11 research outputs found
Thiemann transform for gravity with matter fields
The generalised Wick transform discovered by Thiemann provides a
well-established relation between the Euclidean and Lorentzian theories of
general relativity. We extend this Thiemann transform to the Ashtekar
formulation for gravity coupled with spin-1/2 fermions, a non-Abelian
Yang-Mills field, and a scalar field. It is proved that, on functions of the
gravitational and matter phase space variables, the Thiemann transform is
equivalent to the composition of an inverse Wick rotation and a constant
complex scale transformation of all fields. This result holds as well for
functions that depend on the shift vector, the lapse function, and the Lagrange
multipliers of the Yang-Mills and gravitational Gauss constraints, provided
that the Wick rotation is implemented by means of an analytic continuation of
the lapse. In this way, the Thiemann transform is furnished with a geometric
interpretation. Finally, we confirm the expectation that the generator of the
Thiemann transform can be determined just from the spin of the fields and give
a simple explanation for this fact.Comment: LaTeX 2.09, 14 pages, no figure
Polymer quantization of the free scalar field and its classical limit
Building on prior work, a generally covariant reformulation of free scalar
field theory on the flat Lorentzian cylinder is quantized using Loop Quantum
Gravity (LQG) type `polymer' representations. This quantization of the {\em
continuum} classical theory yields a quantum theory which lives on a discrete
spacetime lattice. We explicitly construct a state in the polymer Hilbert space
which reproduces the standard Fock vacuum- two point functions for long
wavelength modes of the scalar field. Our construction indicates that the
continuum classical theory emerges under coarse graining. All our
considerations are free of the "triangulation" ambiguities which plague
attempts to define quantum dynamics in LQG. Our work constitutes the first
complete LQG type quantization of a generally covariant field theory together
with a semi-classical analysis of the true degrees of freedom and thus provides
a perfect infinite dimensional toy model to study open issues in LQG,
particularly those pertaining to the definition of quantum dynamics.Comment: 58 page
Coherent States for Black Holes
We determine coherent states peaked at classical space-time of the
Schwarzschild black hole in the frame-work of canonical quantisation of general
relativity. The information about the horizon is naturally encoded in the phase
space variables, and the perturbative quantum fluctuations around the classical
geometry depend on the distance from the horizon. For small black holes, space
near the vicinity of the singularity appears discrete with the singular point
excluded from the spectrum.Comment: 48 pages, 18+1 figures, some modifications, references adde
Phenomenological description of quantum gravity inspired modified classical electrodynamics
We discuss a large class of phenomenological models incorporating quantum
gravity motivated corrections to electrodynamics. The framework is that of
electrodynamics in a birefringent and dispersive medium with non-local
constitutive relations, which are considered up to second order in the inverse
of the energy characterizing the quantum gravity scale. The energy-momentum
tensor, Green functions and frequency dependent refraction indices are
obtained, leading to departures from standard physics. The effective character
of the theory is also emphasized by introducing a frequency cutoff. The
analysis of its effects upon the standard notion of causality is performed,
showing that in the radiation regime the expected corrections get further
suppressed by highly oscillating terms, thus forbiding causality violations to
show up in the corresponding observational effects.Comment: 14 pages, to be published in Obregon Festschrift 2006, Gen. Rel. and
Gra
Triangleland. II. Quantum Mechanics of Pure Shape
Relational particle models are of value in the absolute versus relative
motion debate. They are also analogous to the dynamical formulation of general
relativity, and as such are useful for investigating conceptual strategies
proposed for resolving the problem of time in quantum general relativity.
Moreover, to date there are few explicit examples of these at the quantum
level. In this paper I exploit recent geometrical and classical dynamics work
to provide such a study based on reduced quantization in the case of pure shape
(no scale) in 2-d for 3 particles (triangleland) with multiple harmonic
oscillator type potentials. I explore solutions for these making use of exact,
asymptotic, perturbative and numerical methods. An analogy to the mathematics
of the linear rigid rotor in a background electric field is useful throughout.
I argue that further relational models are accessible by the methods used in
this paper, and for specific uses of the models covered by this paper in the
investigation of the problem of time (and other conceptual and technical
issues) in quantum general relativity.Comment: Journal Reference added, minor updates to References and Figure
Direct flux control – sensorless control method of PMSM for all speeds – basics and constraints
The limitations of sensorless control of permanent magnet synchronous machines (PMSMs) are discussed and a viable solution is proposed. The main concept of sensorless control of drives relies on additional information given by the machine during its normal operation. This information provided by the machine is essentially the back-electro motive force and the variance of the stator inductivity, which are dependent on the rotor position. Several approaches and methods have discussed these problems, and in most cases they are not avoidable and that some methods work better on certain speeds of the drives. The direct flux control (DFC) method to combat the above problems at all speeds is presented. The flux linkage signal which contains the necessary information about the rotor position can be measured between the neutral point of a PMSM and an artificial one. The mathematical derivation and the observations from the experiments show that this signal contains a second and a fourth harmonic, which can be used to calculate the rotor position. Furthermore, the limitations of implementing DFC are also addresse