Lorentz Gauge Research Articles

Lorenz gauge formulation for time-dependent density functional theory

We describe the inclusion of electrodynamic fields in Time-Dependent Density Functional Theory (TDDFT) by incorporating both the induced scalar and vector potentials within the time-dependent Kohn-Sham equation. The Hamiltonian is described in both the Coulomb and Lorenz gauges, and the advantages of the latter are outlined. Integral expressions are defined for the retarded potentials of each gauge and a methodological approach to evaluate these nontrivial expressions with low computational cost is adopted. Various molecular structures of relatively small sizes are studied, including water, benzene, and conductive carbon chains. Absorption cross sections resulting from both pulse and boost excitations suggest a preserved gauge-invariance of the proposed formal approach to TDDFT in the weak magnetic field limit.

Search for the K L → π 0 γ decay in the KOTO experiment

We report a preliminary result of a new search for the K L → π 0 γ decay, which is forbidden by the Lorentz invariance and gauge principle. The search was carried out using the data obtained from 2016 to 2018 at the J-PARC proton beam facility using the KOTO detector. The achieved single event sensitivity was (6.9 ± 0.3stat. ± 1.5syst.) × 10−8. No signal candidate was found in the signal region and the upper limit was set to B(K L → π 0 γ) < 1.7 × 10−7 at the 90% con dence level.

Stabilization Results for Well-Posed Potential Formulations of a Current-Controlled Piezoelectric Beam and Their Approximations

Hysteresis is highly undesired for the vibration control of piezoelectric beams especially in high-precision applications. Current-controlled piezoelectric beams cope with hysteresis substantially in comparison to the voltage-controlled counterparts. However, the existing low fidelity current-controlled beam models are finite dimensional, and they are either heuristic or mathematically over-simplified differential equations. In this paper, novel infinite-dimensional models, by a thorough variational approach, are introduced to describe vibrations on a piezoelectric beam. Electro-magnetic effects due to Maxwell’s equations factor in the models via the electric and magnetic potentials. Both models are written in the standard state-space formulation (A, B, C), and are shown to be well-posed in the energy space by fixing the so-called Coulomb and Lorenz gauges. Different from the voltage-actuated counterparts, the control operator B is compact in the energy space, i.e. the exponential stabilizability is not possible. Considering the compact $$C=B^*-$$type state feedback controller (induced voltage), both models fail to be asymptotically stable if the material parameters satisfy certain conditions. To achieve at least asymptotic stability, we propose an additional controller. Finally, the stabilizability of infinite-dimensional electrostatic/quasi-static model (no magnetic effects) is analyzed for comparison. The biggest contrast is that the asymptotic stability is achieved by an electro-mechanical state feedback controller for all material parameters. Our findings are simulated by the filtered semi-discrete Finite Difference Method.

Long range scattering for the Maxwell–Schrödinger system in the Lorenz gauge without any restriction on the size of data

This paper concerns the scattering theory for the Maxwell–Schrödinger (MS) system in the Lorenz gauge, or more precisely, the existence of the modified wave operators for this system in R3+1 space-time. We construct solutions to the MS system which behave as free Maxwell and Schrödinger waves with prescribed asymptotic states when t→∞, without any restriction on the size thereof. Since this system belongs to the borderline between the short range case and the long range case, we need modification of phase for the Schrödinger function.

On the link between the Maxwell and linearised Einstein equations on Schwarzschild

In this short note we shall demonstrate that given a smooth solution to the linearised Einstein equations on Schwarzschild which is supported on the spherical harmonics and expressed relative to a transverse and traceless gauge then one can construct from it a smooth solution to the sourced Maxwell equations expressed relative to a generalised Lorenz gauge. Here the Maxwell current is constructed from those gauge-invariant combinations of the components of which are determined by solutions to the Regge–Wheeler and Zerilli equations. The result thus provides an elegant link between the spin 1 and spin 2 equations on Schwarzschild. We in addition outline how one can apply this result to establish a decay statement for solutions to the linearised Einstein equations on Schwarzschild that are in a transverse and traceless gauge.

Homogenized Dyadic Potential Green’s Function for Planar Metasurface Placed at Two Half Spaces Interface Excited by Vertical and Horizontal Ideal Electric Dipole

In this article, dyadic magnetic vector potential Green’s functions corresponding to electric dipole which illuminates homogenized metasurface have been presented. Metasurface is constructed by a periodic arrangement of planar metallic scatterers and located at the interface of two different dielectric half spaces. The metasurface is replaced by a thin sheet with the dyadic equivalent surface distribution of electric and magnetic susceptibilities. These vector potentials have been derived employing generalized sheet transition condition (GSTC) on the plane of the metasurface. The retrieval relations to obtain equivalent surface susceptibilities of such a surface are calculated by means of the calculated reflection and transmission coefficients due to TE polarized plane waves. Also, the transverse and longitudinal scalar electric potentials relative to the problem have been calculated with the aid of the Lorentz gauge. These vector and scalar potentials together are necessary to use in the mixed potential integral equation (MPIE) formulation of the method of moment (MoM) in an electromagnetic problem.

