Quantization of Electromagnetic Field and Potential in Rindler Space-Time

The article treats quantization of electromagnetic field that is defined in Rindler space-time. Likely the electromagnetic field, the potential did quantizated in inertial frame, the electromagnetic field, the potential can quantizate by the transformation of electromagnetic field or the transformation of the potential in the accelerated frame. We treat Lorentz gauge condition in quantization of electromagnetic potential.

10D super-Yang-Mills scattering amplitudes from its pure spinor action

Using the pure spinor master action for 10D super-Yang-Mills in the gauge b0V = QΞ, tree-level scattering amplitudes are calculated through the perturbiner method, and shown to match those obtained from pure spinor CFT techniques. We find kinematic numerators made of nested b-ghost operators, and show that the Siegel gauge condition b0V = 0 gives rise to color-kinematics duality satisfying numerators whose Jacobi identity follows from the Jacobi identity of a kinematic algebra.

One-loop partition function, gauge accessibility and spectra in AdS3 gravity

We continue the study of the one-loop partition function of AdS3 gravity with focus on the square-integrability condition on the fluctuating fields. In a previous work we found that the Brown-Henneaux boundary conditions follow directly from the L2 condition. Here we rederive the partition function as a ratio of Laplacian determinants by performing a suitable decomposition of the metric fluctuations. We pay special attention to the asymptotics of the fields appearing in the partition function. We also show that in the usual computation using ghost fields for the de Donder gauge, such gauge condition is accessible precisely for square-integrable ghost fields. Finally, we compute the spectrum of the relevant Laplacians in thermal AdS3, in particular noticing that there are no isolated eigenvalues, only essential spectrum. This last result supports the analytic continuation approach of David, Gaberdiel and Gopakumar. The purely essential spectra found are consistent with the independent results of Lee and Delay of the essential spectrum of the TT rank-2 tensor Lichnerowickz Laplacian on asymptotically hyperbolic spaces.

Gauge theory of the Maxwell and semi-simple extended (anti) de Sitter algebra

In this paper, a semi-simple and Maxwell extension of the (anti) de Sitter algebra is constructed. Then, a gauge-invariant model has been presented by gauging the Maxwell semi-simple extension of the (anti) de Sitter algebra. We firstly construct a Stelle–West-like model action for five-dimensional spacetime in which the effects of spontaneous symmetry breaking have been taken into account. In doing so, we get an extended version of Einstein’s field equations. Next, we decompose the five-dimensional extended Lie algebra and establish a MacDowell–Mansouri-like action that contains the Einstein–Hilbert term, the cosmological term as well as new terms coming from Maxwell extension in four-dimensional spacetime where the torsion-free condition is assumed. Finally, we have shown that both models are equivalent for an appropriately chosen gauge condition.

A canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics in first-order formalism

We give a canonical Hamiltonian analysis of Podolsky’s generalized electrodynamics by introducing two sets of new variables which help us transform the Lagrangian into an equivalent first-order formalism. After eliminating the unphysical sector, we calculate the physical degrees of freedom of the higher derivative system and obtain the Dirac brackets in the reduced phase space. Then with the aid of the first-class constraints, we construct the independent gauge generator which is closely connected with the BRST charge and the BRST-invariant Hamiltonian. Finally, by choosing appropriate gauge-fixing fermion, we evaluate the path integral of this higher derivative constrained system in BRST quantization scheme with the generalized Lorenz gauge condition.

Soft-collinear effective theory: BRST formulation

We provide a BRST formalism for the soft-collinear effective theory describing interactions of soft and collinear degrees of freedom in the presence of a hard interaction. In particular, we develop a BRST symmetry transformation for SCET theory. We further generalize the BRST formulation by making the transformation parameter field dependent. This establishes a mapping between several SCET actions consistently when defined in different gauge conditions. In fact, a definite structure of gauge-fixed actions corresponding to any particular gauge condition can be generated for SCET theory using our formulation.

