1,784 research outputs found
The Canonical Approach to Quantum Gravity: General Ideas and Geometrodynamics
We give an introduction to the canonical formalism of Einstein's theory of
general relativity. This then serves as the starting point for one approach to
quantum gravity called quantum geometrodynamics. The main features and
applications of this approach are briefly summarized.Comment: 21 pages, 6 figures. Contribution to E. Seiler and I.-O. Stamatescu
(editors): `Approaches To Fundamental Physics -- An Assessment Of Current
Theoretical Ideas' (Springer Verlag, to appear
Existence of Spinorial States in Pure Loop Quantum Gravity
We demonstrate the existence of spinorial states in a theory of canonical
quantum gravity without matter. This should be regarded as evidence towards the
conjecture that bound states with particle properties appear in association
with spatial regions of non-trivial topology. In asymptotically trivial general
relativity the momentum constraint generates only a subgroup of the spatial
diffeomorphisms. The remaining diffeomorphisms give rise to the mapping class
group, which acts as a symmetry group on the phase space. This action induces a
unitary representation on the loop state space of the Ashtekar formalism.
Certain elements of the diffeomorphism group can be regarded as asymptotic
rotations of space relative to its surroundings. We construct states that
transform non-trivially under a -rotation: gravitational quantum states
with fractional spin.Comment: 26 pages, 6 figures. Changes made to section 2 and Lemma
Consistency of Semiclassical Gravity
We discuss some subtleties which arise in the semiclassical approximation to
quantum gravity. We show that integrability conditions prevent the existence of
Tomonaga-Schwinger time functions on the space of three-metrics but admit them
on superspace. The concept of semiclassical time is carefully examined. We
point out that central charges in the matter sector spoil the consistency of
the semiclassical approximation unless the full quantum theory of gravity and
matter is anomaly-free. We finally discuss consequences of these considerations
for quantum field theory in flat spacetime, but with arbitrary foliations.Comment: 12 pages, LATEX, Report Freiburg THEP-94/2
Group averaging in the (p,q) oscillator representation of SL(2,R)
We investigate refined algebraic quantisation with group averaging in a
finite-dimensional constrained Hamiltonian system that provides a simplified
model of general relativity. The classical theory has gauge group SL(2,R) and a
distinguished o(p,q) observable algebra. The gauge group of the quantum theory
is the double cover of SL(2,R), and its representation on the auxiliary Hilbert
space is isomorphic to the (p,q) oscillator representation. When p>1, q>1 and
p+q == 0 (mod 2), we obtain a physical Hilbert space with a nontrivial
representation of the o(p,q) quantum observable algebra. For p=q=1, the system
provides the first example known to us where group averaging converges to an
indefinite sesquilinear form.Comment: 34 pages. LaTeX with amsfonts, amsmath, amssymb. (References added;
minor typos corrected.
Linear entropy as an entanglement measure in two-fermion systems
We describe an efficient theoretical criterion, suitable for
indistinguishable particles to quantify the quantum correlations of any pure
two-fermion state, based on the Slater rank concept. It represents the natural
generalization of the linear entropy used to treat quantum entanglement in
systems of non-identical particles. Such a criterion is here applied to an
electron-electron scattering in a two-dimensional system in order to perform a
quantitative evaluation of the entanglement dynamics for various spin
configurations and to compare the linear entropy with alternative approaches.
Our numerical results show the dependence of the entanglement evolution upon
the initial state of the system and its spin components. The differences with
previous analyses accomplished by using the von Neumann entropy are discussed.
The evaluation of the entanglement dynamics in terms of the linear entropy
results to be much less demanding from the computational point of view, not
requiring the diagonalization of the density matrix.Comment: 16 pages. Added references in section 1 Corrected typo
Entanglement dynamics of electron-electron scattering in low-dimensional semiconductor systems
We perform the quantitative evaluation of the entanglement dynamics in
scattering events between two insistinguishable electrons interacting via
Coulomb potential in 1D and 2D semiconductor nanostructures. We apply a
criterion based on the von Neumann entropy and the Schmidt decomposition of the
global state vector suitable for systems of identical particles. From the
timedependent numerical solution of the two-particle wavefunction of the
scattering carriers we compute their entanglement evolution for different spin
configurations: two electrons with the same spin, with different spin, singlet,
and triplet spin state. The procedure allows to evaluate the mechanisms that
govern entanglement creation and their connection with the characteristic
physical parameters and initial conditions of the system. The cases in which
the evolution of entanglement is similar to the one obtained for
distinguishable particles are discussed.Comment: 22 pages, 7 figures, submitted to Physical Review
Symplectic Cuts and Projection Quantization
The recently proposed projection quantization, which is a method to quantize
particular subspaces of systems with known quantum theory, is shown to yield a
genuine quantization in several cases. This may be inferred from exact results
established within symplectic cutting.Comment: 12 pages, v2: additional examples and a new reference to related wor
All (qubit) decoherences: Complete characterization and physical implementation
We investigate decoherence channels that are modelled as a sequence of
collisions of a quantum system (e.g., a qubit) with particles (e.g., qubits) of
the environment. We show that collisions induce decoherence when a bi-partite
interaction between the system qubit and an environment (reservoir) qubit is
described by the controlled-U unitary transformation (gate). We characterize
decoherence channels and in the case of a qubit we specify the most general
decoherence channel and derive a corresponding master equation. Finally, we
analyze entanglement that is generated during the process of decoherence
between the system and its environment.Comment: 10 pages, 3 figure
Skyrmions, Spectral Flow and Parity Doubles
It is well-known that the winding number of the Skyrmion can be identified as
the baryon number. We show in this paper that this result can also be
established using the Atiyah-Singer index theorem and spectral flow arguments.
We argue that this proof suggests that there are light quarks moving in the
field of the Skyrmion. We then show that if these light degrees of freedom are
averaged out, the low energy excitations of the Skyrmion are in fact spinorial.
A natural consequence of our approach is the prediction of a state
and its excitations in addition to the nucleon and delta. Using the recent
numerical evidence for the existence of Skyrmions with discrete spatial
symmetries, we further suggest that the the low energy spectrum of many light
nuclei may possess a parity doublet structure arising from a subtle topological
interaction between the slow Skyrmion and the fast quarks. We also present
tentative experimental evidence supporting our arguments.Comment: 22 pages, LaTex. Uses amstex, amssym
A Uniqueness Theorem for Constraint Quantization
This work addresses certain ambiguities in the Dirac approach to constrained
systems. Specifically, we investigate the space of so-called ``rigging maps''
associated with Refined Algebraic Quantization, a particular realization of the
Dirac scheme. Our main result is to provide a condition under which the rigging
map is unique, in which case we also show that it is given by group averaging
techniques. Our results comprise all cases where the gauge group is a
finite-dimensional Lie group.Comment: 23 pages, RevTeX, further comments and references added (May 26. '99
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