اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدConservation Laws in Generalized Riemann-Silberstein Electrodynamics
70
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Starting from positive and negative helicity Maxwell equations expressed in Riemann-Silberstein vectors, we derive the ten usual and ten additional Poincar{e} invariants, the latter being related to the electromagnetic spin, i.e., the intrinsic rotation, or state of polarization, of the electromagnetic fields. Some of these invariants have apparently not been discussed in the literature before.
قيم البحث
اقرأ أيضاً
It is shown that the generalized Riemann equation is equivalent with the multicomponent generalization of the Hunter - Saxton equation. New matrix and scalar Lax representation is presented for this generalization. New class of the conserved densitie
s, which depends explicitly on the time are obtained directly from the Lax operator. The algorithm, which allows us to generate a big class of the non-polynomial conservation laws of the generalized Riemann equation is presented. Due to this new series of conservation laws of the Hunter-Saxton equation is obtained.
In this paper using a Clifford bundle formalism we examine (a): the strong conditions for existence of conservation laws involving only the energy-momentum and angular momentum of the matter fields on a general Riemann-Cartan spacetime and also in th
e particular cases of Lorentzian and teleparallel spacetimes and (b): the conditions for the existence of conservation laws of energy-momentum and angular momentum for the matter and gravitational fields when this latter concept can be rigorously defined. We examine in details some misleading and even erroneous and often quoted statements concerning the issues of the conservation laws in General Relativity and Riemann-Cartan (including the particular case of the teleparallel one) theories.
We extend the generalize conservation law of light propagating in a one-dimensional $cal PT$-symmetric system, i.e., $|T-1|=sqrt{R_LR_R}$ for the transmittance $T$ and the reflectance $R_{L,R}$ from the left and right, to a multimode waveguide with e
ither $cal PT$ or $cal RT$ symmetry, in which higher dimensional investigations are necessary. These conservation laws exist not only in a matrix form for the transmission and reflection matrices; they also exist in a scalar form for real-valued quantities by defining generalized transmittance and reflectance. We then discuss, for the first time, how a multimode $cal PT$-symmetric waveguide can be used to observe spontaneous symmetry breaking of the scattering matrix, which typically requires tuning the non-hermiticity of the system (i.e. the strength of gain and loss). Here the advantage of using a multimode waveguide is the elimination of tuning any system parameters: the transverse mode order $m$ plays the role of the symmetry breaking parameter, and one observes the symmetry breaking by simply performing scattering experiment in each waveguide channel at a single frequency and fixed strength of gain and loss.
We prove that potential conservation laws have characteristics depending only on local variables if and only if they are induced by local conservation laws. Therefore, characteristics of pure potential conservation laws have to essentially depend on
potential variables. This statement provides a significant generalization of results of the recent paper by Bluman, Cheviakov and Ivanova [J. Math. Phys., 2006, V.47, 113505]. Moreover, we present extensions to gauged potential systems, Abelian and general coverings and general foliated systems of differential equations. An example illustrating possible applications of proved statements is considered. A special version of the Hadamard lemma for fiber bundles and the notions of weighted jet spaces are proposed as new tools for the investigation of potential conservation laws.
We analyze the laws of conservation of momentum and angular momentum in classical electrodynamics of material media with bound charges, and explore the possibility to describe the properties of such media via a discrete set of point-like charges of z
ero size (as imposed by special relativity), and via continuous charge/current distributions. This way we put a question: do we have to recognize the infinite fields at the location of elementary charges as the essential physical requirement, or such infinite fields can be ignored via introduction of continuous charge distribution? In order to answer this question, we consider the interaction of a homogeneously charged insulating plate with a compact magnetic dipole, moving along the plate. We arrive at the apparent violation of the angular momentum conservation law and show that this law is re-covered, when the electric field at the location of each elementary charge of the plate is taken infinite. This result signifies that the description of electromagnetic properties of material media via the continuous charge and current distributions is not a universal approximation, and at the fundamental level, we have to deal with a system of elementary discrete charges of zero size, at least in the analysis of laws of conservation of momentum and angular momentum.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
