Alexander G. Kyriakos
In the present paper it is shown that the Dirac electron theory is the approximation of the special nonlinear electromagnetic field theory
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In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such representation allows us to see new possibilities in the connection of the classical and quantum electrodynamics.
It is shown that the hypercomplex Dirac equation describes the system of connected fields: 4-scalar, 4-pseudoscalar, 4-vector, 4-pseudo-vector and antisymmetric 4-tensor second rank field. If mass is assumed to be zero this system splits into two subsystems. Equations containing tensor, scalar and pseudoscalar fields coincide with Maxwell equations complemented by scalar and pseudoscalar fields. This system describes the electrodynamics of non-conserved charges. The scalar and pseudoscalar fields are generated only by the non-conserved charges - electric and hypothetical magnetic. The influenc…
One of the most striking predictions of quantum electrodynamics is that vacuum fluctuations of the electromagnetic field can lead to spontaneous emission of atoms as well as photon-mediated interactions among them. Since these processes strongly depend on the nature of the photonic bath, a current burgeoning field is the study of their modification in the presence of photons with non-trivial energy dispersions, e.g., the ones confined in photonic crystals. A remarkable example is the case of isotropic Dirac-photons, which has been recently shown to lead to non-exponential spontaneous emission …
The ideas behind the nonlocal classical statistical field theory model for the quantized Klein-Gordon field introduced in Morgan(2001, quant-ph/0106141) are extended to accommodate quantum electrodynamics. The anticommutation rules for the quantized Dirac spinor field are given a classical interpretation as a relativistically covariant modification of the minimal coupling interaction between the classical electromagnetic field and a classical Dirac spinor field.
Controlling the time evolution of the population of two states in cavity quantum electrodynamics (QED) is necessary by tunning the \textit{modified} Rabi frequency in which the $\textit{extra}$ classical effect of electromagnetic field is taken into account.The theoretical explanation underlying the perturbation of potential on spatial regime of bloch sphere is by the use of (Bagrov, Baldiotti, Gitman, and Shamshutdinova) BBGS-Darboux transformations \cite{bagrov14darboux} on the electromagnetic field potential in one-dimensional stationary Dirac model in which the Pauli matrices are the centr…
We introduce a new scalable cavity quantum electrodynamics platform which can be used for quantum computing. This system is composed of coupled photonic crystal (PC) cavities which their modes lie on a Dirac cone in the whole super crystal band structure. Quantum information is stored in quantum dots that are positioned inside the cavities. We show if there is just one quantum dot in the system, energy as photon is exchanged between the quantum dot and the Dirac modes sinusoidally. Meanwhile the quantum dot becomes entangled with Dirac modes. If we insert more quantum dots into the system, the…
In this note we generalized the Dirac non-linear electrodynamics, by introducing two potentials (namely, the vector potential A and the pseudo-vector potential gamma^5 B of the electromagnetic theory with charges and magnetic monopoles) and by imposing the pseudoscalar part of the product omega.omega* to be zero, with omega = A + gamma^5 B. We show that the field equations of such a theory possess a soliton-like solution which can represent a priori a "charged particle", since it is endowed with a Coulomb field plus the field of a magnetic dipole. The rest energy of the soliton is finite, and …
Sufficient conditions for linear electrodynamics with real Dirac field are derived.
A common assumption in quantum field theory is that the energy-momentum 4-vector of any quantum state must be time-like. However it has been recently shown [4] that this is not the case for a Dirac-Maxwell field in the coulomb gauge. Here we will present a proof that is simpler then the proof of Ref. [4] that there must exist quantum states which are space-like for a Dirac-Maxwell field in the coulomb gauge.
On the possibility of differential-algebraic elimination of the spinor field from the Maxwell--Dirac electrodynamics
研究在特定规范下Maxwell-Dirac方程中旋量场能否通过微分-代数方法消除，通过构造截断幂级数解并线性化延长系统，分析系数矩阵的秩，发现电磁场及其导数可唯一确定旋量场，电磁四势的四阶时间导数也由低阶导数决定，表明旋量场可被消除，电磁场可独立演化。
Classical electromagnetism is linear. However, fields can polarize the vacuum Dirac sea, causing quantum nonlinear electromagnetic phenomena, e.g., scattering and splitting of photons, that occur only in very strong fields found in neutron stars or heavy ion colliders.We show that strong nonlinearity arises in Dirac materials at much lower fields $\sim 1\:\text{T}$, allowing us to explore the nonperturbative, extremely high field limit of quantum electrodynamics in solids. We explain recent experiments in a unified framework and predict a new class of nonlinear magneto-electric effects, includ…
Recent experimental results on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlinearities in the constitutive equations only, keeping Maxwell's equations unchanged. Combining these with linear or nonlinear Schroedinger equations, e.g. as proposed by Doebner and Goldin, yields a Galilean quantum electrodynamics.
We present the results of low lying excitation of coupled optical cavity arrays. We derive the Dirac equation for this system and explain the existence of Majorana fermion mode in the system. We present quite a few analytical relations between the Rabi frequency oscillation and the atom-photon coupling strength to achieve the different physical situation of our study and also the condition for massless excitation in the system. We present several analytical relations between the Dirac spinor field, order and disorder operators for our systems. We also show that the Luttinger liquid physics is …
We consider the quantum electrodynamics of a binary array of chiral waveguides, each containing many atoms. We show that the one-photon amplitude of a single-excitation state obeys a two-dimensional Dirac equation. Using this result, we develop the scattering theory for the Dirac equation in this setting and illustrate our results with numerical simulations.
