On the new representation of the antisymmetric tensor gauge field

A formalism is presented which provides a framework for analysis of the abelian gauge theory of a second-rank anti-symmetric tensor in terms of the mutually dual auxiliary fields. This new formalism illustrates how the different gauge fixing conditions are related to the different field representations exhibiting the rich dynamical features of the antisymmetric tensor gauge fields. The derivation relies upon an analogy with the simpler case of the two-dimensional Maxwell field.     

Principal null directions of the neutrino and derived Maxwell fields

Bineutrino fields are constructed from neutrinos described by the two-component Weyl equation. If we demand that the bineutrino fields fulfil the set of Maxwell equations, we have a classical version of the “neutrino theory of light”. With the help of the spin coefficient formalism, it is established that the energy tensor of the neutrino fields cannot be positively definite, and that the principal null direction of the bineutrino Maxwell fields does not coincide with the principal null direction of the underlying neutrino fields.     

Hamiltonian path integral formalism with higher derivatives

We study the Hamiltonian path integral formalism for systems containing higher derivatives. First we show the consistency of the formalism in applications involving only scalar fields. Later we use the Maxwell electromagnetic theory with a higher order regularization term to show that the Batalin-Fradkin-Vilkovisky (BFV) theory can also be consistently described.     

Algebraically Special Gravitational Fields with the Cosmological Constant and Energy-Momentum Tensor of Electromagnetic Radiation

A class of rigorous solutions of the Einstein–Maxwell equations is obtained within the Newman–Penrose formalism for algebraically special gravitational fields with the cosmological constant and energy-momentum tensor of electromagnetic radiation given that the photon flux specifying electromagnetic radiation determines isotropic-geodesic congruence. Designations within the Newman–Penrose formalism and numbers of formulas in references are the same as in [1].     

Symmetries of Type D Pure Radiation Fields

The geometrical symmetries corresponding to the continuous groups of collineations and motions generated by a null vector l are considered. These symmetries have been translated into the language of Newman-Penrose formalism for pure radiation (PR) type D fields. It is seen that for such fields, conformal, special conformal and homothetic motions degenerate to motion. The concept of free curvature, matter curvature and matter affine collineations have been introduced and the conditions under which PR type D fields admit such collineations have been obtained. Moreover, it is shown that the projective collineation degenerate to matter affine, special projective, conformal, special conformal, null geodesic and special null geodesic collineations. It is also seen that type D pure radiation fields admit Maxwell collineation along the propagation vector l.     

Loop Quantum Gravity à la Aharonov–Bohm

In this paper we calculate the Bondi mass of asymptotically flat spacetimes with interacting electromagnetic and scalar fields. The system of coupled Einstein–Maxwell–Klein–Gordon equations is investigated and corresponding field equations are written in the spinor form and in the Newman–Penrose formalism. Asymptotically flat solution of the resulting system is found near null infinity. Finally we use the asymptotic twistor equation to find the Bondi mass of the spacetime and derive the Bondi mass-loss formula. We compare the results with our previous work (Bi?ák et al. in Class Quantum Gravity 27(17):175011, 2010) and show that, unlike the conformal scalar field, the (Maxwell–)Klein–Gordon field has negatively semi-definite mass-loss formula.     

Obtaining non-Abelian field theories via the Faddeev-Jackiw symplectic formalism

In this Letter we construct non-Abelian field theories employing the Faddeev-Jackiw symplectic formalism. The original Abelian fields were modified in order to introduce the non-Abelian algebra. We construct the SU(2) and SU(2)⊗U(1) Yang-Mills theories having as starting point the U(1) Maxwell electromagnetic theory.     

The Casimir effect for fields with arbitrary spin

The Casimir force arises when a quantum field is confined between objects that apply boundary conditions to it. In a recent paper we used the two-spinor calculus to derive boundary conditions applicable to fields with arbitrary spin in the presence of perfectly reflecting surfaces. Here we use these general boundary conditions to investigate the Casimir force between two parallel perfectly reflecting plates for fields up to spin-2. We use the two-spinor calculus formalism to present a unified calculation of well-known results for spin-1/2 (Dirac) and spin-1 (Maxwell) fields. We then use our unified framework to derive new results for the spin-3/2 and spin-2 fields, which turn out to be the same as those for spin-1/2 and spin-1. This is part of a broader conclusion that there are only two different Casimir forces for perfectly reflecting plates—one associated with fermions and the other with bosons.     

Maxwell Equations in the Spinning Cosmic String Spacetimes

Maxwell equations are explicitly written in spin weighted form by using NP formalism in general flat spacetimes. Corresponding Maxwell equations are obtained in spinning and straight cosmic string backgrounds.     

