Apparent Paradoxes in Classical Electrodynamics: Relativistic Transformation of Force
Kholmetskii, A. L.; Yarman, T.
2007-01-01
In this paper, we analyse a number of paradoxical teaching problems of classical electrodynamics, dealing with the relativistic transformation of force for complex macro systems, consisting of a number of subsystems with nonzero relative velocities such as electric circuits that change their shape in the course of time. (Contains 7 figures.)
Fourier optics treatment of classical relativistic electrodynamics
In this paper we couple Synchrotron Radiation (SR) theory with a branch of physical optics, namely laser beam optics. We show that the theory of laser beams is successful in characterizing radiation fields associated with any SR source. Both radiation beam generated by an ultra-relativistic electron in a magnetic device and laser beam are solutions of the wave equation based on paraxial approximation. It follows that they are similar in all aspects. In the space-frequency domain SR beams appear as laser beams whose transverse extents are large compared with the wavelength. In practical solutions (e.g. undulator, bending magnet sources), radiation beams exhibit a virtual ''waist'' where the wavefront is often plane. Remarkably, the field distribution of a SR beam across the waist turns out to be strictly related with the inverse Fourier transform of the far-field angle distribution. Then, we take advantage of standard Fourier Optics techniques and apply the Fresnel propagation formula to characterize the SR beam. Altogether, we show that it is possible to reconstruct the near-field distribution of the SR beam outside the magnetic setup from the knowledge of the far-field pattern. The general theory of SR in the near-zone developed in this paper is illustrated for the special cases of undulator radiation, edge radiation and transition undulator radiation. Using known analytical formulas for the far-field pattern and its inverse Fourier transform we find analytical expressions for near-field distributions in terms of far-field distributions. Finally, we compare these expressions with incorrect or incomplete literature. (orig.)
Non-relativistic quantum electrodynamics
The book presents a systematic account of non-relativistic quantum electrodynamics. The subject is discussed under the subject headings: classical equations of motion, canonical formalism, canonical quantization, symmetries and conservation laws, interaction of photons and atoms and lastly, path-dependent electrodynamics. (U.K.)
Bogolubov, N.N.; Prykarpatsky, A. K.
2009-01-01
The work is devoted to studying some new classical electrodynamics models of interacting charged point particles and the aspects of the quantization via the Dirac procedure related to them. Based on the vacuum field theory no-geometry approach developed in [6,7,9], the Lagrangian and Hamiltonian reformulations of some alternative classical electrodynamics models are devised. The Dirac-type quantization procedure for the considered alternative electrodynamics models, based on the obtained cano...
Relativistic Geometry and Quantum Electrodynamics
González-Martin, G R
2000-01-01
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field operator. Because of the inherent geometric algebraic structure these operators obey the standard commutation rules of QED. If we work with excitations, we need to use statistical theory when considering the evolution of microscopic subsystems. The use of classical statistics, in particular techniques of irreversible thermodynamics, determine that the probability of absorption or emission of a geometric excitation is a function of the classical energy density. Emission and absorption of geometric excitations imply discrete changes of certain physical variables, but with a probability determined by its wave energy density. Hence, this geometric theory, without contradicting the fundamental aspects of quantum physics, provides a geometric foundation for the theory.
Field, J H.
2005-01-01
The force due to electromagnetic induction on a test charge is calculated in different reference frames. The Faraday-Lenz Law and different formulae for the fields of a uniformly moving charge are used. The classical Heaviside formula for the electric field of a moving charge predicts that, for the particular spatial configuration considered, the inductive force vanishes in the frame in which the magnet is in motion and the test charge at rest. In contrast, consistent results, in different fr...
Connecting Blackbody Radiation, Relativity, and Discrete Charge in Classical Electrodynamics
Boyer, Timothy H.
2006-01-01
It is suggested that an understanding of blackbody radiation within classical physics requires the presence of classical electromagnetic zero-point radiation, the restriction to relativistic (Coulomb) scattering systems, and the use of discrete charge. The contrasting scaling properties of nonrelativistic classical mechanics and classical electrodynamics are noted, and it is emphasized that the solutions of classical electrodynamics found in nature involve constants which connect together the...
Elementary charges in classical electrodynamics
KAPU'{S}CIK, Edward
1999-01-01
In the framework of classical electrodynamics elementary particles are treated as capacitors. The electrostatic potentials satisfy equations of the Schrödinger type. An interesting "quantization condition" for elementary charges is derived.
The relation between classical and quantum electrodynamics
Mario Bacelar Valente
2012-01-01
Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as an more fundamental theory, but as an upgrade of classical electrodynamics, which permits an ex...
Quantum electrodynamics in a classical approximation, 1
Quantum electrodynamics is formulated in a classical approximation. A quantum mechanical proper-time is employed as a useful parameter, which enables us to elucidate the relationship between quantum electrodynamics and classical electrodynamics. The classical motion of a charged particle is realized as an asymptotic limit of quantum electrodynamics. (author)
To Foundations of Classical Electrodynamics
Bessonov, E. G.
1997-01-01
In the present work foundations of the law of the energy conservation and the introduction of particles in the classical electrodynamics are discussed. We pay attention to a logic error which takes place at an interpretation of the Poynting's theorem as the law of conservation of energy. It was shown that the laws of conservation of energy and momentum of the system of electromagnetic fields and charged particles does not follow from the equations of electrodynamics and the violation of these...
Causality in Classical Electrodynamics
Savage, Craig
2012-01-01
Causality in electrodynamics is a subject of some confusion, especially regarding the application of Faraday's law and the Ampere-Maxwell law. This has led to the suggestion that we should not teach students that electric and magnetic fields can cause each other, but rather focus on charges and currents as the causal agents. In this paper I argue…
The Relation between Classical and Quantum Electrodynamics
Mario Bacelar Valente
2011-01-01
Full Text Available Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as an more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory.
Lagrangian formalism and retarded classical electrodynamics
Jan, Xavier; Llosa, Josep; Molina, Alfred
1989-01-01
Unlike the 1/c2 approximation, where classical electrodynamics is described by the Darwin Lagrangian, here there is no Lagrangian to describe retarded (resp., advanced) classical electrodynamics up to 1/c3 for two-point charges with different masses.
Gauge Invariance in Classical Electrodynamics
Engelhardt, W
2005-01-01
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from the field equations we obtain, however, contradicting solutions. We conclude that the tacit assumption of uniqueness is not justified. The reason for this failure is traced back to the inhomogeneous wave equations which connect the propagating fields and their sources at the same time.
Particles and Events in Classical Off-Shell Electrodynamics
Land, M C
1997-01-01
Despite the many successes of the relativistic quantum theory developed by Horwitz, et. al., certain difficulties persist in the associated covariant classical mechanics. In this paper, we explore these difficulties through an examination of the classical Coulomb problem in the framework of off-shell electrodynamics. As the local gauge theory of a covariant quantum mechanics with evolution parameter $\\tau$, off-shell electrodynamics constitutes a dynamical theory of spacetime events, interacting through five $\\tau$-dependent pre-Maxwell potentials. We present a straightforward solution of the classical equations of motion, which is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical level. We then offer a new model of the particle current -- as a certain distribution of the event currents on the worldline -- which eliminates these difficulties and permits comparison of classical off-shell electrodynamics with the standard Maxwell theory. In this model, the ``fix...
Connecting Blackbody Radiation, Relativity, and Discrete Charge in Classical Electrodynamics
Boyer, T H
2006-01-01
It is suggested that an understanding of blackbody radiation within classical physics requires the presence of classical electromagnetic zero-point radiation, the restriction to relativistic (Coulomb) scattering systems, and the use of discrete charge. The contrasting scaling properties of nonrelativistic classical mechanics and classical electrodynamics are noted, and it is emphasized that the solutions of classical electrodynamics found in nature involve constants which connect together the scales of length, time, and energy. Indeed, there are analogies between the electrostatic forces for groups of particles of discrete charge and the van der Waals forces in equilibrium thermal radiation. The differing Lorentz- or Galilean-transformation properties of the zero-point radiation spectrum and the Rayleigh-Jeans spectrum are noted in connection with their scaling properties. Also, the thermal effects of acceleration within classical electromagnetism are related to the existence of thermal equilibrium within a g...
Advanced action in classical electrodynamics
Boozer, A. D.
2008-01-01
The time evolution of a charged point particle is governed by a second-order integro-differential equation that exhibits advanced effects, in which the particle responds to an external force before the force is applied. In this paper we give a simple physical argument that clarifies the origin and physical meaning of these advanced effects, and we compare ordinary electrodynamics with a toy model of electrodynamics in which advanced effects do not occur.
Hilbert space theory of classical electrodynamics
RAJAGOPAL A K; GHOSE PARTHA
2016-06-01
Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman–von Neumann–Sudarshan prescription for classical mechanics on Hilbert spaces sans the superselection rule which prohibits interference effects in classical mechanics. This is accomplished by transforming from a set of commutingobservables in one Hilbert space to another set of commuting observables in a larger Hilbert space. This is necessary to clarify the theoretical basis of the much recent work on quantum-like features exhibited by classical optics. Furthermore, following Bondar et al, {\\it Phys. Rev.} A 88, 052108 (2013), it is pointed out that quantum processes that preserve the positivity or nonpositivity of theWigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.
N.N. Bogolubov (Jr.
2009-01-01
Full Text Available The work is devoted to the study of the Lagrangian and Hamiltonian properties of some relativistic electrodynamics models and is a continuation of our previous investigations. Based on the vacuum field theory approach, the Lagrangian and Hamiltonian reformulation of some classical electrodynamics models is devised. The Dirac type quantization procedure, based on the canonical Hamiltonian formulation, is developed. Within the approach proposed in the work a possibility of the combined description both of electrodynamics and gravity is analyzed.
Recent developments in premetric classical electrodynamics
Hehl, F W; Obukhov, Yu N; Hehl, Friedrich W.; Itin, Yakov; Obukhov, Yuri N.
2005-01-01
Classical electrodynamics can be based on the conservation laws of electric charge and magnetic flux. Both laws are independent of the metric and the linear connection of spacetime. Within the framework of such a premetric electrodynamics -- provided a local and linear constitutive law of the vacuum is added -- the propagation of electromagnetic waves in the geometric-optics limit can be studied. The wave vectors of the wave fronts obey a quartic extended Fresnel equation. If one forbids birefringence in vacuum, the light cone emerges and Maxwell-Lorentz vacuum electrodynamics can be recovered. If minimal coupling of electrodynamics to gravity is assumed, then only the gravitational potential, i.e., the metric of spacetime, emerges in the constitutive law. We discuss recent results within this general framework.
The chronicle of the classical electrodynamics
In this Chronicle of the classical electrodynamics it is shown how this important branch of classical physics was developed since the mathematical formulation of the electromagnetism empiric laws carried by Maxwell, mainly the laws of Coulomb, Oersted, Ampere, Biot-Savart, Faraday, Henry and Lenz, up to the settlement of the radiation theory, scientific background for the technological development of the wireless telegraphy. Through this chronicle, it is also seen how Maxwell got one of the main results of the past century classical physics - the electromagnetic theory of light -, and how the experimental production of an electromagnetic wave by Hertz, unchained a collection of theoretical papers which explained many experimental results such as dispersion of light, thermical radiation, X-rays and its scattering through the matter. At last, it is still seen that the study of electrodynamics of moving bodies led to the relativity theory, presented by Einstein's famous paper about such subject. (Author)
A neglected topic in relativistic electrodynamics: transformation of electromagnetic integrals
Jefimenko, Oleg D.
2005-01-01
Although relativistic electrodynamics is more than 100 year old, there is one neglected topic in its presentation and application: relativistic transformations of electromagnetic integrals. Whereas in theoretical and applied electrodynamics electric and magnetic fields are mainly expressed in terms of integrals over charge and current distributions, relativistic transformations are traditionally applied to point charges and elementary currents. The purpose of this paper is to show that relati...
Popa, Alexandru
2013-01-01
Applications of Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamical Systems is a reference on the new field of relativistic optics, examining topics related to relativistic interactions between very intense laser beams and particles. Based on 30 years of research, this unique book connects the properties of quantum equations to corresponding classical equations used to calculate the energetic values and the symmetry properties of atomic, molecular and electrodynamical systems. In addition, it examines applications for these methods, and for the calculation of
Apparent Paradoxes in Classical Electrodynamics: A Fluid Medium in an Electromagnetic Field
Kholmetskii, A. L.; Yarman, T.
2008-01-01
In this paper we analyse a number of teaching paradoxes of classical electrodynamics, dealing with the relativistic transformation of energy and momentum for a fluid medium in an external electromagnetic field. In particular, we consider a moving parallel plate charged capacitor, where the electric attraction of its plates is balanced by the…
Classical Electrodynamics A Tutorial on its Foundations
Hehl, F W; Rubilar, G F; Hehl, Friedrich W.; Obukhov, Yuri N.; Rubilar, Guillermo F.
1999-01-01
We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell's equations. They are expressed in terms of the field strengths $(E,{\\cal B})$, the excitations $({\\cal D},H)$, and the sources $(\\rho,j)$. This fundamental set of four microphysical equations has to be supplemented by somewhat less general constitutive assumptions in order to make it a fully determined system with a well-posed initial value problem. It is only at this stage that a distance concept (metric) is required for space-time. We will discuss one set of possible constitutive assumptions, namely ${\\cal D}\\sim E$ and $H\\sim {\\cal B}$. {\\em file erik8a.tex, 1999-07-27}
In-Depth Development of Classical Electrodynamics
Keilman Y. N.
2008-01-01
Full Text Available There is hope that a properly developed Classical Electrodynamics (CED will be able to play a role in a unified field theory explaining electromagnetism, quantum phenomena, and gravitation. There is much work that has to be done in this direction. In this article we propose a move towards this aim by refining the basic principles of an improved CED. Attention is focused on the reinterpretation of the E-M potential. We use these basic principles to obtain solutions that explain the interactions between a constant electromagnetic field and a thin layer of material continuum; between a constant electromagnetic field and a spherical configuration of material continuum (for a charged elementary particle; between a transverse electromagnetic wave and a material continuum; between a longitudinal aether wave (dummy wave and a material continuum.
Comparison between Weber’s electrodynamics and classical electrodynamics
A K T Assis; H Torres Silva
2000-09-01
We present the main aspects of Weber’s electrodynamics and of Maxwell’s equations. We discuss Maxwell’s point of view related to Weber’s electrodynamics. We compare Weber’s force with Lorentz’s force. We analyse the relation between Weber’s law and Maxwell’s equations. Finally, we discuss some experiments performed and proposed with which we can distinguish Weber’s force from Lorentz’s one.
The force exerted by a slowly moving current-carrying loop on a stationary or co-moving charge is derived within two distinct frameworks: Maxwell’s electrodynamics classically interpreted (operating in the Galilean space and time) and relativistic electrodynamics (operating in Minkowski space-time). A comparison between the ‘classical Maxwellian’ and relativistic solutions is presented, offering some intriguing insights that have been neglected in earlier discussions of the issue. (paper)
Redžić, Dragan V.
2014-07-01
The force exerted by a slowly moving current-carrying loop on a stationary or co-moving charge is derived within two distinct frameworks: Maxwell’s electrodynamics classically interpreted (operating in the Galilean space and time) and relativistic electrodynamics (operating in Minkowski space-time). A comparison between the ‘classical Maxwellian’ and relativistic solutions is presented, offering some intriguing insights that have been neglected in earlier discussions of the issue.
On the non-interaction theorems in relativistic classical and quantum mechanics
The non-interaction theorem of Currie-Jordan-Sudarshan in relativistic classical mechanics and the non-interaction Haag theorem in relativistic quantum field theory are stated. It is shown explicitly that the consequences of the latter can be avoided in quantum electrodynamics by dispensing the condition of taking the field variables as canonical variables. (Author)
Relativistic nonlinear electrodynamics the QED vacuum and matter in super-strong radiation fields
Avetissian, Hamlet K
2016-01-01
This revised edition of the author’s classic 2006 text offers a comprehensively updated review of the field of relativistic nonlinear electrodynamics. It explores the interaction of strong and super-strong electromagnetic/laser radiation with the electromagnetic quantum vacuum and diverse types of matter – including free charged particles and antiparticles, acceleration beams, plasma and plasmous media. The appearance of laser sources of relativistic and ultra-relativistic intensities over the last decade has stimulated investigation of a large class of processes under such super-strong radiation fields. Revisions for this second edition reflect these developments and the book includes new chapters on Bremsstrahlung and nonlinear absorption of superintense radiation in plasmas, the nonlinear interaction of relativistic atoms with intense laser radiation, nonlinear interaction of strong laser radiation with Graphene, and relativistic nonlinear phenomena in solid-plasma targets under supershort laser pul...
Relativistic Electrodynamics without Reference Frames. Clifford Algebra Formulation
Ivezic, Tomislav
2002-01-01
In the usual Clifford algebra formulation of electrodynamics the Faraday bivector field $F$ is expressed in terms of \\QTR{em}{the observer dependent} relative vectors $\\QTR{bf}{E}$ and $\\QTR{bf}{B.}$ In this paper we present \\QTR{em}{the observer independent}decomposition of $F$ by using the vectors (grade-1) of electric $E$ and magnetic $B$ fields and we develop the formulation of relativistic electrodynamics which is independent of the reference frame and of the chosen coordinatization. We ...
Popa, Alexandru
2013-01-01
Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamic Systems is intended for scientists and graduate students interested in the foundations of quantum mechanics and applied scientists interested in accurate atomic and molecular models. This is a reference to those working in the new field of relativistic optics, in topics related to relativistic interactions between very intense laser beams and particles, and is based on 30 years of research. The novelty of this work consists of accurate connections between the properties of quantum equations and correspon
A New Formulation for General Relativistic Force-Free Electrodynamics and Its Applications
无
2007-01-01
We formulate the general relativistic force-free electrodynamics in a new 3+1 language. In this formulation, when we have properly defined electric and magnetic fields, the covariant Maxwell equations could be cast in the traditional form with new vacuum con stitutive constraint equations. The fundamental equation governing a stationary, axisymmet ric force-free black hole magnetosphere is derived using this formulation which recasts the Grad-Shafranov equation in a simpler way. Compared to the classic 3+1 system of Thorne and MacDonald, the new system of 3+1 equations is more suitable for numerical use for it keeps the hyperbolic structure of the electrodynamics and avoids the singularity at the event horizon. This formulation could be readily extended to non-relativistic limit and find applications in flat spacetime. We investigate its application to disk wind, black hole magnetosphere and solar physics in both flat and curved spacetime.
Relativistic and quantum electrodynamic effects in superheavy elements
Schwerdtfeger, Peter; Pašteka, Lukáš F.; Punnett, Andrew; Bowman, Patrick O.