Lorenz gauge, electric and magnetic fields study of interaction of gravitationally accelerating ions through the super contorted 'tubular' polar areas of magnetic fields and hassium nanoparticles

Lorenz gauge, electric and magnetic fields study of interaction of gravitationally accelerating ions through the super contorted 'tubular' polar areas of magnetic fields and hassium nanoparticles

Aspects of gravitational wave/particle duality: Bulk torsion ↔boundary gravity correspondence

A geometric torsion (GT) underlying a [Formula: see text]-form in a [Formula: see text]-dimensional [Formula: see text] gauge theory is revisited with a renewed perspective for a nonperturbation (NP) gravity in [Formula: see text]. In this context, we provide evidences to a holographic correspondence between a bulk GT and a boundary NP gravity. Interestingly the Killing symmetries in General Relativity (GR) are shown to provide a subtle clue to the quantum gravity. The NP gravity is shown to incorporate a [Formula: see text] coupling, sourced by a non-Newtonian potential, to an exact geometry in GR. Remarkably the NP correction is identified as a mass dipole and is shown to be sourced by a propagating GT. A detailed analysis is performed in a bulk GT to show a modification to the precession of perihelion in a boundary NP gravity. The perspective of an electromagnetic (EM) wave in the bulk is investigated to reveal a spin [Formula: see text] (mass-less) quantum sourced by an apparent 2-form. A Goldstone scalar is absorbed by the apparent 2-form to describe a massive [Formula: see text]-form in the coulomb gauge. Alternately a Goldstone scalar together with a local degree of GT and 2-form is argued to govern a composite (mass-less) spin [Formula: see text] particle in Lorentz gauge. Both the scenarios, further ensure a graviton in a boundary NP gravity. A qualitative analysis reveals a (noninteracting) graviton underlying a plausible gravitational wave/particle duality in NP gravity.

Superstring field theory with open and closed strings

We construct Lorentz invariant and gauge invariant 1PI effective action for closed and open superstrings and demonstrate that it satisfies the classical BV master equation. We also construct the quantum master action for this theory satisfying the quantum BV master equation and generalize the construction to unoriented theories. The extra free field needed for the construction of closed superstring field theory plays a crucial role in coupling the closed strings to D-branes and orientifold planes.

Almost-Killing equation: Stability, hyperbolicity, and black hole Gauss law

We examine the Hamiltonian formulation and hyperbolicity of the almost-Killing equation (AKE). We find that for all but one parameter choice, the Hamiltonian is unbounded, and in some cases, the AKE has ghost degrees of freedom. We also show the AKE is only strongly hyperbolic for one parameter choice, which corresponds to a case in which the AKE has ghosts. Fortunately, one finds that the AKE reduces to the homogeneous Maxwell equation in a vacuum, so that with the addition of the divergence-free constraint (a "Lorenz gauge"), one can still obtain a well-posed problem that is stable in the sense that the corresponding Hamiltonian is positive definite. An analysis of the resulting Komar currents reveals an exact Gauss law for a system of black holes in vacuum spacetimes and suggests a possible measure of matter content in asymptotically flat spacetimes.

Two-Dimensional Non-abelian BF Theory in Lorenz Gauge as a Solvable Logarithmic TCFT

We study two-dimensional non-abelian BF theory in Lorenz gauge and prove that it is a topological conformal field theory. This opens the possibility to compute topological string amplitudes (Gromov-Witten invariants). We found that the theory is exactly solvable in the sense that all correlators are given by finite-dimensional convergent integrals. Surprisingly, this theory turns out to be logarithmic in the sense that there are correlators given by polylogarithms and powers of logarithms. Furthermore, we found fields with "logarithmic conformal dimension" (elements of a Jordan cell for $L_0$). We also found certain vertex operators with anomalous dimensions that depend on the non-abelian coupling constant. The shift of dimension of composite fields may be understood as arising from the dependence of subtracted singular terms on local coordinates. This generalizes the well-known explanation of anomalous dimensions of vertex operators in the free scalar field theory.

A gauge theory of quantum gravity: quantization of the non-interacting field

The non-interacting field belonging to a new SO(1,3) gauge field theory equivalent to general relativity is canonically quantized in the Lorentz gauge and the physical Fock space for non-interacting gauge particles is constructed. To assure both Lorentz covariance and positivity of the norm and energy expectation value for physical states restrictions needed in the construction of the physical Fock space are put consequentially on state vectors, and not on the algebra of creation and annihilation operators as usual—alltogether providing the second step in consistently quantizing gravitation

Electromagnetic and color memory in even dimensions

We explore memory effects associated to both Abelian and non-Abelian radiation getting to null infinity, in arbitrary even spacetime dimensions. Together with classical memories, linear and non-linear, amounting to permanent kicks in the velocity of the probes, we also discuss the higher-dimensional counterparts of quantum memory effects, manifesting themselves in modifications of the relative phases describing a configuration of several probes. In addition, we analyse the structure of the asymptotic symmetries of Maxwell's theory in any dimension, both even and odd, in the Lorenz gauge.

