Quantum electrodynamic perturbation theory based on electrodynamics with an external field

A method is proposed for construction of mean values of quantum quantities in quantum optics and electrodynamics on the basis of exact solutions of the corresponding problems of electrodynamics with an external field. To illustrate the method the mean energy of a two-level atom in the Raby problem is calculated. It is shown that the mean value obtained with a specified accuracy coincides with the result of exact quantum electrodynamic calculation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–10, September, 1983.     

Operator representation of the wave function for a charged particle in an external field and its applications

A consistent derivation of the operator form for the solution of the wave equation for a charged particle in an arbitrary external electromagnetic field is presented. The expressions obtained can be used for solving any problems in quantum electrodynamics in external fields in the framework of the semiclassical operator method. The peculiarities of the application of this method are demonstrated for the small-angle elastic scattering of a high-energy photon in an arbitrary localized electric field. The problem is solved for the first time without presuming the central symmetry of the external field potential.     

Particles and events in classical off-shell electrodynamics

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 paratmeter τ, off-shell electrodynamics constitutes a dynamical theory of ppacetime events, interacting through five τ-dependent pre-Maxwell potentials. We present a straightforward solution of the classical equations of motion, for a test event traversing the field induced by a “fixed” event (an event moving uniformly along the time axis at a fixed point in space). This solution is seen to be unsatisfactory, and reveals the essential difficulties in the formalism at the classical levels. 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 classisical off-shell electrodynamics with the standard Maxwell theory. In this model, the “fixed” event induces a Yukawa-type potential, permitting a semiclassical identification of the pre-Maxwell time scale λ with the inverse mass of the intervening photon. Numerical solutions to the equations of motion are compared with the standard Maxwell solutions, and are seen to coincide when λ≳10⁻⁶ seconds, providing an initial estimate of this parameter. It is also demonstrated that the proposed model provides a natural interpretation for the photon mass cut-off required for the renormalizability of the off-shell quantum electrodynamics.     

On the Effective Metric for an Electromagnetic Wave Propagating in the Field of an Intense Laser Radiation

It is shown that in the nonlinear electrodynamics of vacuum, which is a corollary of quantum electrodynamics, a weak electromagnetic wave propagates in the field of an intense laser radiation as if this took place in some effective space-time whose metric tensor depends on the electric field of the laser radiation. The components of the metric vector of the effective space-time along the geodesic lines of which the rays of the weak electromagnetic wave propagate in the given case have been found. It is pointed out that this property may serve as a basis for observing the manifestations of the nonlinearity of the electrodynamics of vacuum.     

Coulombic quantum liquids in spin-1/2 pyrochlores

We develop a nonperturbative gauge mean field theory (gMFT) method to study a general effective spin-1/2 model for magnetism in rare earth pyrochlores. gMFT is based on a novel exact slave-particle formulation, and matches both the perturbative regime near the classical spin ice limit and the semiclassical approximation far from it. We show that the full phase diagram contains two exotic phases: a quantum spin liquid and a Coulombic ferromagnet, both of which support deconfined spinon excitations and emergent quantum electrodynamics. Phenomenological properties of these phases are discussed.     

Duality in Two Capacitively Coupled Layered Arrays of Ultrasmall Josephson Junctions

We consider the problem of two capacitively coupled Josephson junction arrays made of ultrasmall junctions. Each one of the arrays can be in the semiclassical or quantum regimes, depending on its physical parameter values. The former case is dominated by a Cooper-pair superfluid, while the quantum case is dominated by dynamic vortices leading to an insulating behavior. We first consider the limit when both arrays are in the semiclassical limit, and next the case when one array is quantum and the other semiclassical. We present WKB and mean-field theory results for the critical temperature of each array when both are in the semiclassical limit. When one array is in the semiclassical regime and the other one is in the quantum-fluctuations-dominated regime, we derive a duality transformation between the charge and vortex-dominated arrays that involves a gauge vector field which is proportional to the site coupling capacitance between the arrays. The system considered here has been fabricated and we make some predictions as to possible experimentally measurable quantities that could be compared with theory.     

