395 research outputs found
I. The Isotopic Foldy-Wouthuysen Representation and Chiral Symmetry
The paper introduces the isotopic Foldy-Wouthuysen representation. This
representation was used to derive equations for massive interacting fermion
fields. When the interaction Hamiltonian commutes with the matrix, these
equations possess chiral invariance irrespective of whether fermions have mass
or are massless. The isotopic Foldy-Wouthuysen representation preserves the
vector and axial currents irrespective of the fermion mass value. In the Dirac
representation, the axial current is preserved only for massless fermions. In
the isotopic Foldy-Wouthuysen representation, the ground state of fermions
(vacuum) turns out to be degenerate, and therefore there is the possibility of
spontaneously breaking parity (P - symmetry). This study considers the example
of constructing a chirally symmetric quantum electrodynamics framework in the
isotopic Foldy-Wouthuysen representation. A number of physical processes are
calculated in the lowest orders of the perturbation theory. Final results of
the calculations agree with the results of the standard quantum
electrodynamics.Comment: 37 pages, 9 figure
Semi-relativistic charge-current density operator
The charge-current density and two-photon operators consistent with a
single-particle semi-relativistic Hamiltonian are derived within a suitable
functional derivative formalism which preserves gauge invariance. An
application to electron scattering is presented and results are compared with a
fully relativistic case and the non-relativistic cases corrected through fourth
order in M^{-1}.Comment: 20 pages, 3 postscript figures, typos correcte
Signatures of the chiral two-pion exchange electromagnetic currents in the 2H and 3He photodisintegration reactions
The recently derived long-range two-pion exchange (TPE) contributions to the
nuclear current operator which appear at next-to-leading order (NLO) of the
chiral expansion are used to describe electromagnetic processes. We study their
role in the photodisintegration of 2H and 3He and compare our predictions with
experimental data. The bound and scattering states are calculated using five
different parametrizations of the chiral next-to-next-to-leading order (N2LO)
nucleon-nucleon (NN) potential which allows us to estimate the theoretical
uncertainty at a given order in the chiral expansion. For some observables the
results are very close to the predictions based on the AV18 NN potential and
the current operator (partly) consistent with this force. In the most cases,
the addition of long-range TPE currents improved the description of the
experimental data.Comment: 11 pages, 6 figures (35 eps files
On the Ground State of Electron Gases at Negative Compressibility
Two- and three-dimensional electron gases with a uniform neutralizing
background are studied at negative compressibility. Parametrized expressions
for the dielectric function are used to access this strong-coupling regime,
where the screened Coulomb potential becomes overall attractive for like
charges. Closely examining these expressions reveals that the ground state with
a periodic modulation of the charge density, albeit exponentially damped,
replaces the homogeneous one at positive compressibility. The wavevector
characterizing the new ground state depends on the density and is complex,
having a positive imaginary part, as does the homogeneous ground state, and
real part, as does the genuine charge density wave.Comment: 6 double-column pages, 2 figures. 2nd version is an extension of the
1st one, giving more detail
A new formulation of the effective theory for heavy particles
We derive the effective theories for heavy particles with a functional
integral approach by integrating away the states with high velocity and with
high virtuality. This formulation is non-perturbative and has a close
connection with the Wilson renormalization group transformation. The fixed
point hamiltonian of our transformation coincides with the static hamiltonian
and irrelevant operators can be identified with the usual corrections to
the static theory. No matching condition has to be imposed between the full and
the static theory operators with our approach. The values of the matching
constants come out as a dynamical effect of the renormalization group flow.Comment: 26 pages, plain Latex + 4 postscript figures (appended at the end),
Preprint Roma1 993-94 (some missing lines in a few formulas have been
restored; minor changes
Relativistic Operator Description of Photon Polarization
We present an operator approach to the description of photon polarization,
based on Wigner's concept of elementary relativistic systems. The theory of
unitary representations of the Poincare group, and of parity, are exploited to
construct spinlike operators acting on the polarization states of a photon at
each fixed energy momentum. The nontrivial topological features of these
representations relevant for massless particles, and the departures from the
treatment of massive finite spin representations, are highlighted and
addressed.Comment: Revtex 9 page
Multicomponent dense electron gas as a model of Si MOSFET
We solve two-dimensional model of -component dense electron gas in the
limit of large and in a range of the Coulomb interaction parameter:
. The quasiparticle interaction on the Fermi circle
vanishes as 1/N. The ground state energy and the effective mass are found as
series in powers of . In the quantum Hall state on the lowest Landau
level at integer filling: , the charge activation energy gap and the
exchange constant are found.Comment: 10 pages, 4 figure
Radiative transitions of high energy neutrino in dense matter
The quantum theory of the ``spin light'' (electromagnetic radiation emitted
by a massive neutrino propagating in dense matter due to the weak interaction
of a neutrino with background fermions) is developed. In contrast to the
Cherenkov radiation, this effect does not disappear even if the medium
refractive index is assumed to be equal to unity. The formulas for the
transition rate and the total radiation power are obtained. It is found out
that radiation of photons is possible only when the sign of the particle
helicity is opposite to that of the effective potential describing the
interaction of a neutrino (antineutrino) with the background medium. Due to the
radiative self-polarization the radiating particle can change its helicity. As
a result, the active left-handed polarized neutrino (right-handed polarized
antineutrino) converting to the state with inverse helicity can become
practically ``sterile''. Since the sign of the effective potential depends on
the neutrino flavor and the matter structure, the ``spin light'' can change a
ratio of active neutrinos of different flavors. In the ultra relativistic
approach, the radiated photons averaged energy is equal to one third of the
initial neutrino energy, and two thirds of the energy are carried out by the
final ``sterile'' neutrinos. This fact can be important for the understanding
of the ``dark matter'' formation mechanism on the early stages of evolution of
the Universe.Comment: 7 pages, latex, one misprint in eq. 12 correcte
Exact Foldy-Wouthuysen transformation for spin 0 particle in curved space
Up to now, the only known exact Foldy- Wouthuysen transformation (FWT) in
curved space is that concerning Dirac particles coupled to static spacetime
metrics. Here we construct the exact FWT related to a real spin-0 particle for
the aforementioned spacetimes. This exact transformation exists independently
of the value of the coupling between the scalar field and gravity. Moreover,
the gravitational Darwin term written for the conformal coupling is one third
of the relevant term in the fermionic case.Comment: 10 pages, revtex, improved version to appear in Phys. Rev.
Effective Hamiltonians with Relativistic Corrections I: The Foldy--Wouthuysen transformation versus the direct Pauli reduction
Two different methods of obtaining ``effective Hamiltonians''
which include relativistic corrections to nonrelativistic calculations are
discussed, the standard Foldy--Wouthuysen transformation and what we call the
``direct Pauli reduction''. We wish to investigate under which circumstances
the two approaches yield the same result. Using a generic interaction with
harmonic time dependence we show that differences in the corresponding
effective S--matrices do arise beyond first--order perturbation theory. We
attribute them to the fact that the use of the direct reduction effective
Hamiltonian involves the additional approximation of neglecting contributions
from the negative--energy intermediate states, an approximation which is
unnecessary in the Foldy--Wouthuysen case as there the Hamiltonian
does not connect positive-- and negative--energy states. We conclude that at
least in the cases where the relativistic Hamiltonian is known, using the
direct Pauli reduction effective Hamiltonian introduces spurious relativistic
effects and therefore the Foldy--Wouthuysen reduction should be preferred.Comment: TRIUMF preprint TRI-PP-93-1
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