1,973 research outputs found
Discrete Time from Quantum Physics
't Hooft has recently developed a discretisation of (2+1) gravity which has a
multiple-valued Hamiltonian and which therefore admits quantum time evolution
only in discrete steps. In this paper, we describe several models in the
continuum with single-valued equations of motion in classical physics, but with
multiple-valued Hamiltonians. Their time displacements in quantum theory are
therefore obliged to be discrete. Classical models on smooth spatial manifolds
are also constructed with the property that spatial displacements can be
implemented only in discrete steps in quantum theory. All these models show
that quantization can profoundly affect classical topology.Comment: 21 pages with 2 figures, SU-4240-579 (figures corrected in this
version
Discrete Time Evolution and Energy Nonconservation in Noncommutative Physics
Time-space noncommutativity leads to quantisation of time and energy
nonconservation when time is conjugate to a compact spatial direction like a
circle. In this context energy is conserved only modulo some fixed unit. Such a
possibility arises for example in theories with a compact extra dimension with
which time does not commute. The above results suggest striking
phenomenological consequences in extra dimensional theories and elsewhere. In
this paper we develop scattering theory for discrete time translations. It
enables the calculation of transition probabilities for energy nonconserving
processes and has a central role both in formal theory and phenomenology.
We can also consider space-space noncommutativity where one of the spatial
directions is a circle. That leads to the quantisation of the remaining spatial
direction and conservation of momentum in that direction only modulo some fixed
unit, as a simple adaptation of the results in this paper shows.Comment: 17 pages, LaTex; minor correction
Dirac operator on the q-deformed Fuzzy sphere and Its spectrum
The q-deformed fuzzy sphere is the algebra of
dim. matrices, covariant with respect to the adjoint action
of \uq and in the limit , it reduces to the fuzzy sphere
. We construct the Dirac operator on the q-deformed fuzzy
sphere- using the spinor modules of \uq. We explicitly obtain
the zero modes and also calculate the spectrum for this Dirac operator. Using
this Dirac operator, we construct the \uq invariant action for the spinor
fields on which are regularised and have only finite modes. We
analyse the spectrum for both being root of unity and real, showing
interesting features like its novel degeneracy. We also study various limits of
the parameter space (q, N) and recover the known spectrum in both fuzzy and
commutative sphere.Comment: 19 pages, 6 figures, more references adde
Topology in Physics - A Perspective
This article, written in honor of Fritz Rohrlich, briefly surveys the role of
topology in physics.Comment: 16pp, 2 figures included (encapsulated postscript
Novel Studies on the \eta' Effective Lagrangian
The effective Lagrangian for \eta' incorporating the effect of the QCD
\theta-angle has been developed previously. We revisit this Lagrangian and
carry out its canonical quantization with particular attention to the test
function spaces of constraints and the topology of the \eta'-field. In this
way, we discover a new chirally symmetric coupling of this field to chiral
multiplets which involves in particular fermions. This coupling violates P and
T symmetries. In a subsequent paper, we will evaluate its contribution to the
electric dipole moment (EDM) of fermions. Our motivation is to test whether the
use of mixed states restores P and T invariance, so that EDM vanishes. This
calculation will be shown to have striking new physical consequences.Comment: 14 pages, 1 figure; V2: NEW TITLE; revised version to be published in
JHEP; references adde
Abelian BF-Theory and Spherically Symmetric Electromagnetism
Three different methods to quantize the spherically symmetric sector of
electromagnetism are presented: First, it is shown that this sector is
equivalent to Abelian BF-theory in four spacetime dimensions with suitable
boundary conditions. This theory, in turn, is quantized by both a reduced phase
space quantization and a spin network quantization. Finally, the outcome is
compared with the results obtained in the recently proposed general quantum
symmetry reduction scheme. In the magnetically uncharged sector, where all
three approaches apply, they all lead to the same quantum theory.Comment: 21 pages, LaTeX2e, v2: minor corrections in some formulas and a new
referenc
Edge states in Gravity and Black Hole Physics
We show in the context of Einstein gravity that the removal of a spatial
region leads to the appearance of an infinite set of observables and their
associated edge states localized at its boundary. Such a boundary occurs in
certain approaches to the physics of black holes like the one based on the
membrane paradigm. The edge states can contribute to black hole entropy in
these models. A ``complementarity principle" is also shown to emerge whereby
certain ``edge" observables are accessible only to certain observers. The
physical significance of edge observables and their states is discussed using
their similarities to the corresponding quantities in the quantum Hall effect.
The coupling of the edge states to the bulk gravitational field is demonstrated
in the context of (2+1) dimensional gravity.Comment: Revtex file, 22 pg. ( refs added , minor typos corrected
Frequency-sweep examination for wave mode identification in multimodal ultrasonic guided wave signal
This article has been made available through the Brunel Open Access Publishing Fund.Ultrasonic guided waves can be used to assess and monitor long elements of a structure from a single position. The greatest challenges for any guided wave system are the plethora of wave modes arising from the geometry of the structural element which propagate with a range of frequency-dependent velocities and the interpretation of these combined signals reflected by discontinuities in the structural element. In this paper, a novel signal processing technique is presented using a combination of frequency-sweep measurement, sampling rate conversion, and Fourier transform. The technique is applied to synthesized and experimental data to identify different modes in complex ultrasonic guided wave signals. It is demonstrated throughout the paper that the technique also has the capability to derive the time of flight and group velocity dispersion curve of different wave modes in field inspections. © 2014 IEEE
Effective base point free theorem for log canonical pairs--Koll\'ar type theorem
We prove Koll\'ar's effective base point free theorem for log canonical
pairs.Comment: 9 pages, v2: Appendix was added, minor revisions, v3: minor
modifications, title changed, v4: minor modifications, to appear in Tohoku
Math.
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