152 research outputs found
Self-amplified Cherenkov radiation from a relativistic electron in a waveguide partially filled with a laminated material
The radiation from a relativistic electron uniformly moving along the axis of
cylindrical waveguide filled with laminated material of finite length is
investigated. Expressions for the spectral distribution of radiation passing
throw the transverse section of waveguide at large distances from the laminated
material are derived with no limitations on the amplitude and variation profile
of the layered medium permittivity and permeability. Numerical results for
layered material consisting of dielectric plates alternated with vacuum gaps
are given. It is shown that at a special choice of problem parameters,
Cherenkov radiation generated by the relativistic electron inside the plates is
self-amplified. The visual explanation of this effect is given and a possible
application is discussed.Comment: 8 pages, 4 figures,1 table, the paper is accepted for publication in
the Journal of Physics: Conference Serie
The Path Integral Quantization And The Construction Of The S-matrix In The Abelian And Non-Abelian Chern-Simons Theories
The cvariant path integral quantization of the theory of the scalar and
spinor particles interacting through the abelian and non-Abelian Chern-Simons
gauge fields is carried out and is shown to be mathematically ill defined due
to the absence of the transverse components of these gauge fields. This is
remedied by the introduction of the Maxwell or the Maxwell-type (in the
non-Abelian case)term which makes the theory superrenormalizable and guarantees
its gauge-invariant regularization and renormalization. The generating
functionals are constructed and shown to be formally the same as those of QED
(or QCD) in 2+1 dimensions with the substitution of the Chern-Simons propagator
for the photon (gluon) propagator. By constructing the propagator in the
general case, the existence of two limits; pure Chern-Simons and QED (QCD)
after renormalization is demonstrated.
By carrying out carefully the path integral quantization of the non-Abelian
Chern-Simons theories using the De Witt-Fadeev-Popov and the Batalin-Fradkin-
Vilkovisky methods it is demonstrated that there is no need to quantize the
dimensionless charge of the theory. The main reason is that the action in the
exponent of the path integral is BRST-invariant which acquires a zero winding
number and guarantees the BRST renormalizability of the model.
The S-matrix operator is constructed, and starting from this S-matrix
operator novel topological unitarity identities are derived that demand the
vanishing of the gauge-invariant sum of the imaginary parts of the Feynman
diagrams with a given number of intermediate on-shell topological photon lines
in each order of perturbation theory. These identities are illustrated by an
explicit example.Comment: LaTex file, 31 pages, two figure
On Equivalence of Duffin-Kemmer-Petiau and Klein-Gordon Equations
A strict proof of equivalence between Duffin-Kemmer-Petiau (DKP) and
Klein-Gordon (KG) theories is presented for physical S-matrix elements in the
case of charged scalar particles interacting in minimal way with an external or
quantized electromagnetic field. First, Hamiltonian canonical approach to DKP
theory is developed in both component and matrix form. The theory is then
quantized through the construction of the generating functional for Green
functions (GF) and the physical matrix elements of S-matrix are proved to be
relativistic invariants. The equivalence between both theories is then proved
using the connection between GF and the elements of S-matrix, including the
case of only many photons states, and for more general conditions - so called
reduction formulas of Lehmann, Symanzik, Zimmermann.Comment: 23 pages, no figures, requires macro tcilate
Flat-space scattering and bulk locality in the AdS/CFT correspondence
The large radius limit in the AdS/CFT correspondence is expected to provide a
holographic derivation of flat-space scattering amplitudes. This suggests that
questions of locality in the bulk should be addressed in terms of properties of
the S-matrix and their translation into the conformal field theory. There are,
however, subtleties in this translation related to generic growth of amplitudes
near the boundary of anti de-Sitter space. Flat space amplitudes are recovered
after a delicate projection of CFT correlators onto normal-mode frequencies of
AdS. Once such amplitudes are obtained from the CFT, possible criteria for
approximate bulk locality include bounds on growth of amplitudes at high