2015-12-01
The current status of relativistic electronic structure theory for superheavy elements is reviewed. Recent developments in relativistic quantum theory have made it possible to obtain accurate electronic properties for the trans-actinide elements with the aim to predict their chemical and physical behaviour. The role of quantum electrodynamic effects beyond the no-virtual-pair approximation, which is usually neglected in relativistic molecular calculations, is discussed. Changes in periodic trends due to relativistic effects are outlined for the superheavy elements with nuclear charge Z = 111- 120. We also analyse the role of the negative energy states for the electronic stability of superheavy elements beyond the critical nuclear charge (Zcrit ≈ 170), where the 1s state enters the negative energy continuum at - 2mec2.
Random electrodynamics : a classical foundation for key quantum concepts
The model of random electrodynamics, in which electromagnetic particles are subjected, in a classical manner, to the forces of radiation damping and the fluctuating zero-point fields provides the framework in which the following results are obtained: (1) The precession dynamics of a long-lived, non-relativistic particle with a magnetic moment proportional to its spin, leads to a self-consistent determination of the spin value as one-half. (2) The internal dynamic underlying the intrinsic magnetic moment of a Dirac particle yields a classically visualizable picture of the spin-magnetic moment. (3) The Bose correlation among indistinguishable, non-interacting, spin-zero Particles arises from the coupling through the common- zero point fields and the radiation reaction fields when the particles are close together in both the r vector and the energy spaces. (4) The (exclusion principle-induced) correlation among identical, non-interacting magnetic particles with spin 1/2 is brought about by the coupling, (through the common fields of radiation reaction and the vacuum fluctuations), of the spins as well as the translational motions when the particles are close together in r vector and the energy spaces. (5) A dilute gas of free electrons has a Maxwellian distribution of velocities and the correct value of the djamagnetic moment in the presence of a magnetic field. Considerations on the centre of mass motion of a composite neutral particle lead to a simple resolution of the foundational paradoxes of statistical mechanics. (6) An approximate treatment of the hydrogen atom leads to a description of the evolution to the ground state at absolute zero and an estimation of the mass frequency and the line-width of the radiation emitted when an excited atom decays. (author)
Classical electrodynamics from image charges to the photon mass and magnetic monopoles
Lacava, Francesco
2016-01-01
This book proposes intriguing arguments that will enable students to achieve a deeper understanding of electromagnetism, while also presenting a number of classical methods for solving difficult problems. Two chapters are devoted to relativistic electrodynamics, covering all aspects needed for a full comprehension of the nature of electric and magnetic fields and, subsequently, electrodynamics. Each of the two final chapters examines a selected experimental issue, introducing students to the work involved in actually proving a law or theory. Classical books on electricity and magnetism are mentioned in many references, helping to familiarize students with books that they will encounter in their further studies. Various problems are presented, together with their worked-out solutions. The book is based on notes from special lectures delivered by the author to students during the second year of a BSc course in Physics, but the subject matter may also be of interest to senior physicists, as many of the themes co...
Classical approximations of relativistic quantum physics
Johnson, Glenn Eric
2016-01-01
A correspondence of classical to quantum physics studied by Schr\\"{o}\\-dinger and Ehrenfest applies without the necessity of technical conjecture that classical observables are associated with Hermitian Hilbert space operators. This correspondence provides appropriate nonrelativistic classical interpretations to realizations of relativistic quantum physics that are incompatible with the canonical formalism. Using this correspondence, Newtonian mechanics for a $1/r$ potential provides approxim...
The relativistic rotation transformation and pulsar electrodynamics
Kichenassamy, S.; Krikorian, R. A.
1994-08-01
The substitution of the relativistic rotation transformation (RRT) of Trocheris and Takeno to the Galilean type one, establishing a nonlinear relation between speed v and angular velocity omega (upsilon = c tanh (omega/c)), not only sends to infinity the 'light cylinder' and modifies the characteristic parameters of pulsars within the corotating source model (Kichenassamy & Krikorian 1991), but also circumvents the change of type of the differential equations for the electromagnetic potential when a quasi-static constraint is assumed; on the other hand, the resulting equations for a force-free magnetosphere reduce to those of Mestel, at the nonrelativistic approximation, when RRT reduces to the usual 'instantaneous Lorentz transformation;' indeed, difficulties related to energy flow across the light cylinder become ipso facto meaningless.
Observers and splitting structures in relativistic electrodynamics
We introduce a relativistic splitting structure as a means to map fields and equations of electromagnetism from curved four-dimensional space–time to three-dimensional observer's space. We focus on a minimal set of mathematical structures that are directly motivated by the language of the physical theory. Space–time, world-lines, time translation, space platforms and time synchronization all find their mathematical counterparts. The splitting structure is defined without recourse to coordinates or frames. This is noteworthy since, in much of the prevalent literature, observers are identified with adapted coordinates and frames. Among the benefits of the approach is a concise and insightful classification of splitting structures that is juxtaposed to a classification of observers. The application of the framework to the Ehrenfest paradox and Schiff's ‘Question in General Relativity’ further illustrates the advantages of the framework, enabling a compact, yet profound analysis of the problems at hand. (paper)
Plimak, L. I.; Ivanov, Misha; Aiello, A.; Stenholm, S.
2015-08-01
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to "doing quantum electrodynamics while thinking classically," allowing one to substitute essentially classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.
Classical Electrodynamics in a Unified Theory
Ghose, Partha
2016-01-01
Some consequences of a fully classical unified theory of gravity and electromagnetism are worked out for the electromagnetic sector such as the occurrence of classical light beams with spin and orbital angular momenta that are topologically quantized in units of $q_e q_m=\\sigma$, independent of the beam size. Empirical fits require $\\sigma = \\hbar$. The theory also predicts a generalized coherency matrix whose consequences are testable.
Symmetries and Couplings of Non-Relativistic Electrodynamics
Festuccia, Guido; Hartong, Jelle; Obers, Niels A
2016-01-01
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell's equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a $U(1)$ current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galile...
Plimak, L. I.; Ivanov, Misha; Aiello, A.; Stenholm, S.
2015-01-01
Quantum electrodynamics under conditions of distinguishability of interacting matter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore...
On refinement of certain laws of classical electrodynamics
Mende, F F
2004-01-01
The problems considered refer to the material equations of electric- and magnetoelectric induction. Some contradictions found in fundamental studies on classical electrodynamics have been explained. The notion magnetoelectric induction has been introduced, which permits symmetrical writing of the induction laws. It is shown that the results of the special theory of relativity can be obtained from these laws through the Galilean transformations. The permittivity and permeability of materials media are shown to be independent of frequency. The notions magnetoelectrokinetic and electromagnetopotential waves and kinetic capacity have been introduced. It is shown that along with the longitudinal Langmuir resonance, the transverse resonance is possible in nonmagnetized plasma, and both the resonances are degenerate. A new notion scalar-vector potential is introduced, which permits solution of all present-day problems of classical electrodynamics. The use of the scalar-vector potential makes the magnetic field notio...
On refinement of certain laws of classical electrodynamics
Mende, F. F.
2004-01-01
The problems considered refer to the material equations of electric- and magnetoelectric induction. Some contradictions found in fundamental studies on classical electrodynamics have been explained. The notion magnetoelectric induction has been introduced, which permits symmetrical writing of the induction laws. It is shown that the results of the special theory of relativity can be obtained from these laws through the Galilean transformations. The permittivity and permeability of materials m...
Universal Newton Time in Classical Electrodynamics Elements of Physical Interpretation
Kotelnikov, K A
2000-01-01
It is shown that the universal Newton time may be introduced in the classical electrodynamics. The statement results from an existence of the generalized symmetry of Maxwell equations with respect to Galilei transformations (physics/9701006). In the case of the extended Galilei transformations the postulate of invariance of the speed of light may be made compatible with the concept of the universal Newton time. Some physical consequences of the extended Galilei symmetry are considered.
Classical and quantum electrodynamics and the B(3) field
Evans, Myron W
2001-01-01
It is well known that classical electrodynamics is riddled with internal inconsistencies springing from the fact that it is a linear, Abelian theory in which the potentials are unphysical. This volume offers a self-consistent hypothesis which removes some of these problems, as well as builds a framework on which linear and nonlinear optics are treated as a non-Abelian gauge field theory based on the emergence of the fundamental magnetizing field of radiation, the B(3) field. Contents: Interaction of Electromagnetic Radiation with One Fermion; The Field Equations of Classical O (3) b Electrodyn
Relativistic Entanglement From Maxwell's Classical Equations
Carroll, John E.; Quarterman, Adrian H.
2013-09-01
With the help of light cone coordinates and light cone field representations of Maxwell's classical equations, quantum polarization entanglement is explained using the relativistic results of a companion paper that shows how conventional or reference waves can have an adjoint wave, travelling in phase with the reference wave, but in a proper relativistic frame that travels in the opposing direction to the proper frame of the reference wave. This subsequently allows waves, travelling in opposite directions, to have the same proper frame and consequently such waves can be regarded as relativistically local. The light cone coordinates offer a classical form of a quantum wave function and demonstrate a classical equivalent of a mixed quantum state.
Stability of the hydrogen atom of classical electrodynamics
De Luca, J
2004-01-01
We study the stability of the circular orbits of the electromagnetic two-body problem of classical electrodynamics. We introduce the concept of resonant dissipation, i.e. a motion that radiates the center-of-mass energy while the interparticle distance performs bounded oscillations about a metastable orbit. The stability mechanism is established by the existence of a quartic resonant constant generated by the stiff eigenvalues of the linear stability problem. This constant bounds the particles together during the radiative recoil. The condition of resonant dissipation predicts angular momenta for the metastable orbits in reasonable agreement with the Bohr atom. The principal result is that the emission lines agree with the predictions of quantum electrodynamics (QED) with 1 percent average error even up to the $40^{th}$ line. Our angular momenta depend logarithmically on the mass of the heavy body, such that the deuterium and the muonium atoms have essentially the same angular momenta, in agreement with QED. ...
Pair production in classical Stueckelberg-Horwitz-Piron electrodynamics
Land, Martin
2016-01-01
In this paper we calculate pair production from bremsstrahlung as a classical effect in Stueckelberg-Horwitz-Piron electrodynamics. In this framework, worldlines are traced out dynamically through the evolution of events $x^\\mu(\\tau)$ parameterized by a chronological time $\\tau$ that is independent of the spacetime coordinates. These events, defined in an unconstrained 8D phase space, interact through five $\\tau$-dependent gauge fields induced by the event evolution. The resulting theory differs in its underlying mechanics from conventional electromagnetism, but coincides with Maxwell theory in an equilibrium limit. In particular, the total mass-energy-momentum of particles and fields is conserved, but the mass-shell constraint is lifted from individual interacting events, so that the standard Feynman-Stueckelberg interpretation of pair creation/annihilation is implemented in classical mechanics.
New Perspective on the Reciprocity Theorem of Classical Electrodynamics
Mansuripur, Masud; 10.1016/j.optcom.2010.09.077
2012-01-01
We provide a simple physical proof of the reciprocity theorem of classical electrodynamics in the general case of material media that contain linearly polarizable as well as linearly magnetizable substances. The excitation source is taken to be a point-dipole, either electric or magnetic, and the monitored field at the observation point can be electric or magnetic, regardless of the nature of the source dipole. The electric and magnetic susceptibility tensors of the material system may vary from point to point in space, but they cannot be functions of time. In the case of spatially non-dispersive media, the only other constraint on the local susceptibility tensors is that they be symmetric at each and every point. The proof is readily extended to media that exhibit spatial dispersion: For reciprocity to hold, the electric susceptibility tensor Chi_E_mn that relates the complex-valued magnitude of the electric dipole at location r_m to the strength of the electric field at r_n must be the transpose of Chi_E_nm...
Relativistic and separable classical hamiltonian particle dynamics
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincare invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light
Relativistic like structure of classical thermodynamics
Quevedo, Hernando; Sánchez, Alberto; Vázquez, Alejandro
2015-04-01
We analyze in the context of geometrothermodynamics a Legendre invariant metric structure in the equilibrium space of an ideal gas. We introduce the concept of thermodynamic geodesic as a succession of points, each corresponding to a state of equilibrium, so that the resulting curve represents a quasi-static process. A rigorous geometric structure is derived in which the thermodynamic geodesics at a given point split the equilibrium space into two disconnected regions separated by adiabatic geodesics. This resembles the causal structure of special relativity, which we use to introduce the concept of adiabatic cone for thermodynamic systems. This result might be interpreted as an alternative indication of the inter-relationship between relativistic physics and classical thermodynamics.
"今枝, 国之助"; "イマエダ, クニノスケ"; Kuninosuke", "Imaeda
1985-01-01
"Quaternionic formulation of classical electrodynamics by using ""biq""(real part of a complex-quaternions) has been presented. Also, the solutions of Maxwell's equations have been given using regular functions of a biq variable."
LOCAL CLASSICAL SOLUTIONS TO THE EQUATIONS OF RELATIVISTIC HYDRODYNAMICS
史一蓬
2001-01-01
In this paper, we prove that the convexity of the negative thermodynamical entropy of the equations of relativistic hydrodynamics for ideal gas keeps its invariance under the Lorentz transformation if and only if the local sound speed is less than the light speed in vacuum. Then a symmetric form for the equations of relativistic hydrodynamics is presented and the local classical solution is obtained. Based on this,we prove that the nonrelativistic limit of the local classical solution to the relativistic hydrodynamics equations for relativistic gas is the local classical solution of the Euler equations for polytropic gas.
Transverse-longitudinal part of a vector potential in classical electrodynamics
Existence of a physical (gauge-invariant) degree of freedom of the vector potential generating no electromagnetic fields is proved in classical electrodynamics within the Dirac generalized Hamiltonian dynamics. The gauge-invariant form of electrodynamics of charged particles is given within which the question of observing the obtained degree of freedom is discussed. It is shown that it caused an electric current in a superconducting ring put on the solenoid. 20 refs
Quantum Electrodynamics Basis of Classical-Field High-Harmonic Generation Theory
王兵兵; 高靓辉; 傅盘铭; 郭东升; R. R. Freeman
2001-01-01
From the nonperturbative quantum electrodynamics theory, we derive the Landau-Dykhne formula which represents the quantum-mechanical formulation of the three-step model. These studies provide a basis for the classical-field approaches to high-order harmonic generation and justify some assumptions used in classical-field modelling.
Restrictions imposed on relativistic two-body interactions by classical relativistic field theory
We show that various relativistic potential models (all sharing exact relativistic two-body kinematics and a common nonrelativistic limit) can be distinguished by agreement or disagreement with relativistic corrections produced by classical field theory. We find that the only one of these models whose relativisic corrections duplicate those of classical field theory is the minimal Todorov equation. Conversely, we derive the Todorov equation from the semirelativistic dynamics of classical field theory, thus exposing the classical field-theoretic origins of its characteristic minimal potential structures and dependences on effective one-body variables
Nonlinear theory of relativistic CRM with resonant electrodynamic systems
Effects associated with the influence of nonsynchronous waves of resonators as well as ponderomotive forces, arising due to the longitudinal nonuniformity of the synchronous waves and of the focusing magnetostatic field, are studied for relativistic CRM with high-Q resonators. A nonlinear theory of a monotron based on the anomalous Doppler effect, in which a relativistic electron beam which is initially rectilinear excites the field in an open two-mirror resonator, is constructed. It is shown that the efficiency of such generators can reach 50%
Fundamental laws of relativistic classical dynamics revisited
By stating that a linear differential form, whose coefficients are the components of the momentum and the energy of a particle, has an antiderivative, the basic equations of the dynamics of points are obtained, in the relativistic case. From the point of view of optimization theory, a connection between our condition and the Bellman-Isaacs equation of dynamic programming is discussed, with a view to extending the theory to relativistic wave mechanics
Di Rocco, Héctor O.; Lanzini, Fernando
2016-04-01
The correction to the Coulomb repulsion between two electrons due to the exchange of a transverse photon, referred to as the Breit interaction, as well as the main quantum electrodynamics contributions to the atomic energies (self-energy and vacuum polarization), are calculated using the recently formulated relativistic screened hydrogenic model. Comparison with the results of multiconfiguration Dirac-Hartree-Fock calculations and experimental X- ray energies is made.
Nieuwenhuizen, Theodorus M.; Liska, Matthew T. P.
2015-10-01
In a recent paper the authors studied numerically the hydrogen ground state in stochastic electrodynamics (SED) within the the non-relativistic approximation. In quantum theory the leading non-relativistic corrections to the ground state energy dominate the Lamb shift related to the photon cloud that should cause the quantum-like behaviour of SED. The present work takes these corrections into account in the numerical modelling. It is found that they have little effect; the self-ionisation that occurs without them remains present. It is speculated that the point-charge approximation for the electron is the cause of the failure.
Galilean symmetry of maxwell's equations in classical electrodynamics
The study presented shows that the Galilean group, like the Lorentz group, is a group of exact symmetry of Maxwell's equation. The Galilean group differs in that, while the field transformations are linear and global in the relativistic case, they are nonlinear in the Galilean and, generally speaking, depend on the coordinates of the event through some weight functions
Galilean symmetry of Maxwell's equations in classical electrodynamics
Kotel'Nikov, G. A.
1985-08-01
It is shown that the Galilean group, like the Lorentz group, is a group of exact symmetry of Maxwell's equation. The Galilean group differs in that, while the field transformations are linear and global in the relativistic case, they are nonlinear in the Galilean and, generally speaking, depend on the coordinates of the event through some weight functions.
The variational method in a reformulated Hamiltonian formalism of quantum electrodynamics (QED) is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels of these equations include one-photon exchange interactions. The equations have the expected Schroedinger non-relativistic limit. Application to some exotic few lepton systems is discussed briefly. (author)
Gsponer, Andre
2009-01-01
The objective of this introduction to Colombeau algebras of generalized functions (in which distributions can be freely multiplied) is to explain in elementary terms the essential concepts necessary for their application to basic nonlinear problems in classical physics. Examples are given in hydrodynamics and electrodynamics. The problem of the…
On the Foundational Equations of the Classical Theory of Electrodynamics
Mansuripur, Masud
2014-01-01
A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes - volumes that nevertheless contain a large number of electric and/or magnetic dipoles. Indeed, Maxwell's macroscopic equations are exact and self-consistent mathematical relations between electromagnetic fields and their sources, which consist of free charge, free current, polarization, and magnetization. When necessary, the discrete nature of the constituents of matter and the granularity of material media can be handled with the aid of special functions, such as Dirac's delta-function. The energy of the electromagnetic field and the exchange of this energy with material media are treated with a single postulate that establishes the Poynting vector S = ExH as the rate of flow of electromagnetic energy under all circumstances. Similarly, the linear and angular momentum densities of the fields are simple functions of the Poy...
