147 research outputs found
Dirac's Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space
The system of two-dimensional damped harmonic oscillator is revisited in the
extended phase space. It is an old problem already addressed by many authors
that we present here in some fresh points of view and carry on smoothly a whole
discussion. We show that the system is singular. The classical Hamiltonian is
proportional to the first-class constraint. We pursue with the Dirac's
canonical quantization procedure by fixing the gauge and provide a reduced
phase space description of the system. As result the quantum system is simply
modeled by the original quantum Hamiltonian.Comment: 12 pages, Open access article distributed under the Creative Commons
Attribution License which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited (CC
BY 4.0
Class of invariants for the 2D time-dependent Landau problem and harmonic oscillator in a magnetic field
We consider an isotropic two dimensional harmonic oscillator with arbitrarily
time-dependent mass and frequency in an arbitrarily
time-dependent magnetic field . We determine two commuting invariant
observables (in the sense of Lewis and Riesenfeld) in terms of some
solution of an auxiliary ordinary differential equation and an orthonormal
basis of the Hilbert space consisting of joint eigenvectors of
. We then determine time-dependent phases such that
the are solutions of the
time-dependent Schr\"odinger equation and make up an orthonormal basis of the
Hilbert space. These results apply, in particular to a two dimensional Landau
problem with time-dependent , which is obtained from the above just by
setting . By a mere redefinition of the parameters, these
results can be applied also to the analogous models on the canonical
non-commutative plane.Comment: 13 pages, 3 references adde
Minimal areas from q-deformed oscillator algebras
We demonstrate that dynamical noncommutative space-time will give rise to
deformed oscillator algebras. In turn, starting from some q-deformations of
these algebras in a two dimensional space for which the entire deformed Fock
space can be constructed explicitly, we derive the commutation relations for
the dynamical variables in noncommutative space-time. We compute minimal areas
resulting from these relations, i.e. finitely extended regions for which it is
impossible to resolve any substructure in form of measurable knowledge. The
size of the regions we find is determined by the noncommutative constant and
the deformation parameter q. Any object in this type of space-time structure
has to be of membrane type or in certain limits of string type.Comment: 14 pages, 1 figur
On the uniqueness of the unitary representations of the non commutative Heisenberg-Weyl algebra
In this paper we discuss the uniqueness of the unitary representations of the
non commutative Heisenberg-Weyl algebra. We show that, apart from a critical
line for the non commutative position and momentum parameters, the Stone-von
Neumann theorem still holds, which implies uniqueness of the unitary
representation of the Heisenberg-Weyl algebra.Comment: 4 page
Nonabelian Global Chiral Symmetry Realisation in the Two-Dimensional N Flavour Massless Schwinger Model
The nonabelian global chiral symmetries of the two-dimensional N flavour
massless Schwinger model are realised through bosonisation and a vertex
operator construction.Comment: To appear in the Proceedings of the Fourth International Workshop on
Contemporary Problems in Mathematical Physics, November 5-11, 2005, Cotonou
(Republic of Benin) (World Scientific, Singapore, 2006), 1+7 pages, no
figure
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