2,371 research outputs found
The Solution of the Relativistic Schrodinger Equation for the -Function Potential in 1-dimension Using Cutoff Regularization
We study the relativistic version of Schr\"odinger equation for a point
particle in 1-d with potential of the first derivative of the delta function.
The momentum cutoff regularization is used to study the bound state and
scattering states. The initial calculations show that the reciprocal of the
bare coupling constant is ultra-violet divergent, and the resultant expression
cannot be renormalized in the usual sense. Therefore a general procedure has
been developed to derive different physical properties of the system. The
procedure is used first on the non-relativistic case for the purpose of
clarification and comparisons. The results from the relativistic case show that
this system behaves exactly like the delta function potential, which means it
also shares the same features with quantum field theories, like being
asymptotically free, and in the massless limit, it undergoes dimensional
transmutation and it possesses an infrared conformal fixed point.Comment: 32 pages, 5 figure
Functionalized crystalline polyactones as toughners for thermosetting resins
A crystalline polylactone is produced having reactive acrylate end groups. When incorporated into a thermosetting resin which includes reactive C.dbd.CH.sub.2 sites, the present functionalized polylactone acts as a toughener, greatly increasing the impact resistance of the final cured product. Also disclosed are carboxyl-bearing polylactones as tougheners for epoxy resin systems
Vacuum Stability of the wrong sign Scalar Field Theory
We apply the effective potential method to study the vacuum stability of the
bounded from above (unstable) quantum field potential. The
stability ( and the mass renormalization
( conditions force the effective
potential of this theory to be bounded from below (stable). Since bounded from
below potentials are always associated with localized wave functions, the
algorithm we use replaces the boundary condition applied to the wave functions
in the complex contour method by two stability conditions on the effective
potential obtained. To test the validity of our calculations, we show that our
variational predictions can reproduce exactly the results in the literature for
the -symmetric theory. We then extend the applications
of the algorithm to the unstudied stability problem of the bounded from above
scalar field theory where classical analysis prohibits the
existence of a stable spectrum. Concerning this, we calculated the effective
potential up to first order in the couplings in space-time dimensions. We
find that a Hermitian effective theory is instable while a non-Hermitian but
-symmetric effective theory characterized by a pure imaginary
vacuum condensate is stable (bounded from below) which is against the classical
predictions of the instability of the theory. We assert that the work presented
here represents the first calculations that advocates the stability of the
scalar potential.Comment: 21pages, 12 figures. In this version, we updated the text and added
some figure
Functionalized crystalline polylactones as tougheners for thermosetting resins
A crystalline polylactone is produced having reactive acrylate end groups. When incorporated into a thermosetting resin which includes reactive C.dbd.CH.sub.2 sites, the present functionalized polylactone acts as a toughener, greatly increasing the impact resistance of the final cured product. Also disclosed are carboxyl-bearing polylactones as tougheners for epoxy resin systems
Degradation of Polymeric Biomaterials
Environmental and processing factors affecting the biostability of medical devices made from traditionally stable polymers, such as isotactic polypropylene (PP) and ultrahigh molecular weight polyethylene (UHMW-PE) , were analyzed and their undesirable degradation was related to performance of typical medical devices. Among the critical phenomena determining the biological performance of UHMW-PE and PP devices are oxidation during melt-processing and the propensity of the polymer chains to radiolyse and radio-oxidize. Polyesters and their biomedical devices , which can be designed to degrade predictably, are addressed with some focus on the less obvious determinants of performance
Relationship of sea level muon charge ratio to primary composition including nuclear target effects
The discrepancy between the muon charge ratio observed at low energies and that calculated using pp data is removed by including nuclear target effects. Calculations at high energies show that the primary iron spectrum is expected to change slope from 2 to 2.2 to 2.4 to 2.5 for energies approx. 4 x 10 to the 3 GeV/nucleon if scaling features continue to the highest energies
Fate of Accidental Symmetries of the Relativistic Hydrogen Atom in a Spherical Cavity
The non-relativistic hydrogen atom enjoys an accidental symmetry,
that enlarges the rotational symmetry, by extending the angular
momentum algebra with the Runge-Lenz vector. In the relativistic hydrogen atom
the accidental symmetry is partially lifted. Due to the Johnson-Lippmann
operator, which commutes with the Dirac Hamiltonian, some degeneracy remains.
When the non-relativistic hydrogen atom is put in a spherical cavity of radius
with perfectly reflecting Robin boundary conditions, characterized by a
self-adjoint extension parameter , in general the accidental
symmetry is lifted. However, for (where is the Bohr
radius and is the orbital angular momentum) some degeneracy remains when
or . In the relativistic case, we
consider the most general spherically and parity invariant boundary condition,
which is characterized by a self-adjoint extension parameter. In this case, the
remnant accidental symmetry is always lifted in a finite volume. We also
investigate the accidental symmetry in the context of the Pauli equation, which
sheds light on the proper non-relativistic treatment including spin. In that
case, again some degeneracy remains for specific values of and .Comment: 27 pages, 7 figure
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