7,965 research outputs found
Noncommutative Coordinates Invariant under Rotations and Lorentz Transformations
Dynamics with noncommutative coordinates invariant under three dimensional
rotations or, if time is included, under Lorentz transformations is developed.
These coordinates turn out to be the boost operators in SO(1,3) or in SO(2,3)
respectively. The noncommutativity is governed by a mass parameter . The
principal results are: (i) a modification of the Heisenberg algebra for
distances smaller than 1/M, (ii) a lower limit, 1/M, on the localizability of
wave packets, (iii) discrete eigenvalues of coordinate operator in timelike
directions, and (iv) an upper limit, , on the mass for which free field
equations have solutions. Possible restrictions on small black holes is
discussed.Comment: 14 pages; LaTex using JHEP3.cl
Drive systems for operation on deep-sea ROVs
Power systems for thruster actuators and other auxiliaries employed on work-class deep-sea ROVs subject to 300bar ambient pressures, are considered. Emphasis on 3×3 matrix converters for thrusters and 3×2 matrix converters for system auxiliaries, is given, along with experimental results showing operation during pressure cycling consistent with typical operational duties
Position-dependent noncommutativity in quantum mechanics
The model of the position-dependent noncommutativety in quantum mechanics is
proposed. We start with a given commutation relations between the operators of
coordinates [x^{i},x^{j}]=\omega^{ij}(x), and construct the complete algebra of
commutation relations, including the operators of momenta. The constructed
algebra is a deformation of a standard Heisenberg algebra and obey the Jacobi
identity. The key point of our construction is a proposed first-order
Lagrangian, which after quantization reproduces the desired commutation
relations. Also we study the possibility to localize the noncommutativety.Comment: published version, references adde
Interplay between curvature and Planck-scale effects in astrophysics and cosmology
Several recent studies have considered the implications for astrophysics and
cosmology of some possible nonclassical properties of spacetime at the Planck
scale. The new effects, such as a Planck-scale-modified energy-momentum
(dispersion) relation, are often inferred from the analysis of some quantum
versions of Minkowski spacetime, and therefore the relevant estimates depend
heavily on the assumption that there could not be significant interplay between
Planck-scale and curvature effects. We here scrutinize this assumption, using
as guidance a quantum version of de Sitter spacetime with known Inonu-Wigner
contraction to a quantum Minkowski spacetime. And we show that, contrary to
common (but unsupported) beliefs, the interplay between Planck-scale and
curvature effects can be significant. Within our illustrative example, in the
Minkowski limit the quantum-geometry deformation parameter is indeed given by
the Planck scale, while in the de Sitter picture the parameter of quantization
of geometry depends both on the Planck scale and the curvature scalar. For the
much-studied case of Planck-scale effects that intervene in the observation of
gamma-ray bursts we can estimate the implications of "quantum spacetime
curvature" within robust simplifying assumptions. For cosmology at the present
stage of the development of the relevant mathematics one cannot go beyond
semiheuristic reasoning, and we here propose a candidate approximate
description of a quantum FRW geometry, obtained by patching together pieces
(with different spacetime curvature) of our quantum de Sitter. This
semiheuristic picture, in spite of its limitations, provides rather robust
evidence that in the early Universe the interplay between Planck-scale and
curvature effects could have been particularly significant.Comment: 26 pages
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