Gravitational and Electromagnetic Perturbations of a Charged Black Hole in a General Gauge Condition

We derive a set of coupled equations for the gravitational and electromagnetic perturbation in the Reissner–Nordström geometry using the Newman–Penrose formalism. We show that the information of the physical gravitational signal is contained in the Weyl scalar function Ψ4, as is well known, but for the electromagnetic signal, the information is encoded in the function χ, which relates the perturbations of the radiative Maxwell scalars φ2 and the Weyl scalar Ψ3. In deriving the perturbation equations, we do not impose any gauge condition and as a limiting case, our analysis contains previously obtained results, for instance, those from Chandrashekhar’s book. In our analysis, we also include the sources for the perturbations and focus on a dust-like charged fluid distribution falling radially into the black hole. Finally, by writing the functions on the basis of spin-weighted spherical harmonics and the Reissner–Nordström spacetime in Kerr–Schild type coordinates, a hyperbolic system of coupled partial differential equations is presented and numerically solved. In this way, we completely solve a system that generates a gravitational signal as well as an electromagnetic/gravitational one, which sets the basis to find correlations between them and thus facilitates gravitational wave detection via electromagnetic signals.

An Analysis of Gravitational waves

The September 14, 2015 gravitational wave observations showed the inspiral of two black holes observed from Hanford and Livingston LIGO observatories. This detection was significant for two reasons: firstly, it coupled the result and avoided the possibility of a false alarm by 5σ , meaning that the detected “noise” was indeed from an astronomical source of gravitational waves. We will discuss the primary landscape of gravitational waves, their mathematical structure and how they can be used to predict the masses of the merger system. We will also discuss gravitational wave detector optimisations, and then we will consider the results from the detected merger GW150914. We will consider a straight-forward mathematical approach, and we will primarily be interested in the mathematical modelling of gravitational waves from General Relativity (Section 1). We will first consider a “perturbed” Minkowski metric, and then we will discuss the properties of the perturbation addition tensor. We will then discuss on the gravitational field tensor, and how it arises from the perturbation tensor. We will then talk about the gauge condition, essentially the gauge “freedom” , and then we will talk about the curvature tensor, leading eventually to the effect of gravitational waves on a ring of particles. We will consider the polarisation tensor, which maps the amplitude and polarisation details. The polarisation splits into plus polarised and cross polarised waves, which is technically the effect of a propagating gravitational wave through a ring of particles. We will then talk about the linearized Einstein Field Equations, and how the physical system of merger is encoded into the mathematical structural unity of the metric. We will then talk about the detection of these gravitational waves and how the detector can be optimised, or how the detector can be set so that any “noise” detected can fall in the error margins, and how the detector can prevent the interferometric “photon-noise” from being detected (Section 2.2). Then, we will discuss data results from the source GW150914 detection by LIGO (Section 3).

3D finite-volume time-domain modeling of geophysical electromagnetic data on unstructured grids using potentials

Unstructured grids are capable of faithfully representing real-life geologic models and topography with relatively few mesh cells. We have developed a finite-volume solution to the 3D time-domain electromagnetic forward modeling problems using unstructured Delaunay-Voronoï dual meshes. We consider the Helmholtz equation for the electric field and a combination of the Helmholtz equation and the conservation of charge equation for the magnetic vector (A) and electric scalar ([Formula: see text]) potentials. The [Formula: see text] formulation requires initial values for A that can be obtained by solving the magnetostatic problem. We use backward Euler time stepping to advance the electric field and the potentials in the time domain. When using the potential method, the electric and magnetic fields are calculated from [Formula: see text] solutions. To obtain consistent potential solutions at different time steps, we enforce the Coulomb gauge condition, using implicit and explicit methods. We validate the proposed method with a simple 3D conductive block model and with a comparison with other numerical methods. By using [Formula: see text] potentials, it is possible to decompose the electric field into galvanic and inductive parts, which is helpful in understanding the physics behind the behavior of the electromagnetic fields in the ground. We use vector plots to visualize the decomposed electric fields for horizontal and vertical thin conductor models with inductive loop sources. This allows the interplay between inductive and galvanic parts as the electric field and current density develop with time to be visualized.

Energy Conservation Law in the Closed Universe and a Concept of the Proper Time

To define time in the homogeneous anisotropic Bianchi-IX model of the universe, we propose a classical equation of motion of the proper time of the universe as an additional gauge condition. This equation is the law of conservation of energy. As a result, a new parameter, called a “mass” of the universe, appears. This parameter is added to the anisotropy energy and regarded as an observed quantity. The “mass” of the universe is decisive when it comes to the dynamics of its origin.