Amano, Takanobu
2016-01-01
A new multidimensional simulation code for relativistic two-fluid electrodynamics (RTFED) is described. The basic equations consist of the full set of Maxwell's equations coupled with relativistic hydrodynamic equations for separate two charged fluids, representing the dynamics of either an electron-positron or an electron-proton plasma. It can be recognized as an extension of conventional relativistic magnetohydrodynamics (RMHD). Finite resistivity may be introduced as a friction between the two species, which reduces to resistive RMHD in the long wavelength limit without suffering from a singularity at infinite conductivity. A numerical scheme based on HLL (Harten-Lax-Van Leer) Riemann solver is proposed that exactly preserves the two divergence constraints for Maxwell's equations simultaneously. Several benchmark problems demonstrate that it is capable of describing RMHD shocks/discontinuities at long wavelength limit, as well as dispersive characteristics due to the two-fluid effect appearing at small sca...
Is the Meissner effect explicable in terms of classical electrodynamics
The core radius r0 of a current-carrying superconducting cylinder in the intermediate state determined from experimental data disagrees with the theoretical value of r0 derived on the basis of the classical interpretation of the Meissner effect. Then the problem arises of whether this interpretation of the Meissner effect corresponds to reality. (Auth.)
Classical electrodynamics in a space with spin noncommutativity of coordinates
Vasyuta, V M
2016-01-01
We propose a new relativistic Lorentz-invariant spin-noncommutative algebra. Using the Weyl ordering of noncommutative position operators, we build an analogue of the Moyal-Groenewald product for the proposed algebra. The Lagrange function of an electromagnetic field in the space with spin noncommutativity is constructed. In such a space electromagnetic field becomes non-abelian. A gauge transformation law of this field is also obtained. Exact nonlinear field equations of noncommutative electromagnetic field are derived from the least action principle. Within the perturbative approach we consider field of a point charge in a constant magnetic field and interaction of two plane waves. An exact solution of a plane wave propagation in a constant magnetic and electric fields is found.
Quantum-to-Classical Transition in Cavity Quantum Electrodynamics (QED)
Fink, J M; Studer, P; Bishop, Lev S; Baur, M; Bianchetti, R; Bozyigit, D; Lang, C; Filipp, S; Leek, P J; Wallraff, A
2010-01-01
The quantum properties of electromagnetic, mechanical or any other type of harmonic oscillator can be revealed by investigating its strong coherent coupling to a single quantum two level system in an approach known as cavity QED. At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a few quanta asserts the quantum nature of the system. Here, we study how the classical response of a quantum cavity QED system emerges when its thermal occupation -- or effective temperature -- is raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous cross-over from a quantum response to a classical response in the spirit of Bohr's correspondence principle. We also demonstrate how to extract effective cavity field temperatures from both spectroscopic and time-resolved vacuum Rabi measurements.
Losing energy in classical, relativistic and quantum mechanics
Atkinson, David
2007-01-01
A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. In relativistic mechanics, however, neit
Field, J H.
2004-01-01
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz Equation may be understood in a simple way by comparing classical electromagnetism and the photonic description of light provided by classical relativistic kinematics. The method used may be described as `inverse correspondence' since quantum phenomena bec...
A generalisation of classical electrodynamics for the prediction of scalar field effects
van Vlaenderen, Koen J.
2003-01-01
Within the framework of Classical Electrodynamics (CED) it is common practice to choose freely an arbitrary gauge condition with respect to a gauge transformation of the electromagnetic potentials. The Lorenz gauge condition allows for the derivation of the inhomogeneous potential wave equations (IPWE), but this also means that scalar derivatives of the electromagnetic potentials are considered to be \\emph{unphysical}. However, these scalar expressions might have the meaning of a new physical...
The Force Law of Classical Electrodynamics: Lorentz versus Einstein and Laub
Mansuripur, Masud
2013-01-01
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and materi...
SIMLA: Simulating laser-particle interactions via classical and quantum electrodynamics
Green, D. G.; Harvey, C. N.
2014-01-01
We present the Fortran code SIMLA, which is designed for the study of charged particle dynamics in laser and other background fields. This can be done classically via the Landau-Lifshitz equation, or alternatively, via the simulation of photon emission events determined by strong-field quantum-electrodynamics amplitudes and implemented using Monte-Carlo type routines. Multiple laser fields can be included in the simulation and the propagation direction, beam shape (plane wave, focussed paraxi...
The Charge-Magnet Paradoxes of Classical Electrodynamics
Mansuripur, Masud
2014-01-01
A number of charge-magnet paradoxes have been discussed in the literature, beginning with Shockley's famous 1967 paper, where he introduced the notion of hidden momentum in electromagnetic systems. We discuss all these paradoxes in a single, general context, showing that the conservation laws of linear and angular momenta can be satisfied without the need for hidden entities, provided that the Einstein-Laub laws of force and torque are used in place of the standard Lorentz law. Einstein and Laub published their paper in 1908, but the simplicity of the conventional Lorentz law overshadowed the subtle features of their formulation which, at first sight, appears somewhat complicated. However, that slight complication turns out to lead to subsequent advantages in light of Shockley's discovery of hidden momentum, which occurred more than a decade after Einstein had passed away. In this paper, we show how the Einstein-Laub formalism handles the underlying problems associated with certain paradoxes of classical elec...
Classical and quantum mechanics of the relativistic particle
It is shown that the standard actions of the relativistic point-like particle are adapted within the corresponding interpretation to describe particle and antiparticle at the same time. Special gauge in which this possibility realize naturally both in classical and in quantum theory is pointed out. A consistent procedure of canonical quantization of relativistic point-like particle without and with spin is considered. the operator formulation of the system in question is manifestly constructed. So built quantum mechanics proves to be equivalent for a spinless particle to Klein-Gordon theory and for spinning particle to Dirac theory. (author). 14 refs
A new approach in classical electrodynamics to protect principle of causality
Biswaranjan Dikshit
2014-03-01
Full Text Available In classical electrodynamics, electromagnetic effects are calculated from solution of wave equation formed by combination of four Maxwell’s equations. However, along with retarded solution, this wave equation admits advanced solution in which case the effect happens before the cause. So, to preserve causality in natural events, the retarded solution is intentionally chosen and the advance part is just ignored. But, an equation or method cannot be called fundamental if it admits a wrong result (that violates principle of causality in addition to the correct result. Since it is the Maxwell’s form of equations that gives birth to this acausal advanced potential, we rewrite these equations in a different form using the recent theory of reaction at a distance (Biswaranjan Dikshit, Physics essays, 24(1, 4-9, 2011 so that the process of calculation does not generate any advanced effects. Thus, the long-standing causality problem in electrodynamics is solved.
Classical and relativistic flux of energy conservation in astrophysical jets
Zaninetti, L.
2016-01-01
The conservation of the energy flux in turbulent jets which propagate in the intergalactic medium (IGM) allows deducing the law of motion in the classical and relativistic cases. Three types of IGM are considered: constant density, hyperbolic and inverse power law decrease of density. An analytical law for the evolution of the magnetic field along the radio-jets is deduced using a linear relation between the magnetic pressure and the rest density. Astrophysical applications are made to the ce...
The effective equations of motion for a point charged particle taking into account the radiation reaction are considered in various space-time dimensions. The divergences stemming from the pointness of the particle are studied and an effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogues of the Lorentz-Dirac equation are explicitly derived
Kazinski, P. O.; Lyakhovich, S. L.; Sharapov, A. A.
2002-07-01
The effective equations of motion for a point charged particle taking into account the radiation reaction are considered in various space-time dimensions. The divergences stemming from the pointness of the particle are studied and an effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogues of the Lorentz-Dirac equation are explicitly derived.
Kazinski, P O; Sharapov, A A
2002-01-01
The effective equations of motion for a point charged particle taking account of radiation reaction are considered in various space-time dimensions. The divergencies steaming from the pointness of the particle are studied and the effective renormalization procedure is proposed encompassing uniformly the cases of all even dimensions. It is shown that in any dimension the classical electrodynamics is a renormalizable theory if not multiplicatively beyond d=4. For the cases of three and six dimensions the covariant analogs of the Lorentz-Dirac equation are explicitly derived.
SIMLA: Simulating laser-particle interactions via classical and quantum electrodynamics
Green, D G
2014-01-01
We present the Fortran code SIMLA, which is designed for the study of charged particle dynamics in laser and other background fields. This can be done classically via the Landau-Lifshitz equation, or alternatively, via the simulation of photon emission events determined by strong-field quantum-electrodynamics amplitudes and implemented using Monte-Carlo type routines. Multiple laser fields can be included in the simulation and the propagation direction, beam shape (plane wave, focussed paraxial, constant crossed, or constant magnetic), and time envelope of each can be independently specified.
Classical and relativistic flux of energy conservation in astrophysical jets
Zaninetti, L
2016-01-01
The conservation of the energy flux in turbulent jets which propagate in the intergalactic medium (IGM) allows deducing the law of motion in the classical and relativistic cases. Three types of IGM are considered: constant density, hyperbolic and inverse power law decrease of density. An analytical law for the evolution of the magnetic field along the radio-jets is deduced using a linear relation between the magnetic pressure and the rest density. Astrophysical applications are made to the centerline intensity of synchrotron emission in NGC315 and to the magnetic field of 3C273.
Multiparty Quantum Secret Sharing of Classical Message using Cavity Quantum Electrodynamic System
HAN Lian-Fang; LIU Yi-Min; ZHANG Zhan-Jun
2006-01-01
@@ An experimental feasible scheme of multiparty secret sharing of classical messages is proposed, based on a cavity quantum electrodynamic system. The secret messages are imposed on atomic Bell states initially in the sender's possession by local unitary operations. By swapping quantum entanglement of atomic Bell states, the secret messages are split into several parts and each part is distributed to a separate party. In this case, any subset of the entire party group can not read out the secret message but the entirety via mutual cooperations. In this scheme, to discriminate atomic Bell states, additional classical fields are employed besides the same highly-detuned single-mode cavities used to prepare atomic Bell states. This scheme is insensitive to the cavity decay and the thermal field, and usual joint Bell-state measurements are unnecessary.
Relativistic semi-classical theory of atom ionization in ultra-intense laser
无
2001-01-01
A relativistic semi-classical theory (RSCT) of H-atom ionizationin ultra-intense laser (UIL) is proposed. A relativistic analytical expression for ionization probability of H-atom in its ground state is given. This expression, compared with non-relativistic expression, clearly shows the effects of the magnet vector in the laser, the non-dipole approximation and the relativistic mass-energy relation on the ionization processes. At the same time, we show that under some conditions the relativistic expression reduces to the non-relativistic expression of non-dipole approximation. At last, some possible applications of the relativistic theory are briefly stated.
Axiomatics of classical electrodynamics and its relation to gauge field theory
Gronwald, F; Nitsch, J; Gronwald, Frank; Hehl, Friedrich W.
2005-01-01
We give a concise axiomatic introduction into the fundamental structure of classical electrodynamics: It is based on electric charge conservation, the Lorentz force, magnetic flux conservation, and the existence of local and linear constitutive relations. The {\\it inhomogeneous} Maxwell equations, expressed in terms of $D^i$ and $H_i$, turn out to be a consequence of electric charge conservation, whereas the {\\it homogeneous} Maxwell equations, expressed in terms of $E_i$ and $B^i$, are derived from magnetic flux conservation and special relativity theory. The excitations $D^i$ and $H_i$, by means of constitutive relations, are linked to the field strengths $E_i$ and $B^i$. Eventually, we point out how this axiomatic approach is related to the framework of gauge field theory.
The Force Law of Classical Electrodynamics: Lorentz versus Einstein and Laub
Mansuripur, Masud
2013-01-01
The classical theory of electrodynamics is built upon Maxwell's equations and the concepts of electromagnetic field, force, energy, and momentum, which are intimately tied together by Poynting's theorem and the Lorentz force law. Whereas Maxwell's macroscopic equations relate the electric and magnetic fields to their material sources (i.e., charge, current, polarization and magnetization), Poynting's theorem governs the flow of electromagnetic energy and its exchange between fields and material media, while the Lorentz law regulates the back-and-forth transfer of momentum between the media and the fields. As it turns out, an alternative force law, first proposed in 1908 by Einstein and Laub, exists that is consistent with Maxwell's macroscopic equations and complies with the conservation laws as well as with the requirements of special relativity. While the Lorentz law requires the introduction of hidden energy and hidden momentum in situations where an electric field acts on a magnetic material, the Einstein...
A generalisation of classical electrodynamics for the prediction of scalar field effects
van Vlaenderen, K J
2003-01-01
Within the framework of Classical Electrodynamics (CED) it is common practice to choose freely an arbitrary gauge condition with respect to a gauge transformation of the electromagnetic potentials. The Lorenz gauge condition allows for the derivation of the inhomogeneous potential wave equations (IPWE), but this also means that scalar derivatives of the electromagnetic potentials are considered to be \\emph{unphysical}. However, these scalar expressions might have the meaning of a new physical field, $\\mathsf S$. If this is the case, then a generalised CED is required such that scalar field effects are predicted and such that experiments can be performed in order to verify or falsify this generalised CED. The IPWE are viewed as a generalised Gauss law and a generalised Ampe\\`re law, that also contain derivatives of $\\mathsf S$, after reformulating the IPWE in terms of fields. Some recent experiment show positive results that are in qualitative agreement with the presented predictions of scalar field effects, b...
Mansuripur, Masud
2015-01-01
The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just as it postulates the existence and properties of electric charges and currents. Maxwell's macroscopic equations are mathematically exact and self-consistent differential equations that relate the electromagnetic (EM) field to its sources, namely, electric charge-density $\\rho_{free}$, electric current-density $J_{free}$, polarization P, and magnetization M. At the level of Maxwell's macroscopic equations, there is no need for models of electric and magnetic dipoles. For example, whether a magnetic dipole is an Amperian current-loop or a Gilbertian pair of north and south magnetic monopoles has no effect on the solution of Maxwell's equations. Electromagnetic fields carry energy as well as linear and angular momenta, which they can exchange with material media - the seat of...
Momentum Maps and Classical Relativistic Fields; 1, Covariant Field Theory
Gotay, M J; Marsden, J E; Gotay, Mark J.; Isenberg, James; Marsden, Jerrold E.
1998-01-01
This is the first paper of a four part work in which we study the Lagrangian and Hamiltonian structure of classical field theories with constraints. Our goal is to explore some of the connections between initial value constraints and gauge transformations in such theories (either relativistic or not). To do this, in the course of these four papers, we develop and use a number of tools from symplectic and multisymplectic geometry. Of central importance in our analysis is the notion of the ``energy-momentum map'' associated to the gauge group of a given classical field theory. We hope to demonstrate that many different and apparently unrelated facets of field theories can be thereby tied together and understood in an essentially new way. In Part I we develop some of the basic theory of classical fields from a spacetime covariant viewpoint. We begin with a study of the covariant Lagrangian and Hamiltonian formalisms, on jet bundles and multisymplectic manifolds, respectively. Then we discuss symmetries, conserva...
Introduction to relativistic statistical mechanics classical and quantum
Hakim, Rémi
2011-01-01
This is one of the very few books focusing on relativistic statistical mechanics, and is written by a leading expert in this special field. It started from the notion of relativistic kinetic theory, half a century ago, exploding into relativistic statisti
Bashinov, Aleksei
2013-01-01
{A simple electrodynamic model is developed to define plasma-field structures in self-consistent ultra-relativistic laser-plasma interactions when the radiation reaction effects come into play. An exact analysis of a circularly polarized laser interacting with plasmas is presented. We define fundamental notations such as nonlinear dielectric permittivity, ponderomotive and dissipative forces acting in a plasma. Plasma-field structures arising during the ultra-relativisitc interactions are also calculated. Based on these solutions we show that about 50% of laser energy can be converted into gamma-rays in the optimal conditions of laser-foil interaction.
Softness of Sn isotopes in relativistic semi-classical approximation
Biswal, S. K.; Singh, S. K.; Bhuyan, M.; Patra, S.K.
2014-01-01
Within the frame-work of relativistic Thomas-Fermi and relativistic extended Thomas-Fermi approximations, we calculate the giant monopole resonance (GMR) excitation energies for Sn and related nuclei. A large number of non-linear relativistic force parameters are used in this calculations. We find that a parameter set is capable to reproduce the experimental monopole energy of Sn isotopes, when its nuclear matter compressibility lies within $210-230$ MeV, however fails to reproduce the GMR en...
Classical and Quantum Mechanics of Free \\k Relativistic Systems
Lukierski, J.; Ruegg, H.; Zakrzewski, W. J.
1993-01-01
We consider the Hamiltonian and Lagrangian formalism describing free \\k-relativistic particles with their four-momenta constrained to the \\k-deformed mass shell. We study the modifications of the formalism which follow from the introduction of space coordinates with nonvanishing Poisson brackets and from the redefinitions of the energy operator. The quantum mechanics of free \\k-relativistic particles and of the free \\k-relativistic oscillator is also presented. It is shown that the \\k-relativ...
Mansuripur, Masud
2015-01-01
The classical theory of electrodynamics cannot explain the existence and structure of electric and magnetic dipoles, yet it incorporates such dipoles into its fundamental equations, simply by postulating their existence and properties, just as it postulates the existence and properties of electric charges and currents. Maxwell's macroscopic equations are mathematically exact and self-consistent differential equations that relate the electromagnetic (EM) field to its sources, namely, electric charge-density 𝜌𝜌free, electric current-density 𝑱𝑱free, polarization 𝑷𝑷, and magnetization 𝑴𝑴. At the level of Maxwell's macroscopic equations, there is no need for models of electric and magnetic dipoles. For example, whether a magnetic dipole is an Amperian current-loop or a Gilbertian pair of north and south magnetic monopoles has no effect on the solution of Maxwell's equations. Electromagnetic fields carry energy as well as linear and angular momenta, which they can exchange with material media—the seat of the sources of the EM field—thereby exerting force and torque on these media. In the Lorentz formulation of classical electrodynamics, the electric and magnetic fields, 𝑬𝑬 and 𝑩𝑩, exert forces and torques on electric charge and current distributions. An electric dipole is then modeled as a pair of electric charges on a stick (or spring), and a magnetic dipole is modeled as an Amperian current loop, so that the Lorentz force law can be applied to the corresponding (bound) charges and (bound) currents of these dipoles. In contrast, the Einstein-Laub formulation circumvents the need for specific models of the dipoles by simply providing a recipe for calculating the force- and torque-densities exerted by the 𝑬𝑬 and 𝑯𝑯 fields on charge, current, polarization and magnetization. The two formulations, while similar in many respects, have significant
Speeds of Propagation in Classical and Relativistic Extended Thermodynamics
Müller Ingo
1999-01-01
Full Text Available The Navier-Stokes-Fourier theory of viscous, heat-conducting fluids provides parabolic equations and thus predicts infinite pulse speeds. Naturally this feature has disqualified the theory for relativistic thermodynamics which must insist on finite speeds and, moreover, on speeds smaller than $c$. The attempts at a remedy have proved heuristically important for a new systematic type of thermodynamics: Extended thermodynamics. That new theory has symmetric hyperbolic field equations and thus it provides finite pulse speeds. Extended thermodynamics is a whole hierarchy of theories with an increasing number of fields when gradients and rates of thermodynamic processes become steeper and faster. The first stage in this hierarchy is the 14-field theory which may already be a useful tool for the relativist in many applications. The 14 fields -- and further fields -- are conveniently chosen from the moments of the kinetic theory of gases. The hierarchy is complete only when the number of fields tends to infinity. In that case the pulse speed of non-relativistic extended thermodynamics tends to infinity while the pulse speed of relativistic extended thermodynamics tends to $c$, the speed of light. In extended thermodynamics symmetric hyperbolicity -- and finite speeds -- are implied by the concavity of the entropy density. This is still true in relativistic thermodynamics for a privileged entropy density which is the entropy density of the rest frame for non-degenerate gases.
