335 research outputs found
Representations of the Generalized Lie Algebra sl(2)_q
We construct finite-dimensional irreducible representations of two quantum
algebras related to the generalized Lie algebra \ssll (2)_q introduced by
Lyubashenko and the second named author. We consider separately the cases of
generic and at roots of unity. Some of the representations have no
classical analog even for generic . Some of the representations have no
analog to the finite-dimensional representations of the quantised enveloping
algebra , while in those that do there are different matrix
elements.Comment: 14 pages, plain-TEX file using input files harvmac.tex, amssym.de
All degree six local unitary invariants of k qudits
We give explicit index-free formulae for all the degree six (and also degree
four and two) algebraically independent local unitary invariant polynomials for
finite dimensional k-partite pure and mixed quantum states. We carry out this
by the use of graph-technical methods, which provides illustrations for this
abstract topic.Comment: 18 pages, 6 figures, extended version. Comments are welcom
Deformations of Multiparameter Quantum gl(N)
Multiparameter quantum gl(N) is not a rigid structure. This paper defines an
essential deformation as one that cannot be interpreted in terms of a
similarity transformation, nor as a perturbation of the parameters. All the
equivalence classes of first order essential deformations are found, as well as
a class of exact deformations. This work provides quantization of all the
classical Lie bialgebra structures (constant r-matrices) found by Belavin and
Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a
cubic root of unity, stands out.Comment: 15 pages. Plain Te
Non-local properties of a symmetric two-qubit system
Non-local properties of symmetric two-qubit states are quantified in terms of
a complete set of entanglement invariants. We prove that negative values of
some of the invariants are signatures of quantum entanglement. This leads us to
identify sufficient conditions for non-separability in terms of entanglement
invariants. Non-local properties of two-qubit states extracted from (i) Dicke
state (ii) state generated by one-axis twisting Hamiltonian, and (iii)
one-dimensional Ising chain with nearest neighbour interaction are analyzed in
terms of the invariants characterizing them.Comment: 5 pages, no figure
At what time does a quantum experiment have a result?
This paper provides a general method for defining a generalized quantum
observable (or POVM) that supplies properly normalized conditional
probabilities for the time of occurrence (i.e., of detection). This method
treats the time of occurrence as a probabilistic variable whose value is to be
determined by experiment and predicted by the Born rule. This avoids the
problematic assumption that a question about the time at which an event occurs
must be answered through instantaneous measurements of a projector by an
observer, common to both Rovelli (1998) and Oppenheim et al. (2000). I also
address the interpretation of experiments purporting to demonstrate the quantum
Zeno effect, used by Oppenheim et al. (2000) to justify an inherent uncertainty
for measurements of times.Comment: To appear in proceedings of 2015 ETH Zurich Workshop on Time in
Physic
On Quantum Lie Algebras and Quantum Root Systems
As a natural generalization of ordinary Lie algebras we introduce the concept
of quantum Lie algebras . We define these in terms of certain
adjoint submodules of quantized enveloping algebras endowed with a
quantum Lie bracket given by the quantum adjoint action. The structure
constants of these algebras depend on the quantum deformation parameter and
they go over into the usual Lie algebras when .
The notions of q-conjugation and q-linearity are introduced. q-linear
analogues of the classical antipode and Cartan involution are defined and a
generalised Killing form, q-linear in the first entry and linear in the second,
is obtained. These structures allow the derivation of symmetries between the
structure constants of quantum Lie algebras.
The explicitly worked out examples of and illustrate the
results.Comment: 22 pages, latex, version to appear in J. Phys. A. see
http://www.mth.kcl.ac.uk/~delius/q-lie.html for calculations and further
informatio
Entanglement and density-functional theory: testing approximations on Hooke's atom
We present two methods of calculating the spatial entanglement of an
interacting electron system within the framework of density-functional theory.
These methods are tested on the model system of Hooke's atom for which the
spatial entanglement can be calculated exactly. We analyse how the strength of
the confining potential affects the spatial entanglement and how accurately the
methods that we introduced reproduce the exact trends. We also compare the
results with the outcomes of standard first-order perturbation methods. The
accuracies of energies and densities when using these methods are also
considered.Comment: 14 pages with 18 figures; corrected typos, corrected expression for
first-order energy in section VI and consequently Fig.13, conclusions and
other results unaffecte
Exceptional Superconformal Algebras
Reductive W-algebras which are generated by bosonic fields of spin-1, a
single spin-2 field and fermionic fields of spin-3/2 are classified. Three new
cases are found: a `symplectic' family of superconformal algebras which are
extended by , an and an superconformal algebra.
The exceptional cases can be viewed as arising a Drinfeld-Sokolov type
reduction of the exceptional Lie superalgebras and , and have an
octonionic description. The quantum versions of the superconformal algebras are
constructed explicitly in all three cases.Comment: 16 page
Auxiliary Fields for Super Yang-Mills from Division Algebras
Division algebras are used to explain the existence and symmetries of various
sets of auxiliary fields for super Yang-Mills in dimensions .
(Contribution to G\"ursey Memorial Conference I: Strings and Symmetries)Comment: 7 pages, plain TeX, CERN-TH.7470/9
Quantum double of Heisenberg-Weyl algebra, its universal R-matrix and their representations
In this paper a new quasi-triangular Hopf algebra as the quantum double of
the Heisenberg-Weyl algebra is presented.Its universal R-matrix is built and
the corresponding representation theory are studied with the explict
construction for the representations of this quantum double. \newpageComment: 12 page
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