Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics

A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral of a family of self-adjoint operators acting in the Hilbert space , where is the Hilbert space of the quantum radiation field. The fiber operator is called the Hamiltonian of the Dirac polaron with total momentum . The main result of this paper is concerned with the non-relativistic (scaling) limit of . It is proven that the non-relativistic limit of yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics.     

Fiber Bundles in Non-relativistic Quantum Mechanics

The problem of describing a quantum mechanical system with symmetry by a fiber bundle is considered. The quantization of a fiber bundle is introduced. Fiber bundles for the Kepler problem and the rotator are constructed. The fiber bundle concept provides a new model for a physical system: it provides us with a model for an elementary particle with extension having integral values of spin.     

Quantum Electrodynamics in Solids

A quantum field theoretical treatment of electromagnetic fields in solid is presented. The photon propagator is obtained when the current-current correlation function is given. From the relations among matrix elements which are a consequence of the local gauge invariance of the theory, the classical Maxwell equations are derived by means of the boson transformation which is the mathematical realization of a boson condensation. The relation of the microscopic functions to the phenomenological quantities is presented.     

Pre-Maxwell Quantum Electrodynamics

In the framework of off-shell quantum electrodynamics—the quantum field theory of a covariant symplectic mechanics, in which events evolve according to a Poincaré-invariant parameter —we study the low-energy scattering of identical scalar particles. It is shown that exchange of mass is permitted in the formalism, and we calculate scattering cross-sections for this case. In these cross-sections, the usual forward pole of the standard scalar QED splits into two poles and a zero, slightly offset from the forward direction. As mass exchange vanishes, a pole-zero pair cancel, the remaining pole moves to = 0, and the standard cross-section is recovered.     

Quantum Parity Conservation in Planar Quantum Electrodynamics

International Journal of Theoretical Physics - Quantum parity conservation is verified at all orders in perturbation theory for a massless parity-even U(1) × U(1) planar quantum...     

Field Equations in Quantum Electrodynamics

A formulation of quantum electrodynamics is presented, based on finite local field equations. These Dirac and Maxwell equations have the usual form except that the current operators f(x) and j^μ (x) are explicitly expressed as local limits of sums of non-local field products and suitable subtraction terms. These limits are shown to exist and to yield finite operators in the sense that the iterative solutions to the field equations are equivalent to conventional renormalized perturbation theory. The various invariance properties of the theory, including Lorentz invariance, gauge invariance, charge conjugation invariance, and renormalization invariance, are discussed and related directly to the field equations and current definitions. Initially only the general forms of the currents, based on dimensional arguments, are given. The electric current, for example, contains the (suitably defined) term :A³(x) :.The corresponding field equations are used to derive renormalized Dyson-Schwinger-type integral equations for the renormalized proper part functions ∑, II^μν, Λ^μ, and X^αβγδ (the four-photon vertex function), etc. Application of the boundary conditions ∑(p̀ = m) = ∑′(p̀ = m) = II(O) = II′(O) = II″(O) = Λ(p̀ = m, o) = X(O, O, O, O) = O completely specifies the current operators. Consistency is established by deriving the same equations from rigorous renormalization theory so that their iterative solutions are proved to reproduce the correct renormalized perturbation expansion. The electric current operator is exhibited in a manifestly gauge invariant form and in a form which is manifestly negative under charge conjugation. It is shown, in fact, that much of j^μ (x) can be determined directly from the requirements of gauge invariance and charge conjugation covariance, without recourse to the integral equations. It is suggested that equal time commutation relations can serve to similarly specify the rest of the current.     

Vacuum Energy-Density in Quantum Electrodynamics

The vacuum energy-density in quantum electrodynamics is studied by renormalization group techniques as well as a diagrammatic analysis is carried out to investigate the dependence of on an ultraviolet cut-off as the latter is led to become large. The study corresponds to the situation of finite electrodynamics with the renormalized fine-structure constant α fixed in the sens of the renormalization group. In this case explicit statements about the problem at hand may be made. In passing a study of the so-called second Legendre transform method for electrodynamics is given in an appendix.     

Amplitude of Elastic Photon Scattering in Scalar Electrodynamics

In the present paper, the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field is calculated. The amplitude of elastic photon scattering in the field of an arbitrary plane electromagnetic wave is calculated by the method of dispersion relations. Special cases of the plane electromagnetic wave field are examined.     

Non-relativistic Quantum Theory at Finite Temperature

We propose the non-relativistic finite temperature quantum wave equations for a single particle and multiple particles. We give the relation between energy eigenvalues, eigenfunctions, transition frequency and temperature, and obtain some results: (1) when the degeneracies of two energy levels are same, the transition frequency between the two energy levels is unchanged when the temperature is changed. (2) When the degeneracies of two energy levels are different, the variance of transition frequency at two energy levels is direct proportion to temperature difference.     

Universal Quantum Cloning Machine in Circuit Quantum Electrodynamics

We propose a scheme for realizing the 1 → 2 universal quantum cloning machine （UQCM） with superconducting quantum interference device （SQUID） qubits in circuit quantum electrodynamics （circuit QED）. In this scheme, in order to implement UQCM, we only need phase shift gate operation on SQUID qubits and the Raman transitions. The cavity number we need is only one. Thus our scheme is simple and has advantages in the experimental realization. Furthermore, both the cavity and the SQUID qubits are virtually excited, so the decoherence can be neglected.     