It is shown that the use of the Foldy-Wouthuysen representation allows one to reduce finding the classical limit of equations of the relativistic quantum mechanics to replacing operators in the Hamiltonian and quantum mechanical equations of motion with corresponding classical quantities when the conditions of the Wentzel-Kramers-Brillouin approximation are satisfied
Classical solutions in a Lorentz-violating Maxwell-Chern-Simons electrodynamics
We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carrol-Field-Jackiw term. We then write and study the extended Maxwell equations and the corresponding wave equations for the potentials. The solution to these equations show some interesting deviations from the usual MCS Electrodynamics, with background-dependent correction terms. In the case of a time-like background, the correction terms dominate over the MCS sector in the region far from the origin, and establish the behaviour of a massless Electrodynamics ( in the electric sector). In the space-like case, the solutions indicate the clear manifestation of spatial anisotropy, which is consistent with the existence of a privileged direction is space. (author)
Classical Solutions in a Lorentz-violating Maxwell-Chern-Simons Electrodynamics
Belich, H; Orlando, M T D
2003-01-01
We take as starting point the planar model arising from the dimensional reduction of the Maxwell Electrodynamics with the (Lorentz-violating) Carroll-Field-Jackiw term. We then write and study the extended Maxwell equations and the corresponding wave equations for the potentials. The solution to these equations show some interesting deviations from the usual MCS Electrodynamics, with background-dependent correction terms. In the case of a time-like background, the correction terms dominate over the MCS sector in the region far from the origin, and establish the behaviour of a massless Electrodynamics (in the electric sector). In the space-like case, the solutions indicate the clear manifestation of spatial anisotropy, which is consistent with the existence of a privileged direction is space.
An asymmetric relativistic model for classical double radio sources
Arshakian, T G
2000-01-01
There is substantial observational evidence against the symmetric relativistic model of FRII radio sources. An asymmetric relativistic model is proposed which takes account of both relativistic effects and intrinsic/environmental asymmetries to explain the structural asymmetries of their radio lobes. A key parameter of the model is the jet-side of the double sources, which is estimated for 80% of the FRII sources in the 3CRR complete sample. Statistical analyses of the properties of these sources show that the asymmetric model is in agreement with a wide range of observational data, and that the relativistic and intrinsic asymmetry effects are of comparable importance. Intrinsic/environmental asymmetry effects are more important at high radio luminosities and small physical scales. The mean translational speed of the lobes is found to be 0.11c, consistent with the speeds found from spectral ageing arguments. According to a Gaussian model, the standard deviation of lobe speeds is 0.04c. The results are in agre...
Classical and quantum mechanics of free {kappa}-relativistic systems
Lukierski, J. [Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE (England); Ruegg, H. [Department de Physique Theorique, Universite de Geneve, 24 quai Ernest-Ansermet, 1211 Geneve 4 (Switzerland); Zakrzewski, W.J. [Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE (England)
1995-10-01
We consider the Hamiltonian and Lagrangian formalism describing free {kappa}-relativistic particles with their four-momenta constrained to the {kappa}-deformed mass shell. We study the formalism with commuting as well as noncommuting (i.e., with nonvanishing Poisson brackets) space-time coordinates; in particular a {kappa}-deformed phase space formalism leading to the {kappa}-deformed covariant Heisenberg algebra is presented. We also describe the dependence of the formalism on the various definitions of the energy operator corresponding to different choices of basic generators in the {kappa}-deformed Poincar{acute e} algebra. The quantum mechanics of free {kappa}-relativistic particles and of the free {kappa}-relativistic oscillator are also presented. It is shown that the {kappa}-relativistic oscillator describes a quantum statistical ensemble with a finite value of the Hagedorn temperature. The relation to a {kappa}-deformed Schr{umlt o}dinger quantum mechanics in which the time derivative is replaced by a finite difference is also discussed. {copyright} 1995 Academic Press, Inc.
Kotikov, A V
2013-01-01
We compute the two-loop fermion self-energy in massless reduced quantum electrodynamics for an arbitrary gauge using the method of integration by parts. Focusing on the limit where the photon field is four-dimensional, our formula involves only recursively one-loop integrals and can therefore be evaluated exactly. From this formula, we deduce the anomalous scaling dimension of the fermion field as well as the renormalized fermion propagator up to two loops. The results are then applied to the ultra-relativistic limit of graphene and compared with similar results obtained for four-dimensional and three-dimensional quantum electrodynamics.
Local model potentials that simulate the self-energy effects on atomic energy levels and magnetic dipole hyperfine integrals are presented. They are proposed for use in relativistic atomic, molecular or solid-state calculations
A Generalized Model for the Classical Relativistic Spinning Particle
Hajihashemi, Mehdi; Shirzad, Ahmad
2015-01-01
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the Lagrangian given in the literature. Then we analyze the dynamics of this generalized system in the Lagrangian formulation and show that the equations of motion support an oscillatory solution corresponding to the spinning nature of the system. Next we analyze the...
Louis-Martinez, Domingo J.
2010-01-01
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using these methods explicit expressions for the particle, energy and entropy density distributions are obtained, which are found to be in agreement with the well known results of the relativistic formulation of Boltzmann's kinetic theory. Explicit expressions fo...
Discrete phase space - I: Variational formalism for classical relativistic wave fields
A. Das
2008-01-01
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and continuous time. The relativistic invariance and covariance of the equations in both versions are established. The partial difference and difference-differential equations are derived as the Euler-Lagrange equations from the variational principle. The differenc...
A generalized model for the classical relativistic spinning particle
Hajihashemi, Mahdi; Shirzad, Ahmad
2016-03-01
Following the Poincaré algebra, in the Hamiltonian approach, for a free spinning particle and using the Casimirs of the algebra, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the Lagrangian given in the literature. We analyze the dynamics of this generalized system in the Lagrangian formulation and show that the equations of motion support an oscillatory solution corresponding to the spinning nature of the system. Then we analyze the canonical structure of the system and present the correct gauge suitable for the spinning motion of the system.
Classical Equation of State for Dilute Relativistic Plasma
Hussein, N. A.; Eisa, D. A.; Sayed, E. G.
2016-06-01
The aim of this paper is to calculate the analytical form of the equation of state for dilute relativistic plasma. We obtained the excess free energy and pressure in the form of a convergent series expansion in terms of the thermal parameter μ where μ = {{m{c^2}} over {KT}}, m is the mass of charge, c is the speed of light, K is the Boltzmann's constant, and T is the absolute temperature. The results are discussed and compared with previous work of other authors.
Silenko, Alexander J
2014-01-01
The fulfilled derivation of equation of spin precession of a particle possessing magnetic and electric dipole moments uses a fully covariant approach and explicitly separates contributions from classical electrodynamics and from the Thomas effect. The expression of the final equation in terms of the fields in the instantly accompanying frame presents it in a very simple form. The Lorentz transformations of the magnetic and electric dipole moments and the spin are derived from basic equations of classical electrodynamics, namely, from the equation connecting the angular momentum and the magnetic moment and from the Maxwell equations in matter. An antisymmetric four-tensor is constructed from the electric and magnetic dipole moments.
Semi-classical limit of relativistic quantum mechanics
L Kocis
2005-07-01
It is shown that the semi-classical limit of solutions to the Klein–Gordon equation gives the particle probability density that is in direct proportion to the inverse of the particle velocity. It is also shown that in the case of the Dirac equation a different result is obtained.
Nguyen Suan Han
2002-01-01
This paper is devoted to the one-loop calculation of the fermion Green function in QED within theframework of the minimal quantization method, based on an explicit solution of the constraint equations and the gaugc-invariance principle. The relativistic invariant expression for the fermion Green function with correct analytical propertiesis obtained.
Horwitz, L. P.; Land, Martin C.; Gill, Tepper; Lusanna, Luca; Salucci, Paolo
2013-04-01
Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There moreover remains the important question of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics. In recent years, the study of high energy plasmas and heavy ion collisions has emphasized the importance of developing the techniques of relativistic mechanics. The results of Lindner et al [Physical Review Letters 95 0040401 (2005)] as well as the more recent proposal of Palacios et al [Phys. Rev. Lett. 103 253001 (2009)] and others, have shown that there must be a quantum theory with coherence in time. Such a theory, manifestly covariant under the transformations of special relativity with an invariant evolution parameter, such as that of Stueckelberg [Helv. Phys. Acta 14 322, 588 (1941); 15 23 (1942); see also R P Feynman Phys. Rev. 80 4401 and J S Schwinger Phys. Rev. 82 664 (1951)] could provide a suitable basis for the study of such questions, as well as many others for which the application of the standard methods of quantum field theory are difficult to manage, involving, in particular
The Wigner-Weyl formalism and the semi-classical relativistic approximation
Mourad, J.
1993-01-01
The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is proposed using the Newton-Wigner position operator. The perturbative solution for the time evolution is found. Causality is found to be perturbatively respected.
Hehl, F W; Hehl, Friedrich W.; Obukhov, Yuri N.
2000-01-01
Coulomb comes in quanta, weber may come in quanta. -- We will base classical electrodynamics on electric charge conservation, the Lorentz force, and on magnetic flux conservation. This yields the Maxwell equations. The consequences will be drawn for the interpretation and the dimension of the electric and magnetic fields.
A derivation of the Derbenev-Kondratenko formula using semi-classical electrodynamics
We present a detailed exposition of the mechanism for the build-up of polarization in electron storage rings. A semi-classical approach is used to derive the rate of growth and asymptotic degree of polarization in an electron storage ring (the Derbenev-Kondratenko formula). Statistical mechanical concepts used to obtain as classical an understanding as possible of this phenomenon. (orig.)
Quantum electrodynamics and the relativistic theory of many-electron atoms
The development of relativistic theories of many-electron atoms is reviewed, with emphasis on the fact that the Dirac-Coulomb Hamiltonian H/sub DC/ has no bound states. This fact implies that neither the Dirac-Hartree-Fock (DHF) equations nor the DHF wavefunction chi have a simple theoretical interpretation. A no-pair hamiltonian H/sub +/ is defined which does not have the fatal flaw of H/sub DC/ and hence can serve as a starting point for a systematic study of relativistic effects in many-electron atoms which can go beyond central-field approximations. H/sub +/ differs from H/sub DC/ by the presence of external-field positive-energy projection operators in the electron-electron interaction terms. Unlike H/sub DC/, H/sub +/ and its eigenfunctions psi have a clear-cut field-theoretic meaning, which is described. Similar remarks hold for a simpler no-pair Hamiltonian h/sub +/, which involves free positive-energy projection operators and for related Hamiltonians H/sub +/' and h/sup +/' which include the Breit operator. Relativistic Hartree-Fock equations are obtained from H/sub +/ and the relation between their solutions psi and the DHF solutions chi is discussed. The DHF equations may be reinterpreted as approximations to the new HF-type equations; this provides a rationale for their success in applications. It is argued that the Breit operator ought to be included even in the original DHF equations
Some problems in classical mechanics and relativistic astrophysics
The first part of this thesis is indirectly related to high energy astrophysics. It concerns the study of binary systems consisting of a normal star and a neutronstar or a black hole. To interpret the observations from such a system; in X-ray, UV, optical, infrared and radio wavelengths; it is helpful to have a general idea of the evolution of the orbital and rotational parameters. Here we enter the old field of classical mechanics, in the form of celestial mechanics. In particular the effects of tidal interaction, precession, and sudden mass loss are treated. The second part starts with an article on thought experiments with a charged black hole enclosed in a huge box and in equilibrium with its own radiation. In this way the thermodynamic aspects of the Hawking radiation are fully explored. The connection between physical and kinematical cosmological parameters, as predicted by general relativity are explored. It is shown how the standard big bang model of cosmology restricts the possible properties of some elementary particle types. The theory of white dwarf structure is compared with observations in order to put low-energy constraints on (super) gravity theories. (Auth.)
The classical modeling of radiation by accelerated charged particles in pulsars predicts a cutoff in photon energy at around 25 GeV. While this is broadly consistent with observations, the classical treatment is not self-consistent, and cannot be extended to explain the rare high-energy detections of photons in the 100s of GeV range. In this paper we revisit the theoretical modeling of high-energy radiation processes in very strong electromagnetic fields, in the context of both single particles and collective plasmas. There are no classical constraints on this description. We find that there is indeed a critical energy of around 50 GeV that arises naturally in this self-consistent treatment, but rather than being a cutoff, this critical energy signals a transition from radiation that is classical to a quasiquantum description, in which the particle is able to radiate almost its total energy in a single event. This new modeling therefore places pulsar radiation processes on a more secure physical basis, and admits the possibility of the production of TeV photons in a self-consistent way.
Galilean Podolsky Electrodynamics
Pompeia, P. J.; de Montigny, M.; Khanna, F. C.
2009-09-01
We analyze non-relativistic limits of Podolsky generalized electrodynamics in the context of the 5-dimensional Galilean formalism. The 'electric' and 'magnetic' limits are studied in analogy with the work of Le Bellac and Levy-Leblond (1973).
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using these methods explicit expressions for the particle, energy and entropy density distributions are obtained, which are found to be in agreement with the well-known results of the relativistic formulation of Boltzmann's kinetic theory. Explicit expressions for the total entropy, total energy and rest mass of the gas are obtained. The position of the center of mass of the gas in equilibrium is found. The non-relativistic and ultrarelativistic approximations are also considered. The phase space volume of the system is calculated explicitly in the ultrarelativistic approximation.
On the Stability of Classical Orbits of the Hydrogen Ground State in Stochastic Electrodynamics
Theodorus M. Nieuwenhuizen
2016-04-01
Full Text Available De la Peña 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics connect to a stable situation, where the electron neither collapses onto the nucleus nor gets expelled from the atom. Although the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Peña-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an 1 / r 2 potential is added, which could stem from a dipolar deformation of the nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium.
Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation
Scheck, Florian
2012-01-01
The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...
Relativistic analogue of the phase space and the Liouville theorem of classical statistics
Different anholonomic subspaces of the general relativistic μ-space (space of states of a free particle in the gravitational field; i.e. the tangent bundle V8=T(V4) on the space time V4) are introduced which, respectively, represent relativistic analogue of the classical phase space or the space on which the classical theory of radiation defines the distribution function of spectral intensity. These subspaces of V8 prove to be holonomic, if the 4-velocity field in V4 the extensions (prolongations) of which are involved in their defining multivector fields is submitted to certain conditions. In this case, from local equations holding for the mapping of sets of points of the subspaces of V8 and describing the development in time of states of particles, laws of conservation in integral form can be derived. (author)
Gauge dependence of world lines and invariance of the S-matrix in relativistic classical mechanics
The notion of world lines is studied in the constraint Hamiltonian formulation of relativistic point particle dynamics. The particle world lines are shown to depend in general (in the presence of interaction) on the choice of the equal-time hyperplane (the only exception being the elastic scattering of rigid balls). However, the relative motion of a two-particle system and the (classical) S-matrix are indepent of this choice. (author)
On plane-wave relativistic electrodynamics in plasmas and in vacuum
Fiore, Gaetano
2016-01-01
We revisit the exact microscopic equations (in differential, and equivalent integral form) ruling a relativistic cold plasma after the plane-wave Ansatz, without customary approximations. We show that in the Eulerian description the motion of a very diluted plasma initially at rest and excited by an arbitrary transverse plane electromagnetic travelling-wave has a very simple and explicit dependence on the transverse electromagnetic potential; for a non-zero density plasma the above motion is a good approximation of the real one as long as the back-reaction of the charges on the electromagnetic field can be neglected, i.e. for a time lapse decreasing with the plasma density, and can be used as initial step in an iterative resolution scheme. As one of many possible applications, we use these results to describe how the ponderomotive force of a very intense and short plane laser pulse hitting normally the surface of a plasma boosts the surface electrons into the ion background. Because of this penetration the el...
Relativistic calculation, in quantum electrodynamic, of the Compton diffusion on a bound electron
In order to explain Compton-peak displacement and broadening, when the incident photon energy is close to the electron binding energy, it is shown that a realistic calculation must include not only the binding and electron movement, but also the core participation, as a third parameter in the quadri-impulse conservation, in both initial and final states. A general equation giving the variation of the photon wavelength is deduced, taking into account all the variation sources and previous studies as limiting cases. It is shown that all the kinematical variables related to the primary electron must be analyzed in a relativistic way, for the deep atomic layers having high atomic number. An equation giving the mean square value of the atomic-electron momentum, which is true for whatever the electron state, is shown. Among the useful wave functions, a general equation for the radial functions of the atomic electrons is given. The applied propagator can explain the intermediate states describing an electron in a Coulombian field. A complete calculation of the covariant-matrice element and cross sections is accomplished. The final equations do not need any integration, except the ponderations related to an angle that is not experimentally accessible. This equation is shown in a computer program form
Hu, Zixuan; Ratner, Mark A.; Seideman, Tamar, E-mail: t-seideman@northwestern.edu [Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113 (United States)
2014-12-14
We develop a numerical approach for simulating light-induced charge transport dynamics across a metal-molecule-metal conductance junction. The finite-difference time-domain method is used to simulate the plasmonic response of the metal structures. The Huygens subgridding technique, as adapted to Lorentz media, is used to bridge the vastly disparate length scales of the plasmonic metal electrodes and the molecular system, maintaining accuracy. The charge and current densities calculated with classical electrodynamics are transformed to an electronic wavefunction, which is then propagated through the molecular linker via the Heisenberg equations of motion. We focus mainly on development of the theory and exemplify our approach by a numerical illustration of a simple system consisting of two silver cylinders bridged by a three-site molecular linker. The electronic subsystem exhibits fascinating light driven dynamics, wherein the charge density oscillates at the driving optical frequency, exhibiting also the natural system timescales, and a resonance phenomenon leads to strong conductance enhancement.