On a relation between Maxwell and Dirac theories

It is shown that the Dirac equation can be written in a form similar to Maxwell equations, where the Maxwell tensor is written as a bilinear expression of the Dirac field and the current is a simple function of the external potential and the Dirac field. Similarly, the Maxwell equations can be written as a self-coupled Dirac equation where the potential is a simple function of the Dirac field itself. It is illustrated by examples how the new formalism helps to find solutions of the coupled field equations.     

Hamilton formalism and variational principle construction

It is widely accepted that a variational principle cannot be constructed for an arbitrary differential equation; a rigorous mathematical condition shows which equations can have a variational formulation. On the other hand, the importance for variational principles in various fields of physics resulted in several methods to circumvent this condition and to construct another type of variational principles for any differential equation. In this paper the common origin of the considered methods is investigated, and a generalized Hamiltonian formalism is formulated. Additionally, constructive algorithms are given by different methods to construct variational principles. Simple examples are presented to make construction methods more transparent: several Lagrangians are constructed for the different forms of the Maxwell equations and for the extended heat conduction equation.     

Kaluza理论的运动定律

本文指出,如同在广义相对论中粒子运动方程是场方程的推论一样,在引力场与电磁场的Kaluza统一理论中,粒子的运动方程也是场方程的一个推论,即带电粒子在引力场和电磁场中的运动方程可以从Kaluza统一理论中的场方程推导出来。本文进而在Minkowski时空的条件下,借助Maxwell理论的Kaluza形式,得到Maxwell方程也包含了带电粒子运动方程的结论。 关键词：     

Behavior of zero rest-mass fields including gravitation in the vicinity of zeros

For free nonradiation zero rest-mass fields, as for example the nonnull Maxwell and the Weyl tensor fields in vacuum, a uniform treatment of the behavior of the principal null vectors in the vicinity of boundary zeros is given. It is shown that a boundary zero of a field is a singular point of at least one of its principal null vectors. In the special case of a Maxwell field for which the Poynting three-vector vanishes for a certain observer-field, a boundary zero of the Maxwell field is a singular point of the corresponding electric and magnetic fields. The results are valid in flat and curved spacetimes independently of whether the zero rest-mass fields act as source of the spacetime curvature or not.     

Computational soliton solutions to $$$$-dimensional generalised Kadomtsev–Petviashvili and $$(2+1)$$(2+1)-dimensional Gardner–Kadomtsev–Petviashvili models and their applications

In this paper, we present a formalism to generate a family of interior solutions to the Einstein–Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner–Nordström space–time. By reducing the Einstein–Maxwell system to a recurrence relation with variable rational coefficients, we show that it is possible to obtain closed-form solutions for a specific range of model parameters. A large class of solutions obtained previously are shown to be contained in our general class of solutions. We also analyse the physical viability of our new class of solutions.     

Formal Similarity Between Mathematical Structures of Electrodynamics and Quantum Mechanics

Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that the Schrödinger equation admits an analogous treatment. We present a Lagrangian theory of a real scalar field φ whose equation of motion turns out to be equivalent to the Schrödinger equation with time independent potential. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics. The field φ is in the same relation to the real and imaginary part of a wave function as the vector potential is in respect to electric and magnetic fields. Preservation of quantum-mechanics probability is just an energy conservation law of the field φ.     

Equivalence of Dirac and Maxwell equations and quantum mechanics

In this paper we present an analysis of the possible equivalence of Dirac and Maxwell equations using the Clifford bundle formalism and compare it with Campolattaro's approach, which uses the traditional tensor calculus and the standard Dirac covariant spinor field. We show that Campolattaro's intricate calculations can be proved in few lines in our formalism. We briefly discuss the implications of our findings for the interpretation of quantum mechanics.     

电磁场的复张量表述

在电磁场的三维复矢量表述基础之上获得对应的四维复张量表述形式,同时又考虑磁荷流密度并引入双势法,将电磁场复张量表述推广到同时包含电荷与磁荷流密度的情形并获得了复张量麦克斯韦方程组.     

各向异性表面光学的格林函数公式及其应用

本文通过对麦克思韦方程组的变换和反演得到各向异性介质的表面光学格林函数.用它计算辐射场可以直接得到s和p偏振波的表示式,因而在计算界面效应时可以自然地引入菲涅耳系数.作为应用,本文计算了当存在界面和薄膜时极化所产生的辐射场.     

Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data—the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2{{\mathcal N}=2} supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner–Nordstrom black holes in ordinary Einstein–Maxwell theory.