An evolution operator in semiclassical electrodynamics

An evolution operatior is described, which acts on the operators of a problem to take it into the solutions of the corresponding problem of semiclassical electrodynamics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 66–69, November, 1981.     

Method of semiclassical representation in quantum electrodynamics

The operators of the classical amplitudes of an electromagnetic field are introduced and a method of transferring from quantum electrodynamics to the semiclassical approximation both in the case of a free field and in the case of the interaction of the field with a quantum system is given. The method considered enables one to set up solutions of quantum electrodynamics in the case of an intense field from the solutions of the semiclassical problem. An operator method of obtaining solutions of the equations of semiclassical electrodynamics is considered. The physical meaning of the quantum corrections to the semiclassical electrodynamics of an intense field is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 77–98, February, 1980.     

Scaling behavior of semiclassical gravity

Using the idea of metric scaling we examine the scaling behavior of the stress tensor of a scalar quantum field in curved space-time. The renormalization of the stress tensor results in a departure from naive scaling. We view the process of renormalizing the stress tensor as being equivalent to renormalizing the coupling constants in the Lagrangian for gravity (with terms quadratic in the curvature included). Thus the scaling of the stress tensor is interpreted as a nonnaive scaling of these coupling constants. In particular, we find that the cosmological constant and the gravitational constant approach UV fixed points. The constants associated with the terms which are quadratic in the curvature logarithmically diverge. This suggests that quantum gravity is asymptotically scale invariant.     

A semiclassical model for quark jet fragmentation

A semiclassical model is presented for the way the energy of a fast quark is transformed into observable hadrons. It reproduces the features of 1+1 dimensional QED (the Schwinger model) concerning a flat rapidity distribution in the central region. It also reproduces results from phenomenological considerations, which, based upon scaling, predict that meson formation in the fragmentation region can be described by an iterative scheme, implying a set of coupled integral equations. In particular the model predicts that the probability to find a meson containing the leading quark is independent of the Feynman scaling variablez. The iterative structure corresponds to a Brownian motion with relevance both to the confinement problems and to the distribution of mass in the quark jet.     

Parametric instability and Hamiltonian chaos in cavity semiclassical electrodynamics

We study the nonlinear dynamics of the interaction of two-level atoms and a selected mode of a high-Q cavity with frequency modulation analytically and numerically. In the absence of modulation, the corresponding semiclassical Heisenberg equations for the expectation values of the collective atomic observables and the field-mode amplitudes allow, in the rotating wave approximation and in the strong-coupling limit, an exact solution with arbitrary detuning. Using this solution, we detect the coherent effect of trapping of the population of atomic levels and of trapping of the number of photons in the cavity. The explanation for this effect lies in the destructive interference of the atomic dipoles and the field mode. The integrable version of the system of equations exhibits a separatrix near which a stochastic layer is formed when modulation is introduced. The width of the layer is found to gradually increase with degree of modulation, and finally it fills the entire energy-permissible volume of the phase space. We show that the rotating wave approximation does not hinder the formation of Hamiltonian chaos in cavity semiclassical electrodynamics. The calculation of the maximum Lyapunov indices of nonlinear (in this approximation) equations of motion as functions of the modulation frequency δ and the frequency of natural Rabi oscillations of the atom-field system, Ω, suggests that Hamiltonian chaos appears first in the area of the fundamental parametric resonance, δ/2Ω≃1. Parametric instability increases with increasing modulation and decreasing detuning from the atom-field resonance, generating at exact resonance new areas of chaos corresponding to multiple parametric resonances. The results of numerical experiments and estimates of the characteristic parameters show that Rydberg atoms placed in a high-Q microwave cavity are possible objects for observing parametric instability and dynamical chaos. Zh. éksp. Teor. Fiz. 115, 740–753 (February 1999)     

Semiclassical states in loop quantum gravity: an introduction

Unifying general relativity and quantum mechanics is a great challenge left to us by Einstein. To face this challenge, considerable progress has been made in non-perturbative canonical (loop) quantum gravity during the past 20 years. The kinematical Hilbert space of the quantum theory is constructed rigorously. However, the semiclassical analysis of the theory is still a crucial and open issue. In this review, we first introduce our work on constructing a semiclassical weave state, using the [ω] operator on the kinematical Hilbert space of loop quantum gravity. Then we give an introduction to the two different approaches currently investigated for constructing coherent states in the kinematical Hilbert space. The current status of semiclassical analysis in loop quantum gravity is then summarized.     

A model of nonlinear electrodynamics

A new model of nonlinear electrodynamics with two parameters is investigated. We also consider a model with one dimensional parameter. It was shown that the electric field of a point-like charge is not singular at the origin and there is the finiteness of the static electric energy of point-like charged particle. We obtain the canonical and symmetrical Belinfante energy–momentum tensors and dilatation currents. It is demonstrated that the dilatation symmetry and dual symmetry are broken in the models suggested. We have calculated the static electric energy of point-like particles.     

Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at “quantum scales” and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a “semiclassical” state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity.     

Instability of flat spacetime in semiclassical gravity

The semiclassical theory of gravity is considered in which an asymptotically flat background metric is coupled to quantized matter. We show that, in general, there are modes with spacelike wave vectors for small metric fluctuations around flat spacetime. Besides the usual axioms of quantum field theory in flat spacetime, the proof rests on the existence of a hard trace anomaly in the energy-momentum tensor due to matter self-couplings. Two possible interpretations of the result are discussed.     

A new semiclassical elementary particle model

A semiclassical model in which elementary particles are represented as systems of charged shells with associated quark-like quantum numbers is presented. Specifically the baryons are considered. Formulas are obtained which express baryon masses and magnetic moments in terms of model parameters which relate baryon and quark properties. Basically, the mass and moment formulas are expressions for mass ratios and magnetic moment ratios. Simple identifications for the model parameters lead to a prediction for the proton-electron mass ratio and to fairly accurate predictions for the baryon magnetic moments in units of the proton moment. The mass and moment formulas, which relate corresponding properties of different particles, are generalised such as to express relationships between the members of a sequence of particles, where such a sequence is conceived of as containing only one (normal) baryon. A specific sequence, containing the proton and electron, is proposed; various physical properties of the particles in the sequence are determined. In particular, a second prediction for the proton-electron mass ratio is obtained; the two predictions differ numerically but both agree with the measured value of the mass ratio within experimental error.