Low-energy structures in strong field ionization revealed by quantum orbits

Experiments on atoms in intense laser pulses and the corresponding exact ab initio solutions of the time-dependent Schr?dinger equation (TDSE) yield photoelectron spectra with low-energy features that are not reproduced by the otherwise successful work horse of strong field laser physics: the "strong field approximation" (SFA). In the semiclassical limit, the SFA possesses an appealing interpretation in terms of interfering quantum trajectories. It is shown that a conceptually simple extension towards the inclusion of Coulomb effects yields very good agreement with exact TDSE results. Moreover, the Coulomb quantum orbits allow for a physically intuitive interpretation and detailed analysis of all low-energy features in the semiclassical regime, in particular, the recently discovered "low-energy structure" [C. I. Blaga, Nature Phys. 5, 335 (2009) and W. Quan, Phys. Rev. Lett. 103, 093001 (2009).     

Spreading of atomic wave packets and semiclassical chaos

The correspondence between the statistical properties of the evolution of a quantum system and Lyapunov instability and the chaos of its semiclassical analog has been demonstrated. The results of the analyses of atomic motion in a laser field in the semiclassical approximation (dynamics is described by several nonlinear equations) and without this approximation (dynamics is described by an infinite system of linear equations) are compared. In the ranges of the parameters for which the semiclassical dynamics of point-like atoms is unstable, the fast “spreading” of quantized wave packets in the momentum space is observed. Thus, deterministic chaos “imitates” the statistics of the quantum nondeterministic effects, although the semiclassical and quantum solutions are fundamentally different.     

Selected Problems of Relativistic Quantum Mechanics and Atomic Physics

The paper presents a brief review of the scientific work performed by the authors in the field of quantum mechanics and atomic, laser, and mathematical physics. The following problems are considered: the semiclassical theory of tunneling and multiphoton ionization of atoms and ions in a strong electromagnetic field; generalization of the Keldysh ionization theory to the relativistic case; calculation of the Coulomb corrections to the ionization rate of atoms for arbitrary values of the adiabaticity parameter γ: from γ ≪ 1 (the adiabatic region) to γ ≫ 1, when the laser field changes its direction and magnitude many times during the time of flight of the electron through the barrier; the Lorentz ionization of atoms moving in a constant magnetic field; the WKB approximation and the imaginary time method for describing electron tunneling through a time-varying barrier; the Stark effect in a strong field; the energy spectrum of a hydrogen atom in a strong and superstrong magnetic field; quantization with account of the barrier transparency; creation of electron-positron pairs from vacuum in a constant electric or intense pulsed (laser) field and the dependence of the number of pairs on the intensity and frequency of the laser field; the Feynman method of disentanglement of noncommuting operators and its applications: transitions between atomic states in an alternating magnetic field (the Majorana problem); a quantum oscillator with time-dependent frequency; and a singular oscillator. The mathematical problems of quantum mechanics are considered: the fall of a particle to the center; modification of the Bohr-Sommerfeld quantization condition for potentials with a barrier and the Kramers matching conditions; divergence of perturbation series and their summation; eigenvalues of the Casimir operators for irreducible representations of Lie groups, including the SU(2), SU(3), and SU(6) groups, which are widely used in physics.     

Generating functional for the average field in quantum electrodynamics with an unstable vacuum

The generating functional for calculating the average field in the case of an unstable vacuum in quantum field theory is proposed. A continuous representation is found for the generating functional of the average field in the case of quantum electrodynamics with an external field, generating electron-positron pairs out of the vacuum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 80–84, October, 1981.     

