Correlation theory of quantized electromagnetic field I

A correlation matrix is defined which describes arbitrary order correlation effects of the electromagnetic field. Dynamical equations are derived which govern the space-time development of the correlation matrix of the quantized electromagnetic field in vacuo. With the help of these equations, propagation laws and non-linear conservation laws for the correlation matrix are obtained.The author wishes to thank Dr. J. Peina for stimulating discussions.     

Ionization in a quantized electromagnetic field

An analytical expression for a matrix element of the transition from a bound state of an electron in an atom to continuum states is obtained by solving the problem of interaction of the electron with a quantized electromagnetic field. This expression is used to derive formulas for the photoelectron spectrum and the rate of ionization of the simplest model atomic system upon absorption of an arbitrary number of photons. The expressions derived are analyzed and compared with the corresponding relationships obtained via other approaches. It is demonstrated that there are differences as compared to the case of the classical field. In particular, the photoelectron spectrum exhibits dips due to the destructive interference of the transition amplitudes in the quantized electromagnetic field.     

Thermodynamics of a quantized electromagnetic field in absorbing media

Because induced emission is an incoherent phenomenon, it is impossible to represent the Gibbs thermodynamic potential of a quantized electromagnetic field in an absorbing medium in terms of the standard refractive index with an imaginary component. This is completely true with respect to the entropy of the electromagnetic field, the heat capacity, and the state equation, as well as to the stationary ponderomotive forces. The so-called causal refractive index arises in the theory, which differs from the standard refractive index in the analytical properties. The ideality condition of the photon gas in dissipative media does not hold without using the causal refractive index. The Kirchhoff law holds true only if the causal refractive index negligibly differs from unity.     

Electron in the field of a plane quantized monochromatic electromagnetic wave

An exact solution of the Dirac equation is found for an electron moving in the field of a plane quantized monochromatic electromagnetic wave of arbitrary polarization.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 55–58, August, 1973.     

Mesoscopic Josephson junctions in the presence of two-mode quantized electromagnetic field

Dynamic behavior of a mesoscopic Josephson junction in the presence of a two-mode quantized electromagnetic field is investigated. It is shown that the currentvoltage- step structures depend apparently on the two basic frequencies of the two-mode field. The voltage jumps are generally not equidistant. It is also shown that for the correlated two-mode squeezed state the time evolution of the supercurrent exhibits quantum collapse and revival(CR) phenomenon, while for the noncorrelated two-mode coherent state the phenomenon does not occur.     

Thermal fluctuations of a quantized electromagnetic field in weakly absorbing media

The quantum fluctuations of an electromagnetic field in thermally excited media are calculated using the quantum electrodynamical method of Γ operators and without invoking phenomenological elements. The drawbacks of the standard theory based on the fluctuation-dissipation theorem and on the Matsubara technique of temperature Green’s functions are indicated. The decisive role of the correct consideration of higher order photon-photon correlators and the inadmissibility of their approximation by products of lower order correlators are underlined. It is shown that, contrary to the accepted opinion, the quantum fluctuations of an electromagnetic field cannot be expressed via the refractive indices of media introduced into the theory for the calculation of mean fields. The results obtained are compared with those previously derived using the Matsubara technique for calculation of the Green’s functions of an electromagnetic field in dispersive media under conditions of thermodynamic equilibrium. The previous results are shown to be incorrect at least for media consisting of atoms or molecules with a discrete energy spectrum.     

An equal-time quantized field theory on the light cone

Semileptonic decays of polarized τ leptons are investigated and the most general angular distribution of two and three meson final states is derived. Emphasis is put on τ studies in electron positron annihilation where the neutrino escapes detection and the τ restframe cannot be reconstructed. It is shown that the most general distribution can be characterized by 16 structure functions, most of which can be determined in currently ongoing high statistics experiments. Of particular interest for the three meson case are the distribution of the normal to the Dalitz plane and the distribution around this normal. Predictions for the structure functions are given for the two and three pion case and forK ^*(→Kπ). Implications for an experiment where the τ restframe could be reconstructed are also considered.     

A topological theory of the electromagnetic field

It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field which represents a map S ³×RS ² and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf index equal to the linking number of any pair of magnetic lines. This allows the classification of the electromagnetic fields into homotopy classes, labeled by the value of the helicity. Although the model makes use of only c-number fields, the helicity always verifies A·Bd³ r=n, n being an integer and an action constant, which necessarily appears in the theory, because of reasons of dimensionality.     

A new look at electromagnetic field theory

The most general expression of electromagnetic theory is examined in the light of (1) Faraday's interpretation of the field as a potentiality for the force of charged matter to act upon a test body, and (2) Einstein's view of the field equations as an example of a covariant expression of special relativity. Faraday's original interpretation, in which all physical variables must be expressible as nonsingular fields, implies a particular generalization of the standard forms of the conservation equations and leads to a removal of the problem of the infinite self-energy of point sources. A further generalization of the mathematical expression of electromagnetism occurs when it is asserted that the form of the laws must be compatible with the symmetry requirements of the irreducible representations of the Poincaré group. This yields a factorization of the vector field equations, giving a set of two uncoupled two-component spinor equations. It is shown that the latter lead to twice as many conservation equations for electromagnetism, compared with the vector formalism, thus making extra predictions that are not made in the latter formalism. It is shown that the extra conservation equations reveal themselves only when incorporating the requirements of Faraday's interpretation of the field solutions.     

The casimir effect as a screening effect in quantized field theory

We study the vacuum energy and the vacuum force in a system of quantized scalar fields (massive and massless) in interaction with a given screening medium. Regularization of the energy is studied and the types of determinable forces are clarified. The Casimir effect—the attraction between two conducting plates in a vacuum, and its extension to different geometries —is re-examined in this framework. Instead of the puzzling repulsion for a spherical shell conductor, an attractive force is obtained in our case. As a by-product, we obtain a potential energy between two balls of large screening power and at remote distance R, ?a₁a₂/4πR³, where a_i are the ball radii.     

Charge symmetry of wave functions for an electron in a quantized electromagnetic wave field

The violation of charge symmetry in the known [1] wave functions for an electron in a quantized wave field is considered. An attempt is made to modify the equations and to construct solutions free of this deficiency.     

Boundedness of electromagnetic form factors in field theory

Asymptotically free non-abelian gauge theories of strong interaction predict that (electro-) magnetic form factors remain (at worst) bounded at large momentum transfer. This property is also discussed in general renormalizable field theories.     

Scattering theory for a model of an atom in a quantized field

We compute the scattering operator for a simplified model of an atom interacting a with a quantized field. The field is restricted to the vacuum and one-particle sectors, and the atom has only two states. We also solve the inverse scattering problem for the same model. The methods used rely on the particular form of the interaction, which is chosen to mimic the interaction between radiation and matter.This work was partially supported by NSF Grant DMS-8922941.     

Entangling two uncoupled flux qubits via their sequential interaction with a quantized electromagnetic field

A theoretical scheme for the generation of maximally entangled states of two superconducting flux qubits via their sequential interaction with a monochromatic quantum field is presented. The coupling of the qubits with the quantized field can be tuned on and off resonance by modulating the effective Josephson energy of each qubit via an externally applied magnetic flux. The system operates in such a way as to transfer the entanglement from a bipartite field-qubit subsystem to the two qubits. This scheme is attractive in view of the implementation of practical quantum processing systems.     

Second quantized quaternion quantum theory

The basic structure of a second quantized relativistic quantum theory is outlined. The vector space is over the ring of complex quaternions instead of the usual field of complex numbers. This is motivated by the simple quaternion structure of the Dirac equation.