energies and reproduction of semiclassical gravitational scattering at long
distances.Comment: 25 pages, harvmac. v2: Very minor corrections to eqs. v3: Minor
improvements of discussion of locality bounds and string scattering v4. Typos
fixe
Confining Properties of the Homogeneous Self-Dual Field and the Effective Potential in SU(2) Yang-Mills Theory
We examine in non-Abelian gauge theory the heavy quark limit in the presence
of the (anti-)self-dual homogeneous background field and see that a confining
potential emerges, consistent with the Wilson criterion, although the potential
is quadratic and not linear in the quark separation. This builds upon the
well-known feature that propagators in such a background field are entire
functions. The way in which deconfinement can occur at finite temperature is
then studied in the static temporal gauge by calculation of the effective
potential at high temperature. Finally we discuss the problems to be surmounted
in setting up the calculation of the effective potential nonperturbatively on
the lattice.Comment: 31 pages, LaTeX, expanded discussion and derivations in Sections 2
and
Worldline path integral for the massive Dirac propagator : A four-dimensional approach
We simplify and generalize an approach proposed by Di Vecchia and Ravndal to
describe a massive Dirac particle in external vector and scalar fields. Two
different path integral representations for the propagator are derived
systematically without the usual five-dimensional extension and shown to be
equivalent due to the supersymmetry of the action. They correspond to a
projection on the mass of the particle either continuously or at the end of the
time evolution. It is shown that the supersymmetry transformations are
generated by shifting and scaling the supertimes and the invariant difference
of two supertimes is given for the general case. A nonrelativistic reduction of
the relativistic propagator leads to a three-dimensional path integral with the
usual Pauli Hamiltonian. By integrating out the photons we obtain the effective
action for quenched QED and use it to derive the gauge-transformation
properties of the general Green function of the theory.Comment: 27 pages, LaTeX, no figures, uses revtex.sty; note with omitted
references added in proo
Hamilton Operator and the Semiclassical Limit for Scalar Particles in an Electromagnetic Field
We successively apply the generalized Case-Foldy-Feshbach-Villars (CFFV) and
the Foldy-Wouthuysen (FW) transformation to derive the Hamiltonian for
relativistic scalar particles in an electromagnetic field. In contrast to the
original transformation, the generalized CFFV transformation contains an
arbitrary parameter and can be performed for massless particles, which allows
solving the problem of massless particles in an electromagnetic field. We show
that the form of the Hamiltonian in the FW representation is independent of the
arbitrarily chosen parameter. Compared with the classical Hamiltonian for point
particles, this Hamiltonian contains quantum terms characterizing the
quadrupole coupling of moving particles to the electric field and the electric
and mixed polarizabilities. We obtain the quantum mechanical and semiclassical
equations of motion of massive and massless particles in an electromagnetic
field.Comment: 17 page
Spin Factor in Path Integral Representation for Dirac Propagator in External Fields
We study the spin factor problem both in and dimensions which are
essentially different for spin factor construction. Doing all Grassmann
integrations in the corresponding path integral representations for Dirac
propagator we get representations with spin factor in arbitrary external field.
Thus, the propagator appears to be presented by means of bosonic path integral
only. In dimensions we present a simple derivation of spin factor
avoiding some unnecessary steps in the original brief letter (Gitman,
Shvartsman, Phys. Lett. {\bf B318} (1993) 122) which themselves need some
additional justification. In this way the meaning of the surprising possibility
of complete integration over Grassmann variables gets clear. In
dimensions the derivation of the spin factor is completely original. Then we
use the representations with spin factor for calculations of the propagator in
some configurations of external fields. Namely, in constant uniform
electromagnetic field and in its combination with a plane wave field.Comment: 34 pages, LaTe
Numerically modelling the ratio of cross-strait voltage to water transport for the Bering Strait
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