A Process Algebra Approach to Quantum Electrodynamics

The process algebra program is directed towards developing a realist model of quantum mechanics free of paradoxes, divergences and conceptual confusions. From this perspective, fundamental phenomena are viewed as emerging from primitive informational elements generated by processes. The process algebra has been shown to successfully reproduce scalar non-relativistic quantum mechanics (NRQM) without the usual paradoxes and dualities. NRQM appears as an effective theory which emerges under specific asymptotic limits. Space-time, scalar particle wave functions and the Born rule are all emergent in this framework. In this paper, the process algebra model is reviewed, extended to the relativistic setting, and then applied to the problem of electrodynamics. A semiclassical version is presented in which a Minkowski-like space-time emerges as well as a vector potential that is discrete and photon-like at small scales and near-continuous and wave-like at large scales. QED is viewed as an effective theory at small scales while Maxwell theory becomes an effective theory at large scales. The process algebra version of quantum electrodynamics is intuitive and realist, free from divergences and eliminates the distinction between particle, field and wave. Computations are carried out using the configuration space process covering map, although the connection to second quantization has not been fully explored.     

Light intensification towards the Schwinger limit

A method to generate ultrahigh intense electromagnetic fields is suggested, based on the laser pulse compression, carrier frequency upshift, and focusing by a counterpropagating breaking plasma wave, relativistic flying parabolic mirror. This method allows us to achieve the quantum electrodynamics critical field (Schwinger limit) with present-day laser systems.     

二维椭圆量子台球中的谱分析

研究了二维椭圆台球中的量子谱和经典轨道之间的对应关系.为尝试求解没有解析波函数和本征能量又不能分离变量的体系，采用了定态展开方法(expansion method for stationary states，简称EMSS)得到尽可能精确的数值解，这是闭合轨道理论被推广到计算开轨道的情况.比较了傅里叶变换谱和经典轨道，发现量子谱的峰位置与经典轨道的长度在可分辨的范围内符合得很好，这是半经典理论为经典与量子力学的联系提供桥梁作用的又一个例子. 关键词： 椭圆量子台球 定态展开方法 闭合轨道理论 量子谱     

Radiation of an electron in an electric field. II

By the methods of quantum electrodynamics, the radiation of an electron moving in the field of a traveling electric wave is considered. It is shown that, in contrast to the classical case, the result given by quantum theory for the spectral-angular distribution of the radiant energy differs from the corresponding expression for an electron in a constant homogeneous electric field, even in the terms proportional to Planck's constant.Translated from Izvestiya Vysshikh Uchbenykh Zavedenii, Fizika, No. 6, pp. 92–98, June, 1976.In conclusion, the authors thank V. G. Bagrov, D. M. Gitman, and Sh. M. Shvartsmau for their interest in the work and for useful discussions.     

Renormalization of QED in an external field

The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these equations are given in terms of appropriate Feynman diagrams. The Green function that is used as an electron propagator in each case is discussed in detail. The general renormalization rules for each of the three equations are provided both in a non perturbative way (Dyson relations) and for Feynman diagrams.     

Field ionization of Rydberg atoms: A semiclassical treatment of complex energy states in intense electric fields

The semiclassical treatment of energy levels and lifetimes of hydrogenic atoms in a homogeneous electric field is discussed. Particular attention is payed to the critical regime of intense fields or high quantum number (Rydberg) states of the atom, where the ionization is fast. An extension of the real-energy resonant-state treatment to a complex-valued (Siegert-type) semiclassical approximation is derived, which is both conceptually and computationally convenient.     

1/c expansion of bound-state energies in QED

A new method for calculating bound-state energies in quantum electrodynamics is proposed. It starts from a non-relativistic Schrödinger equation as a zeroth approximation and treats the relativistic corrections by a systematic expansion. The result is expressed as a sum over Feynman-like graphs. No relativistic bound-state equations are used. Only the case of positronium is considered explicitly, but the method generalizes easily to other cases.     

Prequantum Classical Statistical Field Theory: Schrödinger Dynamics of Entangled Systems as a Classical Stochastic Process

The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) classical random field. Quantum averages can be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger’s equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The “effect of entanglement” is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein.