24 research outputs found
Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework
Recently the Master Constraint Programme for Loop Quantum Gravity (LQG) was
proposed as a classically equivalent way to impose the infinite number of
Wheeler -- DeWitt constraint equations in terms of a single Master Equation.
While the proposal has some promising abstract features, it was until now
barely tested in known models. In this series of five papers we fill this gap,
thereby adding confidence to the proposal. We consider a wide range of models
with increasingly more complicated constraint algebras, beginning with a finite
dimensional, Abelean algebra of constraint operators which are linear in the
momenta and ending with an infinite dimensional, non-Abelean algebra of
constraint operators which closes with structure functions only and which are
not even polynomial in the momenta. In all these models we apply the Master
Constraint Programme successfully, however, the full flexibility of the method
must be exploited in order to complete our task. This shows that the Master
Constraint Programme has a wide range of applicability but that there are many,
physically interesting subtleties that must be taken care of in doing so. In
this first paper we prepare the analysis of our test models by outlining the
general framework of the Master Constraint Programme. The models themselves
will be studied in the remaining four papers. As a side result we develop the
Direct Integral Decomposition (DID) for solving quantum constraints as an
alternative to Refined Algebraic Quantization (RAQ).Comment: 42 pages, no figure
Initial Conditions for Semiclassical Field Theory
Semiclassical approximation based on extracting a c-number classical
component from quantum field is widely used in the quantum field theory.
Semiclassical states are considered then as Gaussian wave packets in the
functional Schrodinger representation and as Gaussian vectors in the Fock
representation. We consider the problem of divergences and renormalization in
the semiclassical field theory in the Hamiltonian formulation. Although
divergences in quantum field theory are usually associated with loop Feynman
graphs, divergences in the Hamiltonian approach may arise even at the tree
level. For example, formally calculated probability of pair creation in the
leading order of the semiclassical expansion may be divergent. This observation
was interpretted as an argumentation for considering non-unitary evolution
transformations, as well as non-equivalent representations of canonical
commutation relations at different time moments. However, we show that this
difficulty can be overcomed without the assumption about non-unitary evolution.
We consider first the Schrodinger equation for the regularized field theory
with ultraviolet and infrared cutoffs. We study the problem of making a limit
to the local theory. To consider such a limit, one should impose not only the
requirement on the counterterms entering to the quantum Hamiltonian but also
the requirement on the initial state in the theory with cutoffs. We find such a
requirement in the leading order of the semiclassical expansion and show that
it is invariant under time evolution. This requirement is also presented as a
condition on the quadratic form entering to the Gaussian state.Comment: 20 pages, Plain TeX, one postscript figur
Giant resonant light forces in microspherical photonics
Resonant light pressure effects can open new degrees of freedom in optical manipulation with microparticles, but they have been traditionally considered as relatively subtle effects. Using a simplified two-dimensional model of surface electromagnetic waves evanescently coupled to whispering gallery modes (WGMs) in transparent circular cavities, we show that under resonant conditions the peaks of the optical forces can approach theoretical limits imposed by the momentum conservation law on totally absorbing particles. Experimentally, we proved the existence of strong peaks of the optical forces by studying the optical propulsion of dielectric microspheres along tapered microfibers. We observed giant optical propelling velocities ∼0.45 mm s−1 for some of the 15-20 µm polystyrene microspheres in water for guided powers limited at ∼43 mW. Such velocities exceed previous observations by more than an order of magnitude, thereby providing evidence for the strongly enhanced resonant optical forces. We analyzed the statistical properties of the velocity distribution function measured for slightly disordered (∼1% size variations) ensembles of microspheres with mean diameters varying from 3 to 20 µm. These results demonstrate a principal possibility of optical sorting of microspheres with the positions of WGM resonances overlapped at the wavelength of the laser source. They can be used as building blocks of the lossless coupled resonator optical waveguides and various integrated optoelectronics devices
Recommended from our members