49 research outputs found
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 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 -pair creation amplitude is
the antisymmetrised product of one-pair creation amplitudes and the vacuum
amplitude. Neglecting contributions coming from exchange terms, we show that
the total probability for 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 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 () and the intermediate regions (). The error is always less than 1% there. The ACP approximation gets
less accurate for large () 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