Hu, Zixuan; Ratner, Mark A.; Seideman, Tamar
2014-12-01
We develop a numerical approach for simulating light-induced charge transport dynamics across a metal-molecule-metal conductance junction. The finite-difference time-domain method is used to simulate the plasmonic response of the metal structures. The Huygens subgridding technique, as adapted to Lorentz media, is used to bridge the vastly disparate length scales of the plasmonic metal electrodes and the molecular system, maintaining accuracy. The charge and current densities calculated with classical electrodynamics are transformed to an electronic wavefunction, which is then propagated through the molecular linker via the Heisenberg equations of motion. We focus mainly on development of the theory and exemplify our approach by a numerical illustration of a simple system consisting of two silver cylinders bridged by a three-site molecular linker. The electronic subsystem exhibits fascinating light driven dynamics, wherein the charge density oscillates at the driving optical frequency, exhibiting also the natural system timescales, and a resonance phenomenon leads to strong conductance enhancement.
We develop a numerical approach for simulating light-induced charge transport dynamics across a metal-molecule-metal conductance junction. The finite-difference time-domain method is used to simulate the plasmonic response of the metal structures. The Huygens subgridding technique, as adapted to Lorentz media, is used to bridge the vastly disparate length scales of the plasmonic metal electrodes and the molecular system, maintaining accuracy. The charge and current densities calculated with classical electrodynamics are transformed to an electronic wavefunction, which is then propagated through the molecular linker via the Heisenberg equations of motion. We focus mainly on development of the theory and exemplify our approach by a numerical illustration of a simple system consisting of two silver cylinders bridged by a three-site molecular linker. The electronic subsystem exhibits fascinating light driven dynamics, wherein the charge density oscillates at the driving optical frequency, exhibiting also the natural system timescales, and a resonance phenomenon leads to strong conductance enhancement
Galilean Conformal Electrodynamics
Bagchi, Arjun; Mehra, Aditya
2014-01-01
Maxwell's Electrodynamics admits two distinct Galilean limits called the Electric and Magnetic limits. We show that the equations of motion in both these limits are invariant under the Galilean Conformal Algebra in D=4, thereby exhibiting non-relativistic conformal symmetries. Remarkably, the symmetries are infinite dimensional and thus Galilean Electrodynamics give us the first example of an infinitely extended Galilean Conformal Field Theory in D>2. We examine details of the theory by looking at purely non-relativistic conformal methods and also use input from the limit of the relativistic theory.
Galilean conformal electrodynamics
Bagchi, Arjun; Basu, Rudranil; Mehra, Aditya
2014-11-01
Maxwell's Electrodynamics admits two distinct Galilean limits called the Electric and Magnetic limits. We show that the equations of motion in both these limits are invariant under the Galilean Conformal Algebra in D = 4, thereby exhibiting non-relativistic conformal symmetries. Remarkably, the symmetries are infinite dimensional and thus Galilean Electrodynamics give us the first example of an infinitely extended Galilean Conformal Field Theory in D > 2. We examine details of the theory by looking at purely non-relativistic conformal methods and also use input from the limit of the relativistic theory.
Classical and relativistic node precessional effects in WASP-33b and perspectives for detecting them
Iorio, Lorenzo
2010-01-01
WASP-33 is a fast rotating, main sequence star which hosts a hot Jupiter moving along a retrograde and almost polar orbit with semi-major axis a = 0.02 au and eccentricity provisionally set to e = 0. The quadrupole mass moment J_2 and the proper angular momentum S of the star are 1900 and 400 times, respectively, larger than those of the Sun. Thus, huge classical and relativistic non-Keplerian orbital effects should take place in such a system. In this paper we investigate the perspectives in detecting them (Abridged)
Gao Yi; Neuhauser, Daniel [Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569 (United States)
2013-05-14
We show how to obtain the correct electronic response of a large system by embedding; a small region is propagated by TDDFT (time-dependent density functional theory) simultaneously with a classical electrodynamics evolution using the Near-Field method over a larger external region. The propagations are coupled through a combined time-dependent density yielding a common Coulomb potential. We show that the embedding correctly describes the plasmonic response of a Mg(0001) slab and its influence on the dynamical charge transfer between an adsorbed H{sub 2}O molecule and the substrate, giving the same spectral shape as full TDDFT (similar plasmon peak and molecular-dependent differential spectra) with much less computational effort. The results demonstrate that atomistic embedding electrodynamics is promising for nanoplasmonics and nanopolaritonics.
We show how to obtain the correct electronic response of a large system by embedding; a small region is propagated by TDDFT (time-dependent density functional theory) simultaneously with a classical electrodynamics evolution using the Near-Field method over a larger external region. The propagations are coupled through a combined time-dependent density yielding a common Coulomb potential. We show that the embedding correctly describes the plasmonic response of a Mg(0001) slab and its influence on the dynamical charge transfer between an adsorbed H2O molecule and the substrate, giving the same spectral shape as full TDDFT (similar plasmon peak and molecular-dependent differential spectra) with much less computational effort. The results demonstrate that atomistic embedding electrodynamics is promising for nanoplasmonics and nanopolaritonics.
Gao, Yi; Neuhauser, Daniel
2013-05-14
We show how to obtain the correct electronic response of a large system by embedding; a small region is propagated by TDDFT (time-dependent density functional theory) simultaneously with a classical electrodynamics evolution using the Near-Field method over a larger external region. The propagations are coupled through a combined time-dependent density yielding a common Coulomb potential. We show that the embedding correctly describes the plasmonic response of a Mg(0001) slab and its influence on the dynamical charge transfer between an adsorbed H2O molecule and the substrate, giving the same spectral shape as full TDDFT (similar plasmon peak and molecular-dependent differential spectra) with much less computational effort. The results demonstrate that atomistic embedding electrodynamics is promising for nanoplasmonics and nanopolaritonics. PMID:23676021
Galilean Conformal Electrodynamics
Bagchi, Arjun; Basu, Rudranil; Mehra, Aditya
2014-01-01
Maxwell’s Electrodynamics admits two distinct Galilean limits called the Electric and Magnetic limits. We show that the equations of motion in both these limits are invariant under the Galilean Conformal Algebra in D = 4, thereby exhibiting non-relativistic conformal symmetries. Remarkably, the symmetries are infinite dimensional and thus Galilean Electrodynamics give us the first example of an infinitely extended Galilean Conformal Field Theory in D > 2. We examine details of the theory by l...
Azadegan, B.; Wagner, W.
2015-01-01
We present a Mathematica package for simulation of spectral-angular distributions and energy spectra of planar channeling radiation of relativistic electrons and positrons channeled along major crystallographic planes of a diamond-structure or tungsten single crystal. The program is based on the classical theory of channeling radiation which has been successfully applied to study planar channeling of light charged particles at energies higher than 100 MeV. Continuous potentials for different planes of diamond, Si, Ge and W single crystals are calculated using the Doyle-Turner approximation to the atomic scattering factor and taking thermal vibrations of the crystal atoms into account. Numerical methods are applied to solve the classical one-dimensional equation of motion. The code is designed to calculate the trajectories, velocities and accelerations of electrons (positrons) channeled by the planar continuous potential. In the framework of classical electrodynamics, these data allow realistic simulations of spectral-angular distributions and energy spectra of planar channeling radiation. Since the generated output is quantitative, the results of calculation may be useful, e.g., for setup configuration and crystal alignment in channeling experiments, for the study of the dependence of channeling radiation on the input parameters of particle beams with respect to the crystal orientation, but also for the simulation of positron production by means of pair creation what is mandatory for the design of efficient positron sources necessary in high-energy and collider physics. Although the classical theory of channeling is well established for long time, there is no adequate library program for simulation of channeling radiation up to now, which is commonly available, sufficiently simple and effective to employ and, therefore, of benefit as for special investigations as for a quick overview of basic features of this type of radiation.
Lobet, M.; d'Humières, E.; Grech, M.; Ruyer, C.; Davoine, X.; Gremillet, L.
2016-03-01
Next generation of ultra-intense laser facilities will lead to novel physical conditions ruled by collective and quantum electrodynamics effects, such as synchrotron-like emission of high-energy photons and e + e - pair generation. In view of the future experiments performed in this regime, the latter processes have been implemented into the particle-in-cell code CALDER.
Understanding the Planck Blackbody Spectrum and Diamagnetism within Classical Electromagnetism
Boyer, Timothy H
2016-01-01
Electromagnetism is a \\textit{relativistic} theory and one must exercise care in coupling this theory with \\textit{nonrelativistic} classical mechanics and with \\textit{nonrelativistic} classical statistical mechanics. Indeed historically, both the blackbody radiation spectrum and diamagnetism within classical theory have been misunderstood because of two crucial failures: 1)the neglect of classical electromagnetic zero-point radiation, and 2) the use of erroneous combinations of nonrelativistic mechanics with relativistic electrodynamics. Here we show that the use of Lorentz-invariant classical electromagnetic zero-point radiation can be used to explain both the Planck blackbody spectrum and diamagnetism at thermal equilibrium within classical electromagnetic theory. The analysis requires that relativistic electromagnetism is joined appropriately with simple nonrelativistic mechanical systems which can be regarded as the zero-velocity limits of relativistic systems, and that nonrelativistic classical statist...
Numerical solution of ordinary differential equations. For classical, relativistic and nano systems
An up-to-date survey on numerical solutions with theory, intuition and applications. Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses. Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved. This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic and nano systems. The examples are carefully explained and compiled into an algorithm, each of which is presented generically, independent of a specific programming language, while each chapter is rounded off with exercises. The text meets the demands of MA200 courses and of the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, as well as for physicists, mathematicians, engineers, and electrical engineers. From the Contents - Euler's Method - Runge-Kutta Methods - The Method of Taylor Expansions - Large Second Order Systems with Application to Nano Systems - Completely Conservative, Covariant Numerical Methodology - Instability - Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems - Approximate Solution of Boundary Value Problems - Special Relativistic Motion - Special Topics - Appendix: Basic Matrix Operations - Bibliography. (orig.) (orig.)
Semi-classical locality for the non-relativistic path integral in configuration space
Gomes, Henrique
2015-01-01
In an accompanying paper, we have put forward an interpretation of quantum mechanics grounded on a non-relativistic Lagrangian 3+1 formalism of a closed Universe, existing on timeless configuration space. However, not much was said there about the role of locality, which was not assumed. In this paper, I describe how subsystems existing in (spatial) regions with fixed boundary conditions can be represented as submanifolds of the complete configuration space. I show that if the action functional can be put in the form of Riemannian distance element, then dynamical independence of the subsystem implies that the respective submanifolds are totally geodesic. When two regions are mutually independent the semi-classical path integral kernel factorizes, showing cluster decomposition. To exemplify these constructions I then construct a specific gravitational system with two propagating physical degrees of freedom and no refoliation-invariance. Finally, considering the path integral in this 3+1 context, I implement an...
Scale-lengths and instabilities in magnetized classical and relativistic plasma fluid models
The validity of the traditional plasma continuum is predicated on a hierarchy of scale-lengths, with the Debye length being considered to be effectively unresolvable in the continuum limit. In this article, we revisit the strong magnetic field case in which the Larmor radius is comparable or smaller than the Debye length in the classical plasma, and also for a relativistic plasma. Fresh insight into the validity of the continuum assumption in each case is offered, including a fluid limit on the Alfvén speed that may impose restrictions on the validity of magnetohydrodynamics (MHD) in some solar and fusion contexts. Additional implications concerning the role of the firehose instability are also explored. (paper)
Horwitz, Lawrence; Hu, Bei-Lok; Lee, Da-Shin; Gill, Tepper; Land, Martin
2011-12-01
Although the subject of relativistic dynamics has been explored from both classical and quantum mechanical points of view since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anamolous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical realtivistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There moreover remains the important question of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics. In recent years, the study of high energy plasmas and heavy ion collisions has emphasized the importance of developing the techniques of relativistic mechanics. The results of Linder et al (Phys. Rev. Lett. 95 0040401 (2005)) as well as the more recent work of Palacios et al (Phys. Rev. Lett. 103 253001 (2009)) and others, have shown that there must be a quantum theory with coherence in time. Such a theory, manifestly covariant under the transformations of special relativity with an invariant evolution parameter, such as that of Stueckelberg (Helv. Phys. Acta 14 322, 588 (1941); 15 23 (1942); see also R P Feynman Phys. Rev. 80 4401 and J S Schwinger Phys. Rev. 82 664 (1951)) could provide a suitable basis for the study of such questions, as well as many others for which the application of the standard methods of quantum field theory are difficult to manage, involving, in particular, local
Soliton-like solution in quantum electrodynamics
Skoromnik, O D; Keitel, C H
2016-01-01
A novel soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method. By writing the Hamiltonian of quantum electrodynamics in the Coulomb gauge, we separate out a classical component in the density operator of the electron-positron field. Then, by modeling the state vector in analogy with the theory of superconductivity, we minimize the functional for the energy of the system. This results in the equations of the self-consistent field, where the solutions are associated with the collective excitation of the electron-positron field---the soliton-like solution. In addition, the canonical transformation of the variables allowed us to separate out the total momentum of the system and, consequently, to find the relativistic energy dispersion relation for the moving soliton.
Relativistic impulse dynamics.
Swanson, Stanley M
2011-08-01
Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion. PMID:21929132
Diffraction radiation from relativistic particles
Potylitsyn, Alexander Petrovich; Strikhanov, Mikhail Nikolaevich; Tishchenko, Alexey Alexandrovich
2010-01-01
This book deals with diffraction radiation, which implies the boundary problems of electromagnetic radiation theory. Diffraction radiation is generated when a charged particle moves in a vacuum near a target edge. Diffraction radiation of non-relativistic particles is widely used to design intense emitters in the cm wavelength range. Diffraction radiation from relativistic charged particles is important for noninvasive beam diagnostics and design of free electron lasers based on Smith-Purcell radiation which is diffraction radiation from periodic structures. Different analytical models of diffraction radiation and results of recent experimental studies are presented in this book. The book may also serve as guide to classical electrodynamics applications in beam physics and electrodynamics. It can be of great use for young researchers to develop skills and for experienced scientists to obtain new results.
Diffraction radiation from relativistic particles
This book deals with diffraction radiation, which implies the boundary problems of electromagnetic radiation theory. Diffraction radiation is generated when a charged particle moves in a vacuum near a target edge. Diffraction radiation of non-relativistic particles is widely used to design intense emitters in the cm wavelength range. Diffraction radiation from relativistic charged particles is important for noninvasive beam diagnostics and design of free electron lasers based on Smith-Purcell radiation which is diffraction radiation from periodic structures. Different analytical models of diffraction radiation and results of recent experimental studies are presented in this book. The book may also serve as guide to classical electrodynamics applications in beam physics and electrodynamics. It can be of great use for young researchers to develop skills and for experienced scientists to obtain new results. (orig.)
Relativistic and nonrelativistic classical field theory on fivedimensional space-time
This paper is a sequel to earlier ones in which, on the one hand, classical field theories were described on a curved Newtonian space-time, and on the other hand, the Newtonian gravitation theory was formulated on a fivedimensional space-time with a metric of signature and a covariantly constant vector field. Here we show that Lagrangians for matter fields are easily formulated on this extended space-time from simple invariance arguments and that stress-energy tensors can be derived from them in the usual manner so that four-dimensional space-time expressions are obtained that are consistent in the relativistic as well as in the Newtonian case. In the former the theory is equivalent to General Relativity. When the magnitude of the distinguished vector field vanishes equations for the (covariant) Newtonian limit follow. We demonstrate this here explicity in the case of the Klein-Gordon/Schroedinger and the Dirac field and its covariant nonrelativistic analogue, the Levy-Leblond field. Especially in the latter example the covariant Newtonian theory simplifies dramatically in this fivedimensional form
Balsara, Dinshaw S; Garain, Sudip; Kim, Jinho
2016-01-01
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. Three important innovations are reported here. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our seco...
Electrodynamics basics and duality principle
Ivanitckiy, A. M.
2014-01-01
The given report proposes general and consistent statement of the classical electrodynamics basis using axiomatic and duality principles for its construct. Vector algebra and vector analysis are created by the application of the duality principle. The last fact allows formulating Maxwell equations in strictly symmetric form. It means the statement of electrodynamics postulates (axioms) under a principle of duality. Electrodynamics basis construction begins immediately using its postulates for...
Photon propagator in skewon electrodynamics
Itin, Yakov
2015-01-01
Electrodynamics with a local and linear constitutive law is used as a framework for models violating Lorentz covariance. The constitutive tensor of such a construction is irreducibly decomposed into three independent pieces. The principal part is the anisotropic generalisation of the standard electrodynamics. The two other parts, axion and skewon, represent non-classical modifications of electrodynamics. We derive the expression for the photon propagator in the Minkowski spacetime endowed wit...
Massive Electrodynamics and Magnetic Monopoles
Israelit, Mark
1996-01-01
Including torsion in the geometric framework of the Weyl-Dirac theory we build up an action integral, and obtain from it a gauge covariant (in the Weyl sense) general relativistic massive electrodynamics. Photons having an arbitrary mass, electric, and magnetic currents (Dirac's monopole) coexist within this theory. Assuming that the space-time is torsionless, taking the photons mass zero, and turning to the Einstein gauge we obtain Maxwell's electrodynamics.
Kopeikin, Sergei M.; Shuygina, N. V.; Vasilyev, M. V.; Yagudina, E. I.; Yagudin, L. I.
2000-01-01
The accuracy of astrometric observations conducted via a space-borne optical interferometer orbiting the Earth is expected to approach a few microarcseconds. Data processing of such extremely high-precision measurements requires access to a rigorous relativistic model of light ray propagation developed in the framework of General Relativity. The data-processing of the space interferometric observations must rely upon the theory of general-relativistic transformations between the spacecraft, g...
SHAO Xiao-Qiang; ZHANG Shou
2008-01-01
We propose a scheme for one-step generation of cluster states with atoms sent through a thermal cavity with strong classical driving field, based on the resonant atom-cavity interaction so that the operating time is sharply short, which is important in the view of decoherence.
Accretion disk electrodynamics
Coroniti, F. V.
1985-01-01
Accretion disk electrodynamic phenomena are separable into two classes: (1) disks and coronas with turbulent magnetic fields; (2) disks and black holes which are connected to a large-scale external magnetic field. Turbulent fields may originate in an alpha-omega dynamo, provide anomalous viscous transport, and sustain an active corona by magnetic buoyancy. The large-scale field can extract energy and angular momentum from the disk and black hole, and be dynamically configured into a collimated relativistic jet.
On the non-relativistic limit of charge conjugation in QED
Perez, B Carballo
2010-01-01
We study the non-relativistic limit of the the charge conjugation operation (C) in Quantum Electrodynamics (QED). We arrive to the conclusion that, in the galilean limit, charge conjugation is not a symmetry in the context of QED. Nevertheless, it is possible to find the non-relativistic limit of C, considering the Dirac field coupled to an electromagnetic classical external field. We report the expressions for both the C matrix and the $\\hat{C}$ operator for "slow" electrons and positrons.
Kopeikin, S M; Vasilev, M V; Yagudina, E I; Yagudin, L I; Kopeikin, Sergei M.
