31 research outputs found
Dirac Hamiltonian with superstrong Coulomb field
We consider the quantum-mechanical problem of a relativistic Dirac particle
moving in the Coulomb field of a point charge . In the literature, it is
often declared that a quantum-mechanical description of such a system does not
exist for charge values exceeding the so-called critical charge with based on the fact that the standard expression for the
lower bound state energy yields complex values at overcritical charges. We show
that from the mathematical standpoint, there is no problem in defining a
self-adjoint Hamiltonian for any value of charge. What is more, the transition
through the critical charge does not lead to any qualitative changes in the
mathematical description of the system. A specific feature of overcritical
charges is a non uniqueness of the self-adjoint Hamiltonian, but this non
uniqueness is also characteristic for charge values less than the critical one
(and larger than the subcritical charge with ). We present the spectra and (generalized) eigenfunctions for all
self-adjoint Hamiltonians. The methods used are the methods of the theory of
self-adjoint extensions of symmetric operators and the Krein method of guiding
functionals. The relation of the constructed one-particle quantum mechanics to
the real physics of electrons in superstrong Coulomb fields where multiparticle
effects may be of crucial importance is an open question.Comment: 44 pages, LaTex file, to be published in Teor.Mat.Fiz.
(Theor.Math.Phys.
BRST Algebra Quantum Double and Quantization of the Proper Time Cotangent Bundle
The quantum double for the quantized BRST superalgebra is studied. The
corresponding R-matrix is explicitly constucted. The Hopf algebras of the
double form an analytical variety with coordinates described by the canonical
deformation parameters. This provides the possibility to construct the
nontrivial quantization of the proper time supergroup cotangent bundle. The
group-like classical limit for this quantization corresponds to the generic
super Lie bialgebra of the double.Comment: 11 pages, LaTe
Quantum gravity correction, evolution of scalar field and inflation
We take the first nontrivial coefficient of the Schwinger-DeWitt expansion as
a leading correction to the action of the second-derivative metric-dilaton
gravity. To fix the ambiguities related with an arbitrary choice of the gauge
fixing condition and the parametrization for the quantum field, one has to use
the classical equations of motion. As a result, the only corrections are the
ones to the potential of the scalar field. It turns out that the parameters of
the initial classical action may be chosen in such a way that the potential
satisfies most of the conditions for successful inflation.Comment: 11 pages, 3 figure
"Gauging" the Fluid
A consistent framework has been put forward to quantize the isentropic,
compressible and inviscid fluid model in the Hamiltonian framework, using the
Clebsch parameterization. The naive quantization is hampered by the
non-canonical (in particular field dependent) Poisson Bracket algebra. To
overcome this problem, the Batalin-Tyutin \cite{12} quantization formalism is
adopted in which the original system is converted to a local gauge theory and
is embedded in a {\it canonical} extended phase space. In a different reduced
phase space scheme \cite{vy} also the original model is converted to a gauge
theory and subsequently the two distinct gauge invariant formulations of the
fluid model are related explicitly. This strengthens the equivalence between
the relativistic membrane (where a gauge invariance is manifest) and the fluid
(where the gauge symmetry is hidden). Relativistic generalizations of the
extended model is also touched upon.Comment: Version to appear in J.Phys. A: Mathematical and Genera
Symplectic quantization of self-dual master Lagrangian
We consider the master Lagrangian of Deser and Jackiw, interpolating between
the self-dual and the Maxwell-Chern-Simons Lagrangian, and quantize it
following the symplectic approach, as well as the traditional Dirac scheme. We
demonstrate the equivalence of these procedures in the subspace of the
second-class constraints. We then proceed to embed this mixed first- and
second-class system into an extended first-class system within the framework of
both approaches, and construct the corresponding generator for this extended
gauge symmetry in both formulations.Comment: 27 page
Alternative commutation relations, star products and tomography
Invertible maps from operators of quantum obvservables onto functions of
c-number arguments and their associative products are first assessed. Different
types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution
are discussed. The recently introduced symplectic tomography map of observables
(tomograms) related to the Heisenberg-Weyl group is shown to belong to the
standard framework of the maps from quantum observables onto the c-number
functions. The star-product for symbols of the quantum-observable for each one
of the maps (including the tomographic map) and explicit relations among
different star-products are obtained. Deformations of the Moyal star-product
and alternative commutation relations are also considered.Comment: LATEX plus two style files, to appear in J. Phys.
Constraint structure of O(3) nonlinear sigma model revisited
We study the constraint structure of the O(3) nonlinear sigma model in the
framework of the Lagrangian, symplectic, Hamilton-Jacobi as well as the
Batalin-Fradkin-Tyutin embedding procedure.Comment: 17 page
New Exactly Solvable Two-Dimensional Quantum Model Not Amenable to Separation of Variables
The supersymmetric intertwining relations with second order supercharges
allow to investigate new two-dimensional model which is not amenable to
standard separation of variables. The corresponding potential being the
two-dimensional generalization of well known one-dimensional P\"oschl-Teller
model is proven to be exactly solvable for arbitrary integer value of parameter
all its bound state energy eigenvalues are found analytically, and the
algorithm for analytical calculation of all wave functions is given. The shape
invariance of the model and its integrability are of essential importance to
obtain these results.Comment: 23 page
Space-Time Supersymmetry of Extended Fermionic Strings in Dimensions
The fermionic string theory is revisited in light of its recently
proposed equivalence to the non-compact fermionic string model. The
issues of space-time Lorentz covariance and supersymmetry for the BRST
quantized strings living in uncompactified dimensions are
discussed. The equivalent local quantum supersymmetric field theory appears to
be the most transparent way to represent the space-time symmetries of the
extended fermionic strings and their interactions. Our considerations support
the Siegel's ideas about the presence of Lorentz symmetry as well as
at least one self-dual space-time supersymmetry in the theory of the
fermionic strings, though we do not have a compelling reason to argue about the
necessity of the {\it maximal} space-time supersymmetry. The world-sheet
arguments about the absence of all string massive modes in the physical
spectrum, and the vanishing of all string-loop amplitudes in the Polyakov
approach, are given on the basis of general consistency of the theory.Comment: 29 pages, LaTeX, ITP-UH-1/9
Yang-Mills gauge anomalies in the presence of gravity with torsion
The BRST transformations for the Yang-Mills gauge fields in the presence of
gravity with torsion are discussed by using the so-called Maurer-Cartan
horizontality conditions. With the help of an operator \d which allows to
decompose the exterior spacetime derivative as a BRST commutator we solve the
Wess-Zumino consistency condition corresponding to invariant Chern-Simons terms
and gauge anomalies.Comment: 24 pages, report REF. TUW 94-1