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The nonstandard quantum plane

Ivo Herzog, Sonia L'Innocente
2008 Annals of Pure and Applied Logic  
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 [page]

1974 Mathematical Reviews  
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

Angelo Plastino
2017 Entropy  
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  
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  
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

Jerzy Lukierski, Pierre Minnaert, Marek Mozrzymas
1996 Physics Letters B  
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  
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  
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  
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

Deepak Parashar
2003 Journal of Geometry and Physics  
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  
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

M.P. Blencowe, A.Y. Shik
1999 Physica. B, Condensed matter  
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  
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]

Jakub Rembielinski
2000 arXiv   pre-print
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  
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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