2000-01-01
The accuracy of astrometric observations conducted via a space-borne optical interferometer orbiting the Earth is expected to approach a few microarcseconds. Data processing of such extremely high-precision measurements requires access to a rigorous relativistic model of light ray propagation developed in the framework of General Relativity. The data-processing of the space interferometric observations must rely upon the theory of general-relativistic transformations between the spacecraft, geocentric, and solar barycentric reference systems allowing unique and unambiguous interpretation of the stellar aberration and parallax effects. On the other hand, the algorithm must also include physically adequate treatment of the relativistic effect of light deflection caused by the spherically-symmetric (monopole-dependent) part of the gravitational field of the Sun and planets as well as the quadrupole- and spin-dependent counterparts of it. In some particular cases the gravitomagnetic field induced by the translati...
Phenomenological aspects of radiation by relativistic electrons in external field, in matter or the vicinity of matter are reviewed, among which: infrared divergence, coherence length effects, shadowing, crystal-assisted radiation, quantum recoil and spin effects, electron side-slipping, photon impact parameter and tunneling in the radiation process
Relativistic ExB polarization drift of light
Yu, Sunkyu; Park, Namkyoo
2016-01-01
The Minkowski representation with the general covariance modifies the classical definition of momentum for moving particles. The relativistic trajectory of a charged particle driven by electromagnetic fields is thus altered from the classical one, including the nonlinear acceleration by the Lorentz force. Here we demonstrate that the classical evolution of optical polarization states in parity-time (PT) symmetric potentials follows the nonlinear trajectory of charged particles under the relativistic ExB drift, without any optical nonlinearity or dynamic modulation. The competition between electric and magnetic pseudo-field each induced by external carriers and birefringence differentiates the acceleration of polarization states on opposite Poincar\\'e hemispheres. We reveal that the perfectly stable pole from zero Lorentz pseudo-force is the origin of strong optical chirality at the exceptional point (EP). Our results linking classical PT symmetry and relativistic electrodynamics bring new insight into the pol...
Dimensions and Units in Electrodynamics
Hehl, F W; Hehl, Friedrich W; Obukhov, Yuri N
2004-01-01
We sketch the foundations of classical electrodynamics, in particular the transition that took place when Einstein, in 1915, succeeded to formulate general relativity. In 1916 Einstein demonstrated that, with a choice of suitable variables for the electromagnetic field, it is possible to put Maxwell's equation into a form that is covariant under general coordinate transformations. This unfolded, by basic contributions of Kottler, Cartan, van Dantzig, Schouten & Dorgelo, Toupin & Truesdell, and Post, to what one may call {\\em premetric classical electrodynamics.} This framework will be described shortly. An analysis is given of the physical dimensions involved in electrodynamics and subsequently the question of units addressed. It will be pointed out that these results are untouched by the generalization of classical to quantum electrodynamics (QED). We compare critically our results with those of {\\sl L.B. Okun} which he had presented at a recent conference.
An asymptotic preserving scheme for the relativistic Vlasov–Maxwell equations in the classical limit
Crouseilles, Nicolas; Einkemmer, Lukas; Faou, Erwan
2016-01-01
We consider the relativistic Vlasov–Maxwell (RVM) equations in the limit when the light velocity c goes to infinity. In this regime, the RVM system converges towards the Vlasov–Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell's equations in order to damp the higher and higher frequencie...
Vernon Cooray
2016-05-01
Full Text Available Electromagnetic energy radiated by antennas working in both the frequency domain and time domain is studied as a function of the charge associated with the current in the antenna. The frequency domain results, obtained under the assumption of sinusoidal current distribution, show that, for a given charge, the energy radiated within a period of oscillation increases initially with L/λ and then starts to oscillate around a steady value when L/λ > 1. The results show that for the energy radiated by the antenna to be equal to or larger than the energy of one photon, the oscillating charge in the antenna has to be equal to or larger than the electronic charge. That is, U ≥ hν or UT ≥ h ⇒ q ≥ e, where U is the energy dissipated over a period, ν is the frequency of oscillation, T is the period, h is Planck’s constant, q is the rms value of the oscillating charge, and e is the electronic charge. In the case of antennas working in the time domain, it is observed that UΔt ≥ h/4π ⇒ q ≥ e, where U is the total energy radiated, Δt is the time over which the energy is radiated, and q is the charge transported by the current. It is shown that one can recover the time–energy uncertainty principle of quantum mechanics from this time domain result. The results presented in this paper show that when quantum mechanical constraints are applied to the electromagnetic energy radiated by a finite antenna as estimated using the equations of classical electrodynamics, the electronic charge emerges as the smallest unit of free charge in nature.
Contrasting Classical and Quantum Vacuum States in Non-Inertial Frames
Boyer, Timothy H
2013-01-01
Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. It makes no difference whether a box of classical zero-point radiati...
Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho
2016-08-01
In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergence-free. This
Photon propagator in skewon electrodynamics
Itin, Yakov
2015-01-01
Electrodynamics with a local and linear constitutive law is used as a framework for models violating Lorentz covariance. The constitutive tensor of such a construction is irreducibly decomposed into three independent pieces. The principal part is the anisotropic generalisation of the standard electrodynamics. The two other parts, axion and skewon, represent non-classical modifications of electrodynamics. We derive the expression for the photon propagator in the Minkowski spacetime endowed with a skewon field. For a relatively small (antisymmetric) skewon field, a modified Coulom law is exhibited.
Quantum corrections to the Larmor radiation formula in scalar electrodynamics
Higuchi, A
2009-01-01
We use the semi-classical approximation in perturbative scalar quantum electrodynamics to calculate the quantum correction to the Larmor radiation formula to first order in Planck's constant in the non-relativistic approximation, choosing the initial state of the charged particle to be a momentum eigenstate. We calculate this correction in two cases: in the first case the charged particle is accelerated by a time-dependent but space-independent vector potential whereas in the second case it is accelerated by a time-independent vector potential which is a function of one spatial coordinate. We find that the corrections in these two cases are different even for a charged particle with the same classical motion. The correction in each case turns out to be non-local in time in contrast to the classical approximation.
New formulation of the classical dynamics of the relativistic string with massive ends
Dynamic equations in the theory of a relativistic string with point masses at the ends are formulated only in terms of geometric invariants of the world trajectories of the massive ends of the string (curvature k1 and torsion k1 of the trajectories). These characteristics allow us to reproduce the string world surface up to shifts and rotations in the Minkowski space E21. The torsions k1(r) (1=1,2) obey a system of differential equations of the second order with shifted arguments describing the retardation effects of the interaction of masses through the string, k1 being constant. New particular solutions to these equations that correspond to periodic torsions will be discussed in the next paper. 12 refs
Dynamic equations in the theory of a relativistic string with point masses at the ends are formulated in terms of geometric invariants of the world trajectories of the massive ends of the string (curvature ki and torsion κi(τ), i=1,2 of the trajectories). With these characteristics we reproduce the string world surface up to its position in Minkowski space E21. The torsions κi(τ), i=1,2 obey a system of second order differential equations with delay arguments describing the retardation effects of the interaction of masses through the string, ki being constants. The constant torsions are investigated in detail. In this case the string world sheet is a helicoid in E21. A nonlinear relation (the Regge trajectory) between the angular momentum of the system, J and the mass squared, M2, is derived. For given meson masses (M) and spin (J), the masses of quarks are calculated. 14 refs., 1 fig., 1 tab
Costella, J.P.; McKellar, B.H.J.; Rawlinson, A.A.
1997-03-01
We review how antiparticles may be introduced in classical relativistic mechanics, and emphasize that many of their paradoxical properties can be more transparently understood in the classical than in the quantum domain. (authors). 13 refs., 1 tab.
The classical relativistic two-body problem with spin and self-interactions
The recent classical model of a spinning Dirac particle with Zitterbewegung is generalized to two particles interacting electromagnetically. A variational principle is formulated which leads to covariant Hamiltonian with separate centre of mass and relative terms much like the quantum 2-body Dirac equation. The relative motion has the same form as the spinless case but with the time dependent modulated coupling constant representing the spin effects. The canonical quantization of the theory is immediate. (author). 10 refs
Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics
Lorenzo Fatibene
2010-04-01
Full Text Available We review the Lagrangian formulation of (generalised Noether symmetries in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-called “Natural Theories” and “Gauge-Natural Theories” that include all relevant Field Theories and physical applications (from Mechanics to General Relativity, to Gauge Theories, Supersymmetric Theories, Spinors, etc.. It is discussed how the use of Poincar´e–Cartan forms and decompositions of natural (or gauge-natural variational operators give rise to notions such as “generators of Noether symmetries”, energy and reduced energy flow, Bianchi identities, weak and strong conservation laws, covariant conservation laws, Hamiltonian-like conservation laws (such as, e.g., so-calledADMlaws in General Relativity with emphasis on the physical interpretation of the quantities calculated in specific cases (energy, angular momentum, entropy, etc.. A few substantially new and very recent applications/examples are presented to better show the power of the methods introduced: one in Classical Mechanics (definition of strong conservation laws in a frame-independent setting and a discussion on the way in which conserved quantities depend on the choice of an observer; one in Classical Field Theories (energy and entropy in General Relativity, in its standard formulation, in its spin-frame formulation, in its first order formulation “à la Palatini” and in its extensions to Non-Linear Gravity Theories; one in Quantum Field Theories (applications to conservation laws in Loop Quantum Gravity via spin connections and Barbero–Immirzi connections.
Scheme of motion as an action organizer in both classical and relativistic mechanics
Gabriel Dias de Carvalho Junior
2015-12-01
Full Text Available This paper reports our appropriation of the concept of scheme as one of the references for the analysis on the relative time process of signification. It has taken place within a current perspective that discusses the inclusion of modern physics in Brazilian high school, by the investigation of what are the conditions for such inclusion may occur. To do this, a didactic sequence was written placed in the transition between key concepts of classical mechanics and the theory of relativity, where one of the central points was the discussion on the influence of a frame of reference in the study of the movements. The research activities lasted 16 hours in a third grade high school and were quite diverse. We analyzed, in this work, episodes of verbal interaction and students written activities related to the concept of frame of reference and its relationship with relative time. It has been identified different epistemic content in the student’s scheme of movement. We conclude our research by the indication that there may be a reciprocal assimilation between time and motion schemes.
On higher order estimates in quantum electrodynamics
Matte, Oliver
2009-01-01
We propose a new method to derive certain higher order estimates in quantum electrodynamics. Our method is particularly convenient in the application to the non-local semi-relativistic models of quantum electrodynamics as it avoids the use of iterated commutator expansions. We re-derive higher order estimates obtained earlier by Fr\\"ohlich, Griesemer, and Schlein and prove new estimates for a non-local molecular no-pair operator.
The classical histories of the relativistic string with massive ends in space-time are examined in terms of geometric invariants of both the string world surface and world lines of the point masses at the string ends. In this formulation the string variables are completely defined by means of the constant curvatures and torsions of the endpoint trajectories which are subjected to a system of differential equations with a delayed arguments that incorporates retardation effects of the interaction of two point masses through the string. The well-known example of the rotating straight-line string with massive ends corresponds to a particular solution of this system for the constant torsions. A new exact solution for the periodic torsions of the world trajectories of the massive string ends is found. In this case the string coordinates are represented in terms of normal elliptic integrals and describe a more intricate motion including its transverse vibrations than rotation of a stretched string in a given plane. 17 refs
On the relativistic electron radiation in monocrystals
Radiation of relativistic electrons moving in a crystal near the crystallographical axis under the conditions of superbarrier motion is considered within the frames of classical electrodynamics. Radiation spectrum of superbarrier electrons is obtained for an averaged potential of the v(e) approximately exp(-e) chain. The maximum is shown to be observed for certain electron inlet angles relatively to the chain in the radiation spectrum. It permits to conclude that the maximum in experimentally detected spectra may be caused by superbarrier particle radiation
Relativistic energy loss in a dispersive medium
The electron energy loss in a dispersive medium is obtained using macroscopic electrodynamics taking advantage of a static frame of reference. Relativistic corrections are described in terms of a dispersive Lorentz factor obtained by replacing the vacuum velocity c by the characteristic phase velocity c/n, where n is the complex index of refraction. The angle-resolved energy-loss spectrum of a Drude conductor is analyzed in detail and it is shown that the low-energy peak due to Ohmic losses is enhanced compared to the classical approximation
Theoretical physics 3 electrodynamics
Nolting, Wolfgang
2016-01-01
This textbook offers a clear and comprehensive introduction to electrodynamics, one of the core components of undergraduate physics courses. It follows on naturally from the previous volumes in this series. The first part of the book describes the interaction of electric charges and magnetic moments by introducing electro- and magnetostatics. The second part of the book establishes deeper understanding of electrodynamics with the Maxwell equations, quasistationary fields and electromagnetic fields. All sections are accompanied by a detailed introduction to the math needed. Ideally suited to undergraduate students with some grounding in classical and analytical mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successful Germa...
Solving field equations in spinor electrodynamics
Bratchikov, A. V.
2009-01-01
Solutions of classical and quantum equations of motion in spinor electrodynamics are constructed within the context of perturbation theory. The solutions possess a graphical representation in terms of diagrams.
Mainland, G.B.
1988-01-01
Zero four-momentum, helicity eigenstates of the Bethe--Salpeter equation are found for a composite system consisting of a charged, spin-0 constituent and a charged, spin- 1/2 constituent bound by minimal electrodynamics. The form of the Bethe--Salpeter equation used to describe the bound state includes the contributions from both single photon exchange (ladder approximation) and the ''seagull'' diagram. Attention is restricted to zero orbital angular momentum states since these appear to be the most interesting physically.
Classical Dynamics of Free Electromagnetic Laser Pulses
Goto, S; Walton, T J
2015-01-01
We discuss a class of exact finite energy solutions to the vacuum source-free Maxwell field equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged test particles. These solutions are classified in terms of their chiral content based on their influence on particular charge configurations in space. Such solutions offer a computationally efficient parameterization of compact laser pulses used in laser-matter simulations and provide a potential means for experimentally bounding the fundamental length scale in the generalized electrodynamics of Bopp, Lande and Podolsky.
An optical-potential model originally developed for low-energy (Tπ ≤ 300 MeV) pion-nucleus scattering in momentum space was extended to treat both kaon-nucleus and high-energy pion-nucleus elastic scattering (300 MeV ≤ Tπ ≤ 1 GeV). The optical model utilizes Lorentz covariantly normalized wave functions, full relativistic kinematics and a Klein-Gordon propagator in the Lippmann-Schwinger equation, finite range nucleon form factors plus various nuclear medium corrections. The fermi-averaging integration can be performed exactly. This work on the K+-12C and K+-40Ca elastic differential cross section at a kaon lab momentum of 800 MeV/c confirms a nucleon swelling effect. An enhancement in the two-body amplitude is needed to eliminate the discrepancy between the data and theory. For the high-energy pion-nucleus scattering problem, the optical model approach has been limited to light nuclei (A ≤ 90) and/or at low energy (Tπ ≤ 500 MeV). A simple but effective eikonal approximation for high-energy pion scattering was developed. Both the Coulomb interaction and the semi-classical Wallace corrections are included in the eikonal approximation. The same target wave functions and two-body amplitude are used in both the optical model and the eikonal calculation. Comparison of the results from both calculations shows that the fermi-averaging integration and various sources of non-locality are not important at high energies. The eikonal approximation gives very reliable results, especially for heavy nuclei (A ≥ 28). Predictions utilizing the eikonal approximation are made for elastic differential cross sections of π± on various target nuclei. Contributions from the Coulomb interaction and the Wallace corrections in this energy region are found to be important. Future prospects of studying high-energy pion scattering utilizing the eikonal approximation are discussed
Relativistic classical strings. II
The interactions of strings with electromagnetic and gravitational fields are extensively discussed. Some concepts of differential geometry are reviewed. Strings in Kaluza-Klein manifolds are studied. (L.C.)
Introduction to modern theoretical physics. Volume I. Classical physics and relativity
The treatment covers vectors, tensors, and the structure of space, Newton's laws of motion and the law of gravitation, analytical mechanics, oscillatory motion, mechanics of a rigid body and of continuous media, classical fields, electromagnetic waves and radiation, the principle of relativity, relativistic electrodynamics and mechanics, general relativity theory and some of its consequences, and unified field theories and other modifications of the general theory of relativity
On Kottler's path: origin and evolution of the premetric program in gravity and in electrodynamics
Hehl, Friedrich W; Obukhov, Yuri N
2016-01-01
In 1922, Kottler put forward the program to remove the gravitational potential, the metric of spacetime, from the fundamental equations in physics as far as possible. He successfully applied this idea to Newton's gravitostatics and to Maxwell's electrodynamics, where Kottler recast the field equations in premetric form and specified a metric-dependent constitutive law. We will discuss the basics of the premetric approach and some of its beautiful consequences, like the division of universal constants into two classes. We show that classical electrodynamics can be developed without a metric quite straightforwardly: the Maxwell equations, together with a local and linear response law for electromagnetic media, admit a consistent premetric formulation. Kottler's program succeeds here without provisos. In Kottler's approach to gravity, making the theory relativistic, two premetric quasi-Maxwellian field equations arise, but their field variables, if interpreted in terms of general relativity, do depend on the met...
Quantum field theory from classical statistics
Wetterich, C
2011-01-01
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schr\\"odinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discret...
Composed particle model in stochastic electrodynamics
We analyse the statistical properties of the non-relativistic motion of a particle that has two constituents having finite nasses and charges. The main interaction is in contact with thermal and zero point radiation of Stochastic Electrodynamics. (M.W.O.)
A Uniﬁed Theory of Interaction: Gravitation and Electrodynamics
Wagener P.
2008-10-01
Full Text Available A theory is proposed from which the basic equations of gravitation and electromagnetism are derived from a single Lagrangian. The total energy of an atom can be expressed in a power series of the fine structure constant, $alpha$. Specific selections of these terms yield the relativistic correction to the Bohr values of the hydrogen spectrum and the Sommerfeld-Dirac equation for the fine structure spectrum of the hydrogen atom. Expressions for the classical electron radius and some of the Large Number Coincidences are derived. A Lorentz-type force equation is derived for both gravitation and electrodynamics. Electron spin is shown to be an effect of fourth order in $alpha$.
This document consists of translations of the following original papers: (A) the fluctuations of charge connected with the formation of matter from radiation, by W. Heisenberg, Sachsiche Akademie der Wissenschaften; 86:(1934) 317-322; (B) theory of the positron, by P.A.M. Dirac, Report to 7th Solvay Physics Conference, structure and properties of Atomic Nuclei (1934) 203-212; (C) comments on the Dirac theory of the positron, by W. Heisenberg, Zeitschrift fur Physik; 90:(1934) 209-231; and (D) the electrodynamics of the vacuum on the basis of the quantum theory of the electron, by V. Weisskopf, Kongelige Danske Videnskabernes Selskab, Mathematiskfysiske Meddelelser XIV, no. 6 (1936) 3-39. (U.K.)
