Search results

...ps0000kass }}</ref> Given a [[Lie algebra]] <math>\mathfrak{g}</math>, the quantum enveloping algebra is typically denoted as <math>U_q(\mathfrak{g})</math>. *[[Quantum group]] ...

...ation}}</ref><ref>{{Citation|last1=Majid|first1=Shahn|title=Foundations of quantum group theory|year=1995|publisher=Cambridge University Press|doi=10.1017/CBO == Drinfeld quantum double == ...

...erator|operators]] are particularly notable for providing solutions to the quantum [[Yang–Baxter equation]], which originated in [[statistical mechanics]], an ...ghtarrow V \otimes_k V</math>. The operator <math>R</math> satisfies the ''quantum Yang-Baxter equation'' if ...