Global well-posedness of axially symmetric weak solutions to the Ginzburg–Landau model in superconductivity

ABSTRACT This paper proves global existence and uniqueness of axially symmetric weak solutions to the 3D time-dependent Ginzburg–Landau model in superconductivity in with initial data and the choice of Lorentz gauge. We are unable to prove a similar result with the Coulomb gauge.

Obtaining consistent Lorentz gauging for a gravitationally coupled fermion

For internal gauge forces, the result of locally gauging, i.e., of performing the substitution $\partial \rightarrow D$, is physically the same whether performed on the action or on the corresponding Euler-Lagrange equations of motion. Rather unsettling, though, such commutativity fails for the standard way of coupling a Dirac fermion to the gravitational field in the setting of a local Lorentz gauge theory of general relativity in the vierbein formalism, the equivalence principle thus seemingly being here violated. This paper will present a formalism in which commutativity holds for the gravitational force as well, the action for the gravitational field itself being still the Einstein-Hilbert one. Notably, in this formalism, the spinor field will carry a world/coordinate index, rather than a Lorentz spinor index as it does standardly. More generally, no Lorentz indices will figure, neither vector indices nor spinor indices, which from a parsimonious point of view seems quite satisfactory.

Metric formulation of the simple theory of 3d massive gravity

We have recently introduced a new and very simple action for three-dimensional massive gravity. This action is written in a first order formulation where the triad and the connection play a manifestly symmetric role, but where internal Lorentz gauge symmetry is broken. The absence of Lorentz invariance, which in this model is the mechanism underlying the propagation of a massive graviton, does however prevent from writing a purely metric non-linear action for the theory. Nonetheless, in this letter, we explain how to disentangle, at the non-linear level, the metric and non-metric degrees of freedom in the equations of motion. Focusing on the metric part, we show that it satisfies modified Einstein equations with higher derivative terms. As a particular case, these equations reproduce a well-studied model known as minimal massive gravity. In the general case, we obtain new metric field equations for massive gravity in three dimensions starting from the simple first order action. These field equations are consistent through a mechanism known as "third way consistency", which our theory therefore provides a new example of.

A Generalization of the Yang—Mills Equations

A generalization of the Yang-Mills equations is proposed. It is shown that any solution of the Yang-Mills equations (in the Lorentz gauge) is also a solution of the new generalized equation. It is also shown that the generalized equation has solutions that do not satisfy the Yang-Mills equations.

Electromagnetic fields on Kerr spacetime, Hertz potentials, and Lorenz gauge

We review two procedures for constructing the vector potential of the electromagnetic field on Kerr spacetime, namely, the classic method of Cohen & Kegeles, yielding $A^\mu$ in a radiation gauge, and the newer method of Frolov et al., yielding $A^\mu$ in Lorenz gauge. We demonstrate that the vector potentials are related by straightforward gauge transformations, which we give in closed form. We obtain a new result for a separable Hertz potential $H^{\mu \nu}$ such that $A_{\text{lor}}^\mu = \nabla_\nu H^{\mu \nu}$.

Maxwell quantum mechanics

We extend classical Maxwell field theory to a first quantized theory of the photon by deriving a conserved Lorentz four-current whose zero component is a positive definite number density. Fields are real and their positive (negative) frequency parts are interpreted as absorption (emission) of a positive energy photon. With invariant plane wave normalization, the photon position operator is Hermitian with instantaneously localized eigenvectors that transform as Lorentz four-vectors. Reality of the fields and wave function ensure causal propagation and zero net absorption of energy in the absence of charged matter. The photon probability amplitude is the real part of the projection of the photon's state vector onto a basis of position eigenvectors and its square implements the Born rule. Manifest covariance and consistency with quantum field theory is maintained through use of the electromagnetic four-potential and the Lorenz gauge.

Gravitational self-force regularization in the Regge-Wheeler and easy gauges

We present numerical results for the gravitational self-force and redshift invariant calculated in the Regge-Wheeler and Easy gauges for circular orbits in a Schwarzschild background, utilizing the regularization framework introduced by Pound, Merlin, and Barack. The numerical calculation is performed in the frequency domain and requires the integration of a single second-order ODE, greatly improving computation times over more traditional Lorenz gauge numerical methods. A sufficiently high-order, analytic expansion of the Detweiler-Whiting singular field is gauge-transformed to both the Regge-Wheeler and Easy gauges and used to construct tensor-harmonic mode-sum regularization parameters. We compare our results to the gravitational self-force calculated in the Lorenz gauge by explicitly gauge-transforming the Lorenz gauge self-force to the Regge-Wheeler and Easy gauges, and find that our results agree to a relative accuracy of $10^{-15}$ for an orbital radius of $r_0=6M$ and $10^{-16}$ for an orbital radius of $r_0=10M$.