Photon Decays in the Radiation-Dominated Universe: Scalar Electrodynamics

The effect of the creation of an arbitrary number of massive pairs by a photon in the spatially flat model of the radiation-dominated Universe is considered. The process added-up probability is calculated within the framework of scalar quantum electrodynamics conformally related to the metric of a curved spacetime. The rate of photon decay in the radiation-dominated universe as well as the mean number of the created particles have been found. Comparison of the rate of the pair creation in the photon decays with the rate of the pair creation in the photon-photon collisions which take place in the Minkowski spacetime has been carried out. The estimates having been made show the number density of the particles created in the processes of the photon decays in the radiation-dominated Universe to be by a factor of 10³⁰ higher than the number density of the particles created from the vacuum of the free scalar field by the gravitational background.     

Normalized Schwinger-Dyson equations in Quantum Electrodynamics

We obtain Schwinger-Dyson equations for the normalized two-point propagators in Quantum Electrodynamics. Exploiting the spectral representations of the Green functions, we deal with normalized quantities everywhere. The explicit form we obtain for the propagator equations allows for non-perturbative approaches.1 On leave from Instituto de Física, UNAM, Mexico.     

Stochastically and Intrinsically Extended Non-relativistic Quantum Particles

Stochastically and intrinsically extended non relativistic quantum particles are described by combining the ideas of a stochastic quantum theory and a quantum functional theory. The former relates the extension to imperfect real measurements while the latter considers it as intrinsic. Physical states, Positive-Operator-Valued measures connected to measurement, and propagators are given and discussed. The stochastic theory is sufficient when the bilocal field describing the particle has a product form.     

Vacuum Polarization in Self-Field Quantum Electrodynamics

We have evaluated analytically the vacuum polarization in a Coulomb field using the relativistic Dirac-Coulomb wave functions by a new method. The result is made finite by an appropriate choice of contour integrations and gives the standard result in the lowest order of iteration. We used the formalism of self-field quantum electrodynamics in the evaluation of the vacuum polarization which needs neither field quantization nor renormalization. There are no infrared or ultraviolet divergences.     

Quantum Electrodynamics of Atomic Resonances

A simple model of an atom interacting with the quantized electromagnetic field is studied. The atom has a finite mass m, finitely many excited states and an electric dipole moment, \({\vec{d}_0 = -\lambda_{0} \vec{d}}\), where \({\| d^{i}\| = 1, i = 1, 2, 3,}\) and \({\lambda_0}\) is proportional to the elementary electric charge. The interaction of the atom with the radiation field is described with the help of the Ritz Hamiltonian, \({-\vec{d}_0 \cdot \vec{E}}\), where \({\vec{E}}\) is the electric field, cut off at large frequencies. A mathematical study of the Lamb shift, the decay channels and the life times of the excited states of the atom is presented. It is rigorously proven that these quantities are analytic functions of the momentum \({\vec{p}}\) of the atom and of the coupling constant \({\lambda_0}\), provided \({\vert\vec{p} \vert < mc}\) and \({\vert \Im \vec{p} \vert}\) and \({\vert \lambda_{0} \vert}\) are sufficiently small. The proof relies on a somewhat novel inductive construction involving a sequence of ‘smooth Feshbach–Schur maps’ applied to a complex dilatation of the original Hamiltonian, which yields an algorithm for the calculation of resonance energies that converges super-exponentially fast.     

Triviality of Quantum Electrodynamics Revisited

Quantum electrodynamics is often considered to be a trivial theory.This is based on a number of evidences,both numerical and analytical.One of the strong indications for triviality of QED is the existence of the Landau pole for the running coupling.We show that by treating QED as the leading order approximation of an effective field theory and including the next-to-leading order corrections,the Landau pole is removed.We also analyze the cutoff dependence of the bare coupling at two-loop order and conclude that the conjecture,that for reasons of self-consistency,QED needs to be trivial is a mere artefact of the leading order approximation to the corresponding effective field theory.     

Higher-Order Kinetic Term for Controlling Photon Mass in Off-Shell Electrodynamics

In relativistic classical and quantum mechanics with Poincaré-invariant parameter, particle worldlines are traced out by the evolution of spacetime events. The formulation of a covariant canonical framework for the evolving events leads to a dynamical theory in which mass conservation is demoted from a priori constraint to the status of conserved Noether current for a certain class of interactions. 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 two opposite physical domains: the low energy motion of a charged event in classical Coulomb scattering, and the renormalization of off-shell quantum electrodynamics. In this paper, we discuss a nonlocal, higher derivative correction to the photon kinetic term, which provides regulation of the photon mass in a manner which preserves the gauge invariance and Poincaré covariance of the original theory. We demonstrate that the inclusion of this term is equivalent to an earlier solution to the classical Coulomb problem, and that the resulting quantum field theory is renormalized.     

Bound States in the Quantum Scalar Electrodynamics

The next relativistic correction to α to for bound state mass of two charged scalar particles is calculated in the quantum scalar electrodynamics by the functional integral method. Contribution of the “nonphysical” time variable turned out to be important and leads to nonanalytic dependence of the bound state mass on α.     

Generalized Uncertainty Principle and Quantum Electrodynamics

In the present work the role that a generalized uncertainty principle could play in the quantization of the electromagnetic field is analyzed. It will be shown that we may speak of a Fock space, a result that implies that the concept of photon is properly defined. Nevertheless, in this new context the creation and annihilation operators become a function of the new term that modifies the Heisenberg algebra, and hence the Hamiltonian is not anymore diagonal in the occupation number representation. Additionally, we show the changes that the energy expectation value suffers as result of the presence of an extra term in the uncertainty principle. The existence of a deformed dispersion relation is also proved.