Based on the precision experimental data of energy-level differences in hydrogenlike atoms, especially the 1S-2S transition of hydrogen and deuterium, the necessity of establishing a reduced Dirac equation (RDE) with reduced mass as the substitution of original electron mass is stressed. The theoretical basis of RDE lies on two symmetries, the invariance under the space-time inversion and that under the pure space inversion. Based on RDE and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated (at one-loop level) as the radiative correction on a bo…
Complex Quaternionic Formulations of Dirac, Electrodynamic, and Electroweak Fields and Interactions
本文通过复四元数构建了狄拉克理论、电动力学及标准模型电弱部分的新描述，揭示了电弱相互作用中轻子场与希格斯场结构的代数差异。
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell electrodynamics), spinor electrodynamics (Dirac-Maxwell electrodynamics), etc. In these models, evolution is typically described by modified Maxwell equations. In the case of scalar electrodynamics, the scalar complex wave function can be made real by a gauge transformation, the wave function can be algebraically eliminated from the equations of scalar electrodynamics, …
An explicit construction is given of field operators satisfying the free Dirac equation. The quantum expectation of these field operators forms a spinor which satisfies the original Dirac equation. The current operators are defined as pair correlation functions. Explicit expressions in terms of creation and annihilation operators are obtained. A small example shows that all relevant quantities are mathematically well-defined.
Dirac's contributions to the discovery of non-relativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described.
In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic field and, in particular, to electromagnetic radiation. If we adopt the standard energy density for the electromagnetic field, then potential energy seems to disappear. However, a closer look at electrodynamics shows that this conclusion actually depends on the kind of matter being considered. Although we cannot get by without attributing energy to the elect…
Clifford number formalism for Maxwell equations is considered. The Clifford imaginary unit for space-time is introduced as coordinate independent form of fully antisymmetric fourth-rank tensor. The representation of Maxwell equations in massless Dirac equation form is considered; we also consider two approaches to the invariance of Dirac equation in respect of the Lorentz transformations. According to the first approach, the unknown column is invariant and according to the second approach it has the transformation properties known as spinorial ones. Clifford number representation for nonlinear…
We investigate the motion of a wave packet of a charged scalar particle linearly accelerated by a static potential in quantum electrodynamics. We calculate the expectation value of the position of the charged particle after the acceleration to first order in the fine structure constant in the hbar -> 0 limit. We find that the change in the expectation value of the position (the position shift) due to radiation reaction agrees exactly with the result obtained using the Lorentz-Dirac force in classical electrodynamics. We also point out that the one-loop correction to the potential may contribut…
Quantum electrodynamics under a quench
本文研究全局量子淬火后量子电动力学的非平衡动力学，发现非费米液体行为的不动点，其反常维度依赖初始淬火参数，并提出了实验特征。
Fundamental principles and applications of nonlinear optical phenomena in classical and quantum electrodynamics
本文针对微纳技术领域中非线性光学现象的应用需求，阐述了非线性光学材料与系统的一般特性，重点研究了参量放大、带泵浦耗尽的倍频、光量子噪声及参量荧光等内容。
In this paper we correct previous work on magnetic charge plus a photon mass. We show that contrary to previous claims this system has a very simple, closed form solution which is the Dirac string potential multiplied by a exponential decaying part. Interesting features of this solution are discussed, namely, (i) the Dirac string becomes a real feature of the solution, (ii) the breaking of gauge symmetry via the photon mass leads to a breaking of the rotational symmetry of the monopole's magnetic field, (iii) the Dirac quantization condition is potentially altered.
We develop fluctuational electrodynamics for media with nonlinear optical response. In a perturbative manner, we amend the stochastic Helmholtz equation to describe fluctuations in a nonlinear setting, in agreement with the fluctuation dissipation theorem, and identify the local (Rytov) current fluctuations. We show how the linear response (the solution of the scattering problem) of a collection of objects is found from the individual responses, as measured in isolation. As an example, we compute the Casimir force acting between nonlinear objects which approaches the result for linear optics f…
We investigate some aspects of the Maxwell-Chern-Simons electrodynamics focusing on physical effects produced by the presence of stationary sources and a perfectly conducting plate (mirror). Specifically, in addition to point charges, we propose two new types of point-like sources called topological source and Dirac point, and we also consider physical effects in various configurations that involve them. We show that the Dirac point is the source of the vortex field configurations. The propagator of the gauge field due to the presence of a conducting plate and the interaction forces between th…
We develop fluctuational electrodynamics for media with nonlinear optical response in and out of thermal equilibrium. Starting from the stochastic nonlinear Helmholtz equation and using the fluctuation dissipation theorem, we obtain perturbatively a deterministic nonlinear Helmholtz equation for the average field, the physical linear response, as well as the fluctuations and Rytov currents. We show that the effects of nonlinear optics, in or out of thermal equilibrium, can be taken into account with an effective, system-aware dielectric function. We discuss the heat radiation of a planar, nonl…
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