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The nonstandard quantum plane
2008
Annals of Pure and Applied Logic
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These points represent nonstandard homogeneous components of the quantum plane. 2 The lattice of K-invariant pp-definable subspaces A pp-definable subspace ϕ(V ) of a U q -module V is called K-invariant ...
Rather than working with the quantum plane directly, it is easier to prove the following theorem for M, and then specialize to the quantum plane in the last section of the paper. ...
doi:10.1016/j.apal.2008.06.009
fatcat:eacrlevtubc35od5dzygaqu6b4
Page 1392 of Mathematical Reviews Vol. 47, Issue 5
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1974
Mathematical Reviews
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writers have hitherto held, in the plane of single quantum-mechanical events” (p. 96). ...
“The author has proposed the view
1392
QUANTUM MECHANICS
that the locus of nonclassical logic in quantum mechanic is in the plane in which physical contexts are related to one another, and not, as all ...
Entropic Aspects of Nonlinear Partial Differential Equations: Classical and Quantum Mechanical Perspectives
2017
Entropy
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Acknowledgments: I express my thanks to the authors of the above contributions, and to the journal Entropy and MDPI for their support during this work. ...
Conflicts of Interest: The author declares no conflict of interest. Entropy 2017, 19, 166 ...
equations inspired on quantum mechanics. ...
doi:10.3390/e19040166
fatcat:o2xnreocfbdxbey7fapwb72nqy
Page 2139 of Mathematical Reviews Vol. , Issue 99c
[page]
1991
Mathematical Reviews
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This is proved by a nonlinear transformation of the stan- dard basis for the null-plane quantum Poincaré algebra. ...
(E-VALD-TP; Valladolid)
Bicrossproduct structure of the null-plane quantum Poincaré algebra. (English summary)
J. Phys. A 31 (1998), no. 1, L1-L7. ...
Page 627 of Mathematical Reviews Vol. , Issue 92b
[page]
1992
Mathematical Reviews
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Then the affine nonstandard plane generated by the vectors w; and centered in c(t) is infinitely close (in the Grassmannian manifold) to the (standard) plane generated by the c“)(t). ...
Now it is easy for the author to give a characterisation of the osculating plane: he takes three consecutive nonstandard points *c(so), *c(s,), *c(s2) on c with 5; =s, 5; € (a,b). ...
Quantum deformations of conformal algebras introducing fundamental mass parameters
1996
Physics Letters B
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1995 pre-print arXiv:q-alg/9507005v1 fatcat:em4t7acr4jbjhgsrfqgo3yz6mi
It appears that for D=4 the deformation of the Poincare algebra sector coincides with "null plane" quantum Poincare algebra. ...
In such a way we generalize the lowest order of known nonstandard quantum deformation of sl(2) to the Lie algebras sp(4) = so(5) and sl(4) = so(6). ...
The mass Casimir is given by the formula [24] C 2 = P 2 1 + P 2 2 − MP − sinh( P + M ) (5.10) Because the deformation U M (P 4 ) of the Poincaré algebra, called in [24] the "null plane" quantum Poincaré ...
doi:10.1016/0370-2693(96)01604-8
fatcat:bsanod2hqffa5hsdrbzloayr5q
Page 1109 of Mathematical Reviews Vol. , Issue 95b
[page]
1995
Mathematical Reviews
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In order to now set up a nonstandard Dirac bra-ket formal- ism the author introduces an additional “spectral axiom” besides the usual quantum logical axioms. ...
is bound to contain finite nonstandard reals). ...
Page 5451 of Mathematical Reviews Vol. , Issue 94i
[page]
1994
Mathematical Reviews
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The Manin quantum plane has two parameters qg and p, and is denoted by Q,,. ...
A 26 (1993), no. 5, L217- L220; MR 94d:16035] associated to the nonstandard R-matrix is isomorphic to a quantum deformation of SU(2). ...
Page 4731 of Mathematical Reviews Vol. , Issue 92i
[page]
1992
Mathematical Reviews
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The methods used are nonstandard methods which allow the author to characterize differentiability of a function f by the fact that the graph of f has a non-S-vertical, S-tangent plane over all standard ...
and to characterize a function f of class C' by the fact that the graph of f has a non-S-vertical, S-tangent plane over all finite points in R?*. The results are related to those of J. ...
The coloured quantum plane
2003
Journal of Geometry and Physics
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2002 pre-print arXiv:math/0202183v1 fatcat:37vzax63hnddfjr4oig6h42xpy
We study the quantum plane associated to the coloured quantum group GL_q^λ,μ(2) and solve the problem of constructing the corresponding differential geometric structure. ...
The coloured h-plane corresponding to the coloured Jordanian quantum group GL_h^λ,μ(2) is also obtained by contraction of the coloured q-plane. ...
Coloured h-plane We now look at the nonstandard (or Jordanian) counterpart of the q-plane, known as the h-plane [4, 5] . ...
doi:10.1016/s0393-0440(02)00051-7
fatcat:vsataxe5ubfc5eattcahj3hdsm
Page 3296 of Mathematical Reviews Vol. , Issue 98E
[page]
1998
Mathematical Reviews
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The presented approach is illustrated by an example of a system with its phase space equal to a half-plane. ...
The idea of the paper is based on the similar but much simpler nonstandard construction of Wiener measure from a nonstandard flat integral given by Cutland [J. London Math. ...
Acoustoconductance of quantum contacts
1999
Physica. B, Condensed matter
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We describe theoretically the acoustoconductance (AC) of quantum contacts. ...
Electrons which are forward scattered by phonons can contribute to AC and, furthermore, AC can have positive sign (i.e. a conductance-increase under the influence of phonons). ...
ACKNOWLEDGMENTS The authors would like to thank the organizers of Phonons 98 for providing the opportunity to present this work. Funding by the EPSRC under Grant Nos. ...
doi:10.1016/s0921-4526(98)01250-2
fatcat:c2a6msnejbfk5lgsgrfwcypn5m
Page 495 of Mathematical Reviews Vol. , Issue 92a
[page]
1992
Mathematical Reviews
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Furthermore, we illustrate the method by discussing some specific potential problems on the Poincaré up- per half-plane. The first one is Vi(x,y) = y?[V(x) +(m/2)w?y?] ...
The pur- pose of the authors is to investigate to what extent Haag duality holds in conformal quantum field theory. ...
Superluminal Phenomena and the Quantum Preferred Frame
[article]
2000
arXiv
pre-print
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experiments, we discuss in this paper a speculative but physically admissible form and solutions of effective Maxwell-like equations describing propagation of electromagnetic field in a medium which "feels" a quantum ...
This paper was financially supported by the University of Lodz. ...
It is convenient to consider our plane wave solution in the preferred frame. ...
arXiv:quant-ph/0010026v2
fatcat:6da375octvfcpmls63udrn63re
Page 4711 of Mathematical Reviews Vol. , Issue 2003f
[page]
2003
Mathematical Reviews
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Summary: “We give solutions of the quantum conformal defor- mations of the Maxwell and potential equations in terms of defor- mations of the plane wave. ...
Motivated by some problems in theoretical physics, the authors
2003f:8 1 128
set out to construct nonstandard bases for finite-dimensional irre-
ducible representations of the quantum algebra su,(2) by ...
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