Stern, David P.
1990-01-01
The present one-dimensional model analysis of substorm electrodynamics proceeds from the standard scenario in which the plasma sheet collapses into a neutral sheet, and magnetic merging occurs between the two tail lobes; plasma flows into the neutral sheet from the lobes and the sides, undergoing acceleration in the dawn-dusk direction. The process is modified by the tendency of the accelerated plasma to unbalance charge neutrality, leading to an exchange of electrons with the ionosphere in order to maintain neutrality. The cross-tail current is weakened by the diversion: this reduces the adjacent lobe-field intensity, but without notable effects apart from a slight expansion of the tail boundary.
Role of superconducting shields in electrodynamic propulsion
Sanmartín Losada, Juan Ramón; Lorenzini, Enrico C.
2008-01-01
An electrodynamic tether can propel a spacecraft through a planetary magnetized plasma without using propellant. In the classical embodiment of an electrodynamic tether, the ambient magnetic fleld exerts a Lorentz force on the current along the tether, the ambient plasma providing circuit closure for the current A suggested propulsion scheme would hypothetically eliminate tether performance dependence on the plasma density by using a full wire loop to close the current circuit, and a supercon...
Boyer, Timothy H.
2011-01-01
The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect...
Scheck, Florian [Mainz Univ. (Germany). Fachbereich Physik
2010-07-01
Stringent presentation of field theory, mediates the connection from the classicalelectrodynamics up to modern gauge theories. The compact presentation is ideal for the bachelor study. New chapter on general relativity theory. Deepens the learned by numerous application from laser physic, metamaterials and different more. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian, and gravitation is the third of five volumes on theoretical physics by professor Scheck. The cycle theoretical physics comprehends: Volume 1: Mechanics. From Newtons law to the deterministic chaos. Volume 2: Nonrelativistic quantum theory. From the hydrogen atom to the many-particle systems. Volume 3: Classical field theory. From the electrodynamics to the gauge theories. Volume 5: From the laws of thermodynamics to the quantum statistics. This textbook mediates modern theoretical physics in string presentation illustrated by many examples. It contains numerous problems with solution hints ore exemplary, complete solutions. The third edition was revised in many single topics, especially the chapter on general relativity theory was supplemented by an extensive analysis of the Schwarzschild solution. [German] Stringente Darstellung der Feldtheorie, vermittelt den Zusammenhang von der klassischen Elektrodynamik bis zu modernen Eichtheorien. Die kompakte Darstellung ist ideal fuer das Bachelor-Studium. Neues Kapitel zur Allgemeinen Relativitaetstheorie. Vertieft das Erlernte durch zahlreiche Anwendungsbeispiele aus Laserphysik, Metamaterialien uvm. Theoretische Physik 3. Klassische Feldtheorie. Von Elektrodynamik, nicht-Abelschen Eichtheorien und Gravitation ist der dritte von fuenf Baenden zur Theoretischen Physik von Professor Scheck. Der Zyklus Theoretische Physik umfasst: Band 1: Mechanik. Von den Newtonschen Gesetzen zum deterministischen Chaos. Band 2: Nichtrelativistische Quantentheorie. Vom Wasserstoffatom zu den Vielteilchensystemen. Band 3: Klassische Feldtheorie
On the Electrodynamics of Moving Particles in Gravitational Fields
Nassif, Claudio
2007-01-01
We will look for an implementation of new symmetries in the space-time structure, which allows us to find a unified vision for electrodynamics and gravitation. We will atempt to develop a simple model of the electromagnetic nature of the electron such that the influence of the gravitational field over the electrodynamics in subatomic scales leads us to a reformulation in our comprehention of the space-time structure through the elimination of the classical idea of rest. This will lead to a reformulation of the relativistic theory by introducing the idea about a universal minimum limit of speed in the space-time. Such limit, unattainable by the particles, represents a perfect and absolute inertial reference frame associated to a universal background field (a kind of non-local vacuum energy), enabling a fundamental understanding of the quantum uncertainties. The structure of space-time becomes extended due to such vacuum energy density which leads to a negative pressure in cosmological scales like a cosmologica...
Middle atmospheric electrodynamics
Kelley, M. C.
1983-01-01
A review is presented of the advances made during the last few years with respect to the study of the electrodynamics in the earth's middle atmosphere. In a report of the experimental work conducted, attention is given to large middle atmospheric electric fields, the downward coupling of high altitude processes into the middle atmosphere, and upward coupling of tropospheric processes into the middle atmosphere. It is pointed out that new developments in tethered balloons and superpressure balloons should greatly increase the measurement duration of earth-ionospheric potential measurements and of stratospheric electric field measurements in the next few years. Theoretical work considered provides an excellent starting point for study of upward coupling of transient and dc electric fields. Hays and Roble (1979) were the first to construct a model which included orographic features as well as the classical thunderstorm generator.
Nonlinear Electrodynamics and QED
Delphenich, David
2003-01-01
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a guide for understanding the nature of the nonlinearity of electrodynamics at the subatomic level. Some established theories of nonlinear electrodynamics, namely, those of Mie, Born, and Infeld are presented in the language of the modern geometrical and topologi...
Cremaschini, Claudio; 10.1140/epjp/i2011-11063-3
2012-01-01
A notorious difficulty in the covariant dynamics of classical charged particles subject to non-local electromagnetic (EM) interactions arising in the EM radiation-reaction (RR) phenomena is due to the definition of the related non-local Lagrangian and Hamiltonian systems. The lack of a standard Lagrangian/Hamiltonian formulation in the customary asymptotic approximation for the RR equation may inhibit the construction of consistent kinetic and fluid theories. In this paper the issue is investigated in the framework of Special Relativity. It is shown that, for finite-size spherically-symmetric classical charged particles, non-perturbative Lagrangian and Hamiltonian formulations in standard form can be obtained, which describe particle dynamics in the presence of the exact EM RR self-force. As a remarkable consequence, based on axiomatic formulation of classical statistical mechanics, the covariant kinetic theory for systems of charged particles subject to the EM RR self-force is formulated in Hamiltonian form....
Higher-Order Kinetic Term for Controlling Photon Mass in Off-Shell Electrodynamics
Land, M
2003-01-01
In a relativistic classical and quantum mechanics with Poincare-invariant parameter, particle worldlines are traced out by the evolution of spacetime events. In pre-Maxwell electrodynamics -- the local gauge theory associated with this framework -- events induce five local off-shell fields, which mediate interactions between instantaneous events, not between the worldlines which represent entire particle histories. The fifth field, required to compensate for dependence of gauge transformations on the evolution parameter, enables the exchange of mass between particles and fields. In the equilibrium limit, these pre-Maxwell fields are pushed onto the zero-mass shell, but during interactions there is no mechanism regulating the mass that photons may acquire, even when event trajectories evolve far into the spacelike region. This feature of the off-shell formalism requires the application of some ad hoc mechanism for controlling the photon mass in low energy classical Coulomb scattering of charged events, and in ...
Pachon, L A
2010-01-01
We study the electromagnetic and gravitational fields of the proton and electron in terms of the Einstenian gravity, by the introduction of an arbitrary Lande $g$-factor in the Kerr-Newman solution. We show that at length scales of the order of the Compton wavelength, corrections from different values of the $g$-factor are not negligible and predict the presence of general relativistic effects in highly ionized heavy atoms. On the other hand, since at the Compton-wavelength scale the gravitational field becomes spin dominated rather than mass dominated, we also point out the necessity of including angular momentum as a source of corrections to Newtonian gravity in the quantum description of gravity at this scale.
Dyson-Schwinger equations in quantum electrodynamics
A quantum field theory is completely determined by the knowledge of its Green functions and this thesis is concerned with the Salam and Delbourgo approximation method for the determination of the Green functions. In chapter 2 a Lorentz covariant, canonical formulation for quantum electrodynamics is described. In chapter 3 the definition of the Green functions in quantum electrodynamics is given with a derivation of the Dyson-Schwinger equations. The Ward-Takahashi identities, which are a consequence of current conservation, are derived and finally renormalization is briefly mentioned and the equations for the renormalized quantities are given. The gauge transformations, changing the gauge-parameter, a, discussed in Chapter 2 for the field operators, also have implications for the Green functions, and these are worked out in Chapter 4 for the electron propagator, which is not gauge-invariant. Before developing the main approximation, a simple, non-relativistic model is studied in Chapter 5. It has the feature of being exactly solvable in a way which closely resembles the approximation method of Chapter 6 for relativistic quantum electrodynamics. There the Dyson-Schwinger equations for the electron and photon propagator are studied. In chapter 7, the Johnson-Baker-Willey program of finite quantum electrodynamics is considered, in connection with the Ansatz of Salam and Delbourgo, and the question of a possible fixed point of the coupling constant is considered. In the last chapter, some remarks are made about how the results of the approximation scheme can be improved. (Auth.)
Galilean electrodynamics. Part 1. Fields in vacuum
Formulation of Galilean invariant electrodynamics is achieved by means of non-tensorial transformation rules for the fields. The basic concept of compensative fields as solutions of additional Maxwell equations allows to use one absolute time through-out the theory. There is an analogy between the obtained formulae and those of the relativistic theory and transition to the well-known formulae in the case of small velocities. 5 refs. (author)
Recent advances in bound state quantum electrodynamics
Recent developments are reviewed in four areas of computational quantum electrodynamics: a new relativistic two-body formalism equal in rigor to the Bethe-Salpeter formalism but with strong calculational advantages is discussed; recent work on the computation of the decay rate of bound systems (positronium in particular) is presented; limits on possible composite structure of leptons are discussed; a new multidimensional integration program ('VEGAS') suitable for higher order calculations is presented
We review a recently introduced unified approach to the analytical quantification of correlations in Gaussian states of bosonic scalar fields by means of Rényi-2 entropy. This allows us to obtain handy formulae for classical, quantum, total correlations, as well as bipartite and multipartite entanglement. We apply our techniques to the study of correlations between two modes of a scalar field as described by observers in different states of motion. When one or both observers are in uniform acceleration, the quantum and classical correlations are degraded differently by the Unruh effect, depending on which mode is detected. Residual quantum correlations, in the form of quantum discord without entanglement, may survive in the limit of an infinitely accelerated observer Rob, provided they are revealed in a measurement performed by the inertial Alice. (paper)
Boyer, Timothy H.
2010-01-01
The Planck spectrum of thermal scalar radiation is derived suggestively within classical physics by the use of an accelerating coordinate frame. The derivation has an analogue in Boltzmann's derivation of the Maxwell velocity distribution for thermal particle velocities by considering the thermal equilibrium of noninteracting particles in a uniform gravitational field. For the case of radiation, the gravitational field is provided by the acceleration of a Rindler frame through Minkowski space...
Off-shell quantum electrodynamics
Land, M C
1996-01-01
More than twenty years have passed since the threads of the `proper time formalism' in covariant classical and quantum mechanics were brought together to construct a canonical formalism for the relativistic mechanics of many particles. Drawing on the work of Fock, Stueckelberg, Nambu, Schwinger, and Feynman, the formalism was raised from the status of a purely formal mathematical technique to a covariant evolution theory for interacting particles. In the context of this theory, solutions have been found for the relativistic bound state problem, classical and quantum scattering in relativistic potentials, as well as applications in statistical mechanics. It has been shown that a generalization of the Maxwell theory is required in order that the electromagnetic interaction be well-posed in the theory. The resulting theory of electromagnetism involves a fifth gauge field introduced to compensate for the dependence of the gauge transformation on the invariant time parameter; permitting such dependence relaxes the...
Linear Response Laws and Causality in Electrodynamics
Yuffa, Alex J.; Scales, John A.
2012-01-01
Linear response laws and causality (the effect cannot precede the cause) are of fundamental importance in physics. In the context of classical electrodynamics, students often have a difficult time grasping these concepts because the physics is obscured by the intermingling of the time and frequency domains. In this paper, we analyse the linear…
Poliakovsky, Arkady
2015-01-01
Under the classical non-relativistic consideration of the space-time we propose the model of the laws of gravitation and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian coordinate system. Being in the frames of non-relativistic model of the space-time, we adopt some general ideas of the General Theory of Relativity, like the assumption of covariance of the most general physical laws in every inertial and non-inertial coordinate system and equivalence of factious forces in non-inertial coordinate systems and the force of gravitation.
Poliakovsky, Arkady
2015-01-01
Under the classical non-relativistic consideration of the space-time we propose the model of the laws of gravitation and Electrodynamics, invariant under the galilean transformations and moreover, under every change of non-inertial cartesian coordinate system. Being in the frames of non-relativistic model of the space-time, we adopt some general ideas of the General Theory of Relativity, like the assumption of invariance of the most general physical laws in every inertial and non-inertial coo...
Universe acceleration and nonlinear electrodynamics
Kruglov, S I
2016-01-01
A new model of nonlinear electrodynamics with a dimensional parameter $\\beta$ coupled to gravity is considered. We show that an accelerated expansion of the universe takes place if the nonlinear electromagnetic field is the source of the gravitational field. A pure magnetic universe is investigated and the magnetic field drives the universe to accelerate. In this model, after the big bang, the universe undergoes inflation, and the accelerated expansion and then decelerates approaching Minkowski spacetime asymptotically. We demonstrate the causality of the model and a classical stability at the deceleration phase.
Multipole Expansion in Generalized Electrodynamics
Bonin, C A; Ortega, P H
2016-01-01
In this article we study some classical aspects of Podolsky Electrodynamics in the static regime. We develop the multipole expansion for the theory in both the electrostatic and the magnetostatic cases. We also address the problem of consistently truncating the infinite series associated with the several kinds of multipoles, yielding approximations for the static Podolskian electromagnetic field to any degree of precision required. Moreover, we apply the general theory of multipole expansion to some specific physical problems. In those problems we identify the first terms of the series with the monopole, dipole and quadrupole terms in the generalized theory. We also propose a situation in which Podolsky theory can be experimentally tested.
On the relativistic calculation of spontaneous emission
In a recent work, Barut and Salamin (1988) have derived a method for calculating the relativistic decay rates in atoms, in a formulation of quantum electrodynamics based upon the electron's self-energy. The decay rate appears as the imaginary part of a formula giving a complex energy shift, the real part of the formula being the Lamb shift. The presence of the the decay rate in the imaginary part of a formula, giving an energy in its real part, may appear a bit strange. A confirmation of the Barut and Alamin calculation, by means of a quite different point of view, would be useful. Therefore in this work the Einstein A coefficients are calculated, in all cases of degeneracies of the Dirac transition currents, by means of the energy balance method. This point of view is based on the balance between the energy released during the transitions of electrons from a higher state to a lower one, and the flux of the Poynting vector of the classical electromagnetic field, created by the electrons, through a sphere a large radius. The particularity of the present work lies in the direct calculation of the relativistic Dirac transition currents and the fact that the dipole and Pauli approximations are avoided. The quantum part of the relativistic calculation is based on the determination of the transition charge currents in the Darwin solutions of the Dirac equation. 13 refs
A 3+1 formalism for quantum electrodynamical corrections to Maxwell equations in general relativity
Pétri, J.
2015-08-01
Magnetized neutron stars constitute a special class of compact objects harbouring gravitational fields that deviate strongly from the Newtonian weak field limit. Moreover, strong electromagnetic fields anchored into the star give rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). Electromagnetic fields close to or above the critical value of BQ = 4.4 × 109 T are probably present in some pulsars and for most of the magnetars. To account properly for emission emanating from the neutron star surface like for instance thermal radiation and its polarization properties, it is important to include general relativistic (GR) effects simultaneously with non-linear electrodynamics. This can be achieved through a 3+1 formalism known in general relativity and that incorporates QED perturbations to Maxwell equations. Starting from the lowest order corrections to the Lagrangian for the electromagnetic field, as given for instance by Born-Infeld or Euler-Heisenberg theory, we derive the non-linear Maxwell equations in general relativity including quantum vacuum effects. We also derive a prescription for the force-free limit and show that these equations can be solved with classical finite volume methods for hyperbolic conservation laws. It is therefore straightforward to include general relativity and QED in the description of neutron star magnetospheres by using standard classical numerical techniques borrowed from Maxwell and Newton theory. As an application, we show that spin-down luminosity corrections associated with QED effects are negligible with respect to GR corrections.
Energy conservation laws in classical electrodynamics
Dmitriyev, Valery P.
2004-01-01
There are three electromagnetic integrals of motion that can be interpreted as the energy. These are the background energy, the elastic energy and the integral in the torsion field commonly referred to as the energy of the electromagnetic field. The integral in the torsion field gains the meaning of the energy insomuch as it is concerned with the mechanical energy of a charged particle.
Electrodynamics of a Cosmic Dark Fluid
Balakin, Alexander B
2016-01-01
Cosmic Dark Fluid is considered as a non-stationary medium, in which electromagnetic waves propagate, and magneto-electric field structures emerge and evolve. A medium - type representation of the Dark Fluid allows us to involve into analysis the concepts and mathematical formalism elaborated in the framework of classical covariant electrodynamics of continua, and to distinguish dark analogs of well-known medium-effects, such as optical activity, pyro-electricity, piezo-magnetism, electro- and magneto-striction and dynamo-optical activity. The Dark Fluid is assumed to be formed by a duet of a Dark Matter (a pseudoscalar axionic constituent) and Dark Energy (a scalar element); respectively, we distinguish electrodynamic effects induced by these two constituents of the Dark Fluid. The review contains discussions of ten models, which describe electrodynamic effects induced by Dark Matter and/or Dark Energy. The models are accompanied by examples of exact solutions to the master equations, correspondingly extende...
On the electrodynamics of Minkowski at low velocities
Rousseaux, G.
2008-10-01
The Galilean constitutive equations for the electrodynamics of moving media are derived for the first time. They explain all the historic and modern experiments which were interpreted so far in a relativistic framework assuming the constant light celerity principle. Here, we show the latter to be sufficient but not necessary.
