19 research outputs found
Ground-state Wigner functional of linearized gravitational field
The deformation quantization formalism is applied to the linearized
gravitational field. Standard aspects of this formalism are worked out before
the ground state Wigner functional is obtained. Finally, the propagator for the
graviton is also discussed within the context of this formalism.Comment: 18 pages, no figure
Construction of a photon position operator with commuting components from natural axioms
A general form of the photon position operator with commuting components
fulfilling some natural axioms is obtained. This operator commutes with the
photon helicity operator, is Hermitian with respect to the Bialynicki-Birula
scalar product and defined up to a unitary transformation preserving the
transversality condition. It is shown that, using the procedure analogous to
the one introduced by T. T. Wu and C. N. Yang for the case of the Dirac
magnetic monopole, the photon position operator can be defined by a flat
connection in some trivial vector bundle over . This observation enables us to reformulate quantum mechanics of
a~single photon on .Comment: 19 pages, some corrections, to appear in Phys. Rev.
The damped harmonic oscillator in deformation quantization
We propose a new approach to the quantization of the damped harmonic
oscillator in the framework of deformation quantization. The quantization is
performed in the Schr\"{o}dinger picture by a star-product induced by a
modified "Poisson bracket". We determine the eigenstates in the damped regime
and compute the transition probability between states of the undamped harmonic
oscillator after the system was submitted to dissipation.Comment: Plain LaTex file, 11 page