry of Riemannian spacetime manifold without appeal to anything else from outside. The driving differential geometric property is the Bianchi identity satisfied by the Riemann curvature tensor. Similarly it is geometry of the principal tangent bundle of fibre spacetime manifold that may account for dynamics of the gauge vector fields. It is the classical electric force for the Abelian gauge symmetry group while the non-Abelian symmetry leads to the non-Abelian forces, the weak and the strong. We shall also reflect on a unified picture of the basic forces, and the duality correspondences it may inspire.

Stueckelberg and Higgs Mechanisms: Frames and Scales

We consider Yang–Mills theory with a compact gauge group G on Minkowski space R3,1 and compare the introduction of masses of gauge bosons using the Stueckelberg and Higgs mechanisms. The Stueckelberg field ϕ is identified with a G-frame on the gauge vector bundle E and the kinetic term for ϕ leads to the mass of the gauge bosons. The Stueckelberg mechanism is extended to the Higgs mechanism by adding to the game a scalar field describing rescaling of metric on fibres of E. Thus, we associate Higgs fields as well as running coupling parameters with conformal geometry on fibres of gauge bundles. In particular, a running coupling tending to zero or to infinity is equivalent to an unbounded expansion of G-fibres or its contraction to a point. We also discuss scale connection, space-time dependent Higgs vacua and compactly supported gauge and quark fields as an attribute of confinement.

Dual description of gauge theories from an iterative Noether approach

An iterative Noether scheme, advocated by Deser, is used to introduce gauge invariant couplings to nonrelativistic matter with global symmetries related to usual charge conservation and dipole conservation recently discussed in fractonic theories. No reference to any gauge principle, fractonic or otherwise, is required. A dual description is found where the theory is defined either in terms of the usual vector gauge field or, alternatively, in terms of higher derivatives of a symmetric tensor field given in fractonic theories. A connection between these two descriptions is obtained by providing an explicit map between the vector and tensor fields. This method yields a novel ‘minimal’ prescription involving tensor fields which is identified with the usual minimal prescription that involves vector fields, by using the mapping. It also spells out the structure of the pure gauge field action in both formulations. Extension of the abelian U(1) invariance to the nonabelian SU(N) invariance is done for the standard formulation.

Nonperturbative renormalization of the lattice Sommerfield vector model

The lattice Sommerfield model, describing a massive vector gauge field coupled to a light fermion in 2d, is an ideal candidate to verify perturbative conclusions. In contrast with continuum exact solutions, we prove that there is no infinite field renormalization, implying the reduction of the degree of the ultraviolet divergence, and that anomalies are non renormalized. Such features are the counterpart of analogue properties at the basis of the Standard model perturbative renormalizability. The results are non-perturbative, in the sense that the averages of gauge invariant observables are expressed in terms of convergent expansions uniformly in the lattice and volume.

Massive gauge particles versus Goldstone bosons in non-Hermitian non-Abelian gauge theory

We investigate the Englert–Brout–Higgs–Guralnik–Hagen–Kibble mechanism for non-Hermitian field theories with local non-Abelian gauge symmetry in different regions of their parameter spaces. We demonstrate that the two aspects of the mechanism, that is giving mass to gauge vector bosons and at the same time preventing the existence of massless Goldstone bosons, remain to be synchronized in all regimes characterized by a modified CPT symmetry. In the domain of parameter space where the “would be Goldstone bosons” can be identified the gauge vector bosons become massive and the Goldstone bosons cease to exist. The mechanism is also in tact at the standard exceptional points. However, at the zero exceptional points, that is when the eigenvalues of the mass squared matrix vanish irrespective of the symmetry breaking, the mechanism breaks down as the Goldstone bosons cannot be identified and the gauge vector bosons remain massless. This breakdown coincides with the vanishing of the CPT inner product of symmetry breaking vacua defined on the eigenvector space of mass squared matrix. We verify this behaviour for a theory with SU(2) symmetry in which the complex scalar fields are taken in the fundamental as well as in the adjoint representation.

Double copy of spontaneously broken Abelian gauge theory

Similarity in the structure of scattering amplitudes in Yang-Mills theories and General Relativity led to the idea that graviton could be described as the double copy of a vector gauge field. In this letter we discuss a realization of this idea emerging directly from solutions of equations of General Relativity. A general form of the energy momentum tensor for the electric field is derived that leads to the metric tensor in terms of the double copy of a corresponding gauge potential. We then use this general property to find the double copy of spontaneously broken scalar electrodynamics. The result is a screened Reissner-Nordström-like metric. When the horizon radius and the Compton wavelength of the massive photon become comparable the black hole becomes a quantum object. An exact solution of the horizon wave equation is found and the corresponding energy spectrum is described. It turns out that highly excited states show a characteristic string-like behavior.

Two-point functions from chiral kinetic theory in magnetized plasma

We study the two-point functions from chiral kinetic theory which characterize the response to perturbative vector and axial gauge fields in magnetized chiral plasma. In the lowest Landau level approximation, the solution of chiral kinetic equations gives density waves of electric and axial charges, which contain chiral magnetic wave implied by the axial anomaly and magnetic field. We then obtain the constitutive relations for covariant currents and stress tensor that involving the density waves. By considering the difference between consistent and covariant anomalies explicitly, the correlators of consistent currents and stress tensor satisfy derivative symmetry, and therefore allow an effective action for the perturbative gauge fields as the generating functional of the correlators. We also verify the derivative symmetry of the correlators agrees with the Onsager relations.

Quantum Yang-Mills theory in de Sitter ambient space formalism

We present the quantum Yang-Mills theory in the four-dimensional de Sitter ambient space formalism. In accordance with the SU(3) gauge symmetry the interaction Lagrangian is formulated in terms of interacting color charged fields in curved space-time. The gauge-invariant field equations are obtained in an independent coordinate description, and their corresponding color conserved currents are computed. It is shown that the Faddeev-Popov ghost fields appear similarly to their Minkowskian counterparts. We obtain that the free ghost fields are massless minimally coupled scalar fields. The problems of the vacuum state, namely the breaking of de Sitter invariance, and the appearance of infrared divergence in its quantization procedure, are discussed. The existence of an axiomatic quantum Yang-Mills theory within the framework of the Krein space quantization is examined. The infrared divergence regularization of the interaction between the gauge vector fields and the ghost fields is studied in the one-loop approximation. Two different regularization methods are discussed: cut-off regularization and Krein space regularization. A mass term for the gauge vector fields is obtained, which may explain the mass gap and the color confinement problems at the quantum level in de Sitter background. The large curvature limit at the early universe or inflationary epoch is considered.