85 research outputs found
Covariant Poisson equation with compact Lie algebras
The covariant Poisson equation for Lie algebra-valued mappings defined in
3-dimensional Euclidean space is studied using functional analytic methods.
Weighted covariant Sobolev spaces are defined and used to derive sufficient
conditions for the existence and smoothness of solutions to the covariant
Poisson equation. These conditions require, apart from suitable continuity,
appropriate local integrability of the gauge potentials and global weighted
integrability of the curvature form and the source. The possibility of
nontrivial asymptotic behaviour of a solution is also considered. As a
by-product, weighted covariant generalisations of Sobolev embeddings are
established.Comment: 31 pages, LaTeX2
Inequivalent representations of commutator or anticommutator rings of field operators and their applications
Hamiltonian of a system in quantum field theory can give rise to infinitely
many partition functions which correspond to infinitely many inequivalent
representations of the canonical commutator or anticommutator rings of field
operators. This implies that the system can theoretically exist in infinitely
many Gibbs states. The system resides in the Gibbs state which corresponds to
its minimal Helmholtz free energy at a given range of the thermodynamic
variables. Individual inequivalent representations are associated with
different thermodynamic phases of the system. The BCS Hamiltonian of
superconductivity is chosen to be an explicit example for the demonstration of
the important role of inequivalent representations in practical applications.
Its analysis from the inequivalent representations' point of view has led to a
recognition of a novel type of the superconducting phase transition.Comment: 25 pages, 6 figure
From the Feynman-Schwinger representation to the non-perturbative relativistic bound state interaction
We write the 4-point Green function in QCD in the Feynman-Schwinger
representation and show that all the dynamical information are contained in the
Wilson loop average. We work out the QED case in order to obtain the usual
Bethe-Salpeter kernel. Finally we discuss the QCD case in the non-perturbative
regime giving some insight in the nature of the interaction kernel.Comment: 25 pages, RevTex, 3 figures included, typos corrected, to appear in
Phys. Rev. D 5
QCD Sum Rules for Hyperons in Nuclear Matter
Within finite-density QCD sum-rule approach we investigate the self-energies
of hyperons propagating in nuclear matter from a correlator of
interpolating fields evaluated in the nuclear matter ground state. We
find that the Lorentz vector self-energy of the is similar to the
nucleon vector self-energy. The magnitude of Lorentz scalar self-energy of the
is also close to the corresponding value for nucleon; however, this
prediction is sensitive to the strangeness content of the nucleon and to the
assumed density dependence of certain four-quark condensate. The scalar and
vector self-energies tend to cancel, but not completely. The implications for
the couplings of to the scalar and vector mesons in nuclear matter and
for the spin-orbit force in a finite nucleus are discussed.Comment: 20 pages in revtex, 6 figures available under request as ps files,
UMD preprint #94--11
Fractional Dynamics of Relativistic Particle
Fractional dynamics of relativistic particle is discussed. Derivatives of
fractional orders with respect to proper time describe long-term memory effects
that correspond to intrinsic dissipative processes. Relativistic particle
subjected to a non-potential four-force is considered as a nonholonomic system.
The nonholonomic constraint in four-dimensional space-time represents the
relativistic invariance by the equation for four-velocity u_{\mu}
u^{\mu}+c^2=0, where c is a speed of light in vacuum. In the general case, the
fractional dynamics of relativistic particle is described as non-Hamiltonian
and dissipative. Conditions for fractional relativistic particle to be a
Hamiltonian system are considered
In-medium operator product expansion for heavy-light-quark pseudoscalar mesons
The operator product expansion (OPE) for heavy-light-quark pseudoscalar
mesons (D-mesons and B-mesons) in medium is determined, both for a moving meson
with respect to the surrounding medium as well as for a meson at rest. First of
all, the OPE is given in terms of normal-ordered operators up to mass dimension
5, and the mass of the heavy-quark and the mass of the light-quark are kept
finite. The Wilson coefficients of such an expansion are infrared (IR)
divergent in the limit of a vanishing light-quark mass. A consistent separation
of scales necessitates an OPE in terms of non-normal-ordered operators, which
implies operator mixing, where the IR-divergences are absorbed into the
operators. It is shown that the Wilson coefficients of such an expansion are
IR-stable, and the limit of a vanishing light-quark mass is perfomed. Details
of the major steps for the calculation of the Wilson coefficients are
presented. By a comparison with previous results obtained by other theoretical
groups we have found serious disagreements.Comment: 51 pages, 3 figure
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