Dynamical mapping method in nonrelativistic models of quantum field theory

The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, \Theta$ model are obtained in the frameworks of dynamical mapping method. The equivalence of different types of dynamical mapping is shown. The connection between renormalization procedure and theory of selfadjoint extensions is elucidated.Comment: 14 page

Renormalized Electron Mass in Nonrelativistic QED

Within the framework of nonrelativistic QED, we prove that, for small values of the coupling constant, the energy function, E_|P|, of a dressed electron is twice differentiable in the momentum P in a neighborhood of P = 0. Furthermore, (E_|P|)" is bounded from below by a constant larger than zero. Our results are proven with the help of iterative analytic perturbation theory

Evidence from the Special Relativity and Blackbody Radiation Theories for the Existence of Photons Possessing Zero Kinetic Energy

The traditional interpretation of radiative emission and absorption asserts that photons are created and annihilated in such processes. A Gedanken experiment is considered in which kinetic energy from observed photons is systematically removed until a limit of zero is reached. With the help of the relativistic Doppler effect it is shown that even for infinitesimally small kinetic energies the photons continue to exist, since in other inertial systems they will be observed to have a much higher energy/frequency falling in an easily detectable range. It is possible to formulate an alternative explanation for absorption and emission processes on this basis in terms of real photons with exactly zero kinetic energy being present before or after radiative interactions. Bolstering this hypothesis is the fact that the statistical mechanical treatment of photons interacting with oscillators in blackbody radiation theory predicts an infinite density of photons of this energy, both in the original Planck formulation employing Maxwell-Boltzmann statistics and in the subsequent Bose-Einstein description. These considerations demonstrate that the E = 0 state is greatly preferred as the product of absorption because of the requirement to have the interaction occur in a relatively narrow region of space- time. There is thus strong evidence that photons are not created and annihilated in radiative processes but simply have their kinetic energy changed either to or from a zero value. Accordingly a very high density of zero-energy photons is expected to exist uniformly throughout the universe. Finally, this development suggests that one should subject the creation-annihilation hypothesis to careful scrutiny in other areas of physics as well.Comment: 26 pages, 2 figure

Regularizing Property of the Maximal Acceleration Principle in Quantum Field Theory

It is shown that the introduction of an upper limit to the proper acceleration of a particle can smooth the problem of ultraviolet divergencies in local quantum field theory. For this aim, the classical model of a relativistic particle with maximal proper acceleration is quantized canonically by making use of the generalized Hamiltonian formalism developed by Dirac. The equations for the wave function are treated as the dynamical equations for the corresponding quantum field. Using the Green's function connected to these wave equations as propagators in the Feynman integrals leads to an essential improvement of their convergence properties.Comment: 9 pages, REVTeX, no figures, no table

Higher Order Processes in Electromagnetic Production of Electron Positron Pairs in Relativistic Heavy Ion Collisions

We study higher-order effects in the electromagnetic production of electron-positron pairs in relativistic heavy ion collisions. Treating the field of the heavy ions as an external field and neglecting the interaction among electrons and positrons, we show that the $N$-pair creation amplitude is the antisymmetrised product of $N$ one-pair creation amplitudes and the vacuum amplitude. Neglecting contributions coming from exchange terms, we show that the total probability for $N$ pairs is approximately a Poisson distribution. We investigate further the structure of the reduced one-pair amplitude, concentrating especially on multiple-particle corrections. We calculate the first of these corrections in second order Magnus theory based on our previous result in second-order Born approximation for impact parameter $b$ zero. Explicit calculations show that the total probability is increased up to 10 \% by this correction for realistic collider parameters. The calculations can also be used to confirm the use of the Poisson distribution for the total probability.Comment: 29 pages RevTeX and 12 uuencoded figures (compressed postscript

Coupled-Cluster Approach to Electron Correlations in the Two-Dimensional Hubbard Model

We have studied electron correlations in the doped two-dimensional (2D) Hubbard model by using the coupled-cluster method (CCM) to investigate whether or not the method can be applied to correct the independent particle approximations actually used in ab-initio band calculations. The double excitation version of the CCM, implemented using the approximate coupled pair (ACP) method, account for most of the correlation energies of the 2D Hubbard model in the weak ($U/t \simeq 1$) and the intermediate $U/t$ regions ($U/t \simeq 4$). The error is always less than 1% there. The ACP approximation gets less accurate for large $U/t$ ($U/t \simeq 8$) and/or near half-filling. Further incorporation of electron correlation effects is necessary in this region. The accuracy does not depend on the system size and the gap between the lowest unoccupied level and the highest occupied level due to the finite size effect. Hence, the CCM may be favorably applied to ab-initio band calculations on metals as well as semiconductors and insulators.Comment: RevTeX3.0, 4 pages, 4 figure

Self-consistent solution of the Schwinger-Dyson equations for the nucleon and meson propagators

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagator and bare nucleon-meson vertices. It is known that such an approximation scheme produces the appearance of ghost poles in the propagators. In this paper the coupled system of Schwinger-Dyson equations for the nucleon and the meson propagators are solved self-consistently including vertex corrections. The interplay of self-consistency and vertex corrections on the ghosts problem is investigated. It is found that the self-consistency does not affect significantly the spectral properties of the propagators. In particular, it does not affect the appearance of the ghost poles in the propagators.Comment: REVTEX, 7 figures (available upon request), IFT-P.037/93, DOE/ER/40427-12-N9

Generalizations of normal ordering and applications to quantization in classical backgrounds

A nonlocal method of extracting the positive (or the negative) frequency part of a field, based on knowledge of a 2-point function, leads to certain natural generalizations of the normal ordering of quantum fields in classical gravitational and electromagnetic backgrounds and illuminates the origin of the recently discovered nonlocalities related to a local description of particles. A local description of particle creation by gravitational backgrounds is given, with emphasis on the case of black-hole evaporation. The formalism reveals a previously hidden relation between various definitions of the particle current and those of the energy-momentum tensor. The implications to particle creation by classical backgrounds, as well as to the relation between vacuum energy, dark matter, and cosmological constant, are discussed.Comment: 17 pages, revised, title shortened, to appear in Gen. Rel. Gra

Boson-fermion unification, superstrings, and Bohmian mechanics

Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an objective definition of particles makes the Bohmian interpretation of particle quantum mechanics more appealing. The superstring current allows a consistent Bohmian interpretation of superstrings themselves, including a Bohmian description of string creation and destruction in terms of string splitting. The Bohmian equations of motion and the corresponding probabilistic predictions are fully relativistic covariant and do not depend on the preferred foliation.Comment: 30 pages, 1 figure, revised, to appear in Found. Phy

Physics and the measurement of continuous variables

Wigner had expressed the opinion that the impossibility of exact measurements of single operators like position operators rendered the notion of geometrical points somewhat dubious in physics. Using Sewell's recent resolution of the measurement problem (collapse of the wave packet) in quantum mechanics and extending it to the measurement of operators with continuous spectra, we are able to compare the situation in quantum mechanics with that in quantum mechanics. Our conclusion is that the notion of a geometrical point is as meaningful in quantum mechanics as it is in classical mechanics.Comment: 20 page