Electrodynamics of Magnetoactive Media
'Electrodynamics of Magnetoactive Media' is an unusual book in that it cuts across conventional physics discipline boundaries. The unifying theme allowing this is, quite simply, the physics of magnetic fields in various media. I believe the authors are correct in stating that the book is unique in specifically covering electrodynamic phenomena associated with magnetic fields, though of course some of the more elementary aspects are covered in the classical textbooks on electromagnetism, which are duly acknowledged. This interdisciplinarity makes the book very interesting to people with a range of backgrounds. For example, as a plasma physicist, I was familiar with most of the material on plasmas, but liquid crystals and superconductors were entirely new territory for me. These chapters were indeed both accessible and interesting, and it was surprising for me to see how much commonality there is in the physics of these various media. The first part of the book covers some fundamentals of electrodynamics and magnetostatics, and of electromagnetic waves. Most of this material is covered in textbooks on electromagnetism, and some of it is very basic (for example, LRC circuit theory, surely covered in most first year physics courses, is included) but it is perhaps a useful prelude for what is to come. The generic topic of charged particle motion in electromagnetic fields is well covered. Three main magnetoactive media are then discussed: plasmas (focusing on waves), liquid crystals and superconductors. It is all too easy to criticise a book on the grounds of omitted material, but I do feel that a chapter on magnetostatics in plasmas would have been very helpful, covering force-free fields and so on. Some interesting analogies could then have been exploited. For example, I was intrigued to discover an equation for magnetic fields in superconductors (equation (9.36)) which, apart from a change of sign, is identical to the Helmholtz equation used to model linear force
Electrodynamics of Magnetoactive Media
Browning, P K [Department of Physics, UMIST, PO Box 88, Sackville Street, Manchester, M60 1QD (United Kingdom)
2004-11-12
'Electrodynamics of Magnetoactive Media' is an unusual book in that it cuts across conventional physics discipline boundaries. The unifying theme allowing this is, quite simply, the physics of magnetic fields in various media. I believe the authors are correct in stating that the book is unique in specifically covering electrodynamic phenomena associated with magnetic fields, though of course some of the more elementary aspects are covered in the classical textbooks on electromagnetism, which are duly acknowledged. This interdisciplinarity makes the book very interesting to people with a range of backgrounds. For example, as a plasma physicist, I was familiar with most of the material on plasmas, but liquid crystals and superconductors were entirely new territory for me. These chapters were indeed both accessible and interesting, and it was surprising for me to see how much commonality there is in the physics of these various media. The first part of the book covers some fundamentals of electrodynamics and magnetostatics, and of electromagnetic waves. Most of this material is covered in textbooks on electromagnetism, and some of it is very basic (for example, LRC circuit theory, surely covered in most first year physics courses, is included) but it is perhaps a useful prelude for what is to come. The generic topic of charged particle motion in electromagnetic fields is well covered. Three main magnetoactive media are then discussed: plasmas (focusing on waves), liquid crystals and superconductors. It is all too easy to criticise a book on the grounds of omitted material, but I do feel that a chapter on magnetostatics in plasmas would have been very helpful, covering force-free fields and so on. Some interesting analogies could then have been exploited. For example, I was intrigued to discover an equation for magnetic fields in superconductors (equation (9.36)) which, apart from a change of sign, is identical to the Helmholtz equation used to model linear
Alternative formulations of magnetospheric plasma electrodynamics
Cragin, B. L.; Heikkila, W. J.
1981-01-01
The fundamental equations of magnetospheric plasma electrodynamics are considered from a theoretical standpoint that stresses the basic equivalence of various seemingly different formal representations. The mathematical properties of vector fields are reviewed, and their implications in electrodynamics are studied. The irrotational and solenoidal parts of the electric field are associated with two physically distinct types of sources. Relativistic covariance and gauge invariance in electromagnetic theory are reviewed and discussed in the context of an approach in which the mathematical properties of vector fields are taken as primary concepts. Special attention is given to the use and interpretation of the Coulomb gauge potential functions. This choice of gauge is sometimes regarded with undue suspicion, possibly because of a certain paradox concerning causality. The paradox is discussed and resolved. Useful properties of the Coulomb gauge are identified. These need not be limited to the case of slow time variations and can extend beyond the limits of validity of ideal MHD theory.
Electrodynamics in rotating and other accelerated frames of reference
A systematic description of the various aspects of electrodynamics in accelerated frames, with a special emphasis to that in frames rotating about a fixed axis, at a constant rate, is attempted here. The related basic problems and controversies are of such nature that these can not be covered briefly in books on classical electrodynamics. For this reason all authors of such books avoid any presentation of this electrodynamics, even for very small rotational velocities. These problems have been clearly exposed here. (author). 10 refs
Off-Shell Quantum Electrodynamics
Land, M. C.; Horwitz, L. P.
1996-01-01
More than twenty years have passed since the threads of the `proper time formalism' in covariant classical and quantum mechanics were brought together to construct a canonical formalism for the relativistic mechanics of many particles. Drawing on the work of Fock, Stueckelberg, Nambu, Schwinger, and Feynman, the formalism was raised from the status of a purely formal mathematical technique to a covariant evolution theory for interacting particles. In the context of this theory, solutions have...
On the self-force in Bopp–Podolsky electrodynamics
In the classical vacuum Maxwell–Lorentz theory the self-force of a charged point particle is infinite. This makes classical mass renormalization necessary and, in the special relativistic domain, leads to the Abraham–Lorentz–Dirac equation of motion possessing unphysical run-away and pre-acceleration solutions. In this paper we investigate whether the higher-order modification of classical vacuum electrodynamics suggested by Bopp, Landé, Thomas and Podolsky in the 1940s, can provide a solution to this problem. Since the theory is linear, Green-function techniques enable one to write the field of a charged point particle on Minkowski spacetime as an integral over the particle’s history. By introducing the notion of timelike worldlines that are ‘bounded away from the backward light-cone’ we are able to prescribe criteria for the convergence of such integrals. We also exhibit a timelike worldline yielding singular fields on a lightlike hyperplane in spacetime. In this case the field is mildly singular at the event where the particle crosses the hyperplane. Even in the case when the Bopp–Podolsky field is bounded, it exhibits a directional discontinuity as one approaches the point particle. We describe a procedure for assigning a value to the field on the particle worldline which enables one to define a finite Lorentz self-force. This is explicitly derived leading to an integro-differential equation for the motion of the particle in an external electromagnetic field. We conclude that any worldline solutions to this equation belonging to the categories discussed in the paper have continuous four-velocities. (paper)
Strong-field Relativistic Processes in Highly Charged Ions
Postavaru, Octavian
2010-01-01
In this thesis we investigate strong-field relativistic processes in highly charged ions. In the first part,we study resonance fluorescence of laser-driven highly charged ions in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Dirac equation allows for investigating highly relativistic ions, and, consequently, provides a sensitive means to test correlated relativistic dynamics, bound-state quantum electrodynamic...
Strong-field relativistic processes in highly chargerd ions
Postavaru, O.
2010-01-01
In this thesis we investigate strong-field relativistic processes in highly charged ions. In the first part, we study resonance fluorescence of laser-driven highly charged ions in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Diracv equation allows for investigating highly relativistic ions, and, consequently, provides a sensitive means to test correlated relativistic dynamics, bound-state quantum electrodynam...
Electrodynamics of a Cosmic Dark Fluid
Balakin, Alexander B.
2016-01-01
Cosmic Dark Fluid is considered as a non-stationary medium, in which electromagnetic waves propagate, and magneto-electric field structures emerge and evolve. A medium - type representation of the Dark Fluid allows us to involve into analysis the concepts and mathematical formalism elaborated in the framework of classical covariant electrodynamics of continua, and to distinguish dark analogs of well-known medium-effects, such as optical activity, pyro-electricity, piezo-magnetism, electro- an...
Flury, J.
2016-06-01
Quantum metrology enables new applications in geodesy, including relativistic geodesy. The recent progress in optical atomic clocks and in long-distance frequency transfer by optical fiber together pave the way for using measurements of the gravitational frequency redshift for geodesy. The remote comparison of frequencies generated by calibrated clocks will allow for a purely relativistic determination of differences in gravitational potential and height between stations on Earth surface (chronometric leveling). The long-term perspective is to tie potential and height differences to atomic standards in order to overcome the weaknesses and inhomogeneity of height systems determined by classical spirit leveling. Complementarily, gravity measurements with atom interferometric setups, and satellite gravimetry with space borne laser interferometers allow for new sensitivities in the measurement of the Earth's gravity field.
The exact radiation-reaction equation for a classical charged particle
Tessarotto, M; Cremaschini, C; Nicolini, P; Beklemishev, A
2008-01-01
An unsolved problem of classical mechanics and classical electrodynamics is the search of the exact relativistic equations of motion for a classical charged point-particle subject to the force produced by the action of its EM self-field. The problem is related to the conjecture that for a classical charged point-particle there should exist a relativistic equation of motion (RR equation) which results both non-perturbative, in the sense that it does not rely on a perturbative expansion on the electromagnetic field generated by the charged particle and non-asymptotic, i.e., it does not depend on any infinitesimal parameter. In this paper we intend to propose a novel solution to this well known problem, and in particular to point out that the RR equation is necessarily variational. The approach is based on two key elements: 1) the adoption of the relativistic hybrid synchronous Hamilton variational principle recently pointed out (Tessarotto et al, 2006). Its basic feature is that it can be expressed in principle...
Asymptotic algebra of quantum electrodynamics
Herdegen, Andrzej
2004-01-01
The Staruszkiewicz quantum model of the long-range structure in electrodynamics is reviewed in the form of a Weyl algebra. This is followed by a personal view on the asymptotic structure of quantum electrodynamics.
Electrodynamics in Arbitrary Reference Frames and in Arbitrary Material Media
Full text: The investigation of electromagnetic phenomena in material media still belongs to the most difficult tasks of electrodynamics. Complexity and variability of material media practically exclude effective applications of methods and computational techniques elaborated in the framework of standard microscopic electrodynamics with classical vacuum as a ground state. In order to obtain satisfactorily exact descriptions of electromagnetic properties of complex material media one is enforced to use methods and approximations which are difficult to control. Moreover, they usually break covariance properties and the results obtained are valid in one reference frame which choice remains subjective and model dependent. Some time ago we have proposed a reformulation of Maxwell electrodynamics which opens new ways in study of electromagnetic processes in material media. The formalism gets rid of assumptions characteristic for vacuum electrodynamics only and it avoids the usage of constitutive relations as primary relations put on quantities needed for a complete description of an electromagnetic system. Fundamental properties of all electromagnetic quantities are their uniquely defined transformation rules and their analysis allows to determine the possible relations between them. Within such a scheme it is possible to introduce constitutive relations which do not have analogies in macroscopic classical electrodynamics. They may be used in description of microscopic electromagnetic processes in a different way than it is done in the framework of quantum electrodynamics. (author)
Differential formalism aspects of the gauge classical theories
The classical aspects of the gauge theories are shown using differential geometry as fundamental tool. Somme comments are done about Maxwell Electro-dynamics, classical Yang-Mills and gravitation theories. (L.C.)
Molecular quantum electrodynamics
Craig, D P
1998-01-01
This systematic introduction to quantum electrodynamics focuses on the interaction of radiation with outer electrons and nuclei of atoms and molecules, answering the long-standing need of chemists and physicists for a comprehensive text on this highly specialized subject.Geared toward postgraduate students in the chemical sciences who require an understanding of quantum electrodynamics as applied to the interpretation of optical experiments on atoms and molecules, the text offers a detailed explanation of the quantum theory of electromagnetic radiation and its interaction with matter. It feat
Electrodynamics panel presentation
Mccoy, J.
1986-01-01
The Plasma Motor Generator (PMG) concept is explained in detail. The PMG tether systems being used to calculate the estimated performance data is described. The voltage drops and current contact geometries involved in the operation of an electrodynamic tether are displayed illustrating the comparative behavior of hollow cathodes, electron guns, and passive collectors for current coupling into the ionosphere. The basic PMG design involving the massive tether cable with little or no satellite mass at the far end(s) are also described. The Jupiter mission and its use of electrodynamic tethers are given. The need for demonstration experiments is stressed.
Electrodynamics, wind and temperature
Schmidlin, F. J.
1988-01-01
This RTOP provides for correlative meteorological wind and temperature measurements with atmospheric electrodynamic measurements. Meteorological rocketsondes were launched as part of a number of electrodynamic investigations in Alaska, Norway, Peru, Sweden, and at the Wallops Flight Facility, Wallops Island, Virginia. Measurements obtained as part of the MAC/Epsilon campaign during October 1987 from Andoya, Norway, were in conjunction with electric field, ion mobility, conductivity, and energy deposition studies. The measurements obtained between 30 and 90 km are to evaluate and correlate changes in the atmospheric electrical structure caused by the neutral wind and temperature, or changes in the neutral atmosphere resulting from electrical anomalies.
Applications of conformal symmetry in quantum electrodynamics
Quantum electrodyanmics is a system in which the only scale is provided by the electron mass. A topic of continuing interest has been the structure of this field theory for spatial separations small in comparison to the scale defined by the Compton size ((h/2π)/mc), and one is thus led to consider 'massless' quantum electrodynamics (m equivalent to 0). The classical field equations for massless electrodynamics are invariant under a much larger group of space-time transformations than the massive theory, namely the full fifteen parameter conformal group. However, in contrast to the massive theory where calculations can be formulated in terms of a set of fully Lorentz covariant Green's functions, no fully conformally covariant formalism exists for the massless theory because of complications associated with gauge invariance. The authors present what they regard as the most salient aspects of the conformal symmetry when it is used to simplify calculations. (Auth.)
Limits of electrodynamics: paraphotons
The paper discusses the accuracy with which electromagnetic interaction is studied at large distances. Possible deviations from standard electrodynamics are investigated. The consideration is carried out the framework of a model which contains two (para) photons, the mass of one of them being non-negligible
Testability of nonlinear electrodynamics
Laser interferometry combined with present-day electronic techniques now make it possible to test nonlinear-electrodynamics predictions in the weak-field limit, up to a sensitivity of 10-23 in the relative variation of the velocity of light. The significance of such tests in regard to QED predictions is noted
Electrodynamics with radiation reaction
Hammond, Richard T.
2011-01-01
The self force of electrodynamics is derived from a scalar field. The resulting equation of motion is free of all of the problems that plague the Lorentz Abraham Dirac equation. The age-old problem of a particle in a constant field is solved and the solution has intuitive appeal.
Galilean electrodynamics. Part 2. Charged particle force and conservation laws
From the general formulae for the transformation of fields in Galilean electrodynamics there are derived the expression for the force acting on a charged particle and the equation of motion of a charged particle. Without any additional assumptions these equations are performed into the relativistic form, that is with the relativistic momentum and energy. Hence, in an elementary way, Einstein's formula of the equivalence of energy and mass results. Then the conservation laws of energy and momentum for the fields are derived. 3 refs. (author)
Relativistic energy loss in a dispersive medium
Houlrik, Jens Madsen
2002-01-01
The electron energy loss in a dispersive medium is obtained using macroscopic electrodynamics taking advantage of a static frame of reference. Relativistic corrections are described in terms of a dispersive Lorentz factor obtained by replacing the vacuum velocity c by the characteristic phase...
Stable discrete representation of relativistically drifting plasmas
Kirchen, Manuel; Godfrey, Brendan B; Dornmair, Irene; Jalas, Soeren; Peters, Kevin; Vay, Jean-Luc; Maier, Andreas R
2016-01-01
Representing the electrodynamics of relativistically drifting particle ensembles in discrete, co-propagating Galilean coordinates enables the derivation of a Particle-in-Cell algorithm that is intrinsically free of the Numerical Cherenkov Instability, for plasmas flowing at a uniform velocity. Application of the method is shown by modeling plasma accelerators in a Lorentz-transformed optimal frame of reference.
Relativistic Quantum Communication
Hosler, Dominic
2013-01-01
In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tend...
A Toy Model of Electrodynamics in (1 + 1) Dimensions
Boozer, A. D.
2007-01-01
A model is presented that describes a scalar field interacting with a point particle in (1+1) dimensions. The model exhibits many of the same phenomena that appear in classical electrodynamics, such as radiation and radiation damping, yet has a much simpler mathematical structure. By studying these phenomena in a highly simplified model, the…
Stochastic Electrodynamics and the Compton effect
Some of the main qualitative features of the Compton effect are tried to be described within the realm of Classical Stochastic Electrodynamics (SED). It is found indications that the combined action of the incident wave (frequency ω), the radiation reaction force and the zero point fluctuating electromagnetic fields of SED, are able to given a high average recoil velocity v/c=α/(1+α) to the charged particle. The estimate of the parameter α gives α ∼ ℎω/mc2 where 2Πℎ is the constant and mc2 is the rest energy of the particle. It is verified that this recoil is just that necessary to explain the frequency shift, observed in the scattered radiation as due to a classical double Doppler shift. The differential cross section for the radiation scattered by the recoiling charge using classical electromagnetism also calculated. The same expression as obtained by Compton in his fundamental work of 1923 is found. (author)
Minimal Quantum Electrodynamics
Jauregui, R.; Berrondo, M.
1985-01-01
A simple and coherent formulation of quantum electrodynamics is obtained within the general framework of the LSZ field theory. The commutation relations for the interacting fields are obtained rather than being postulated a priori and the current densities fulfill the one particle stability conditions. Thus, the inconsistencies which appear in the canonical formalism are avoided. The resulting spectral representations do not have any ambiguities so that we do not have to introduce the renormalization concept.
Minimal quantum electrodynamics
A simple and coherent formulation of quantum electrodynamics is obtained within the general framework of the LSZ field theory. The commutation relations for the intereacting fields are obtained rather than being postulated a priori and the current densities fulfill the one particle stability conditions. Thus, the inconsistencies which appear in the canonical formalism are avoided. The resulting spectral representations do not have any ambiguities so that we do not have to introduce the ''renormalization'' concept
Minimal Quantum Electrodynamics
A simple and coherent formulation of quantum electrodynamics is obtained within the general framework of the LSZ field theory. The commutation relations for the interacting fields are obtained rather than being postulated a priori and the current densities fulfill the one particle stability conditions. Thus, the inconsistencies which appear in the canonical formalism are avoided. The resulting spectral representations do not have any ambiguities so that we do not have to introduce the renormalization concept
Electrodynamics of a Cosmic Dark Fluid
Alexander B. Balakin
2016-06-01
Full Text Available Cosmic Dark Fluid is considered as a non-stationary medium, in which electromagnetic waves propagate, and magneto-electric field structures emerge and evolve. A medium-type representation of the Dark Fluid allows us to involve in its analysis the concepts and mathematical formalism elaborated in the framework of classical covariant electrodynamics of continua, and to distinguish dark analogs of well-known medium-effects, such as optical activity, pyro-electricity, piezo-magnetism, electro- and magneto-striction and dynamo-optical activity. The Dark Fluid is assumed to be formed by a duet of a Dark Matter (a pseudoscalar axionic constituent and Dark Energy (a scalar element; respectively, we distinguish electrodynamic effects induced by these two constituents of the Dark Fluid. The review contains discussions of 10 models, which describe electrodynamic effects induced by Dark Matter and/or Dark Energy. The models are accompanied by examples of exact solutions to the master equations, correspondingly extended; applications are considered for cosmology and space-times with spherical and pp-wave symmetries. In these applications we focused the attention on three main electromagnetic phenomena induced by the Dark Fluid: first, emergence of Longitudinal Magneto-Electric Clusters; second, generation of anomalous electromagnetic responses; third, formation of Dark Epochs in the Universe history.
A Simple Relativistic Bohr Atom
Terzis, Andreas F.
2008-01-01
A simple concise relativistic modification of the standard Bohr model for hydrogen-like atoms with circular orbits is presented. As the derivation requires basic knowledge of classical and relativistic mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics. In addition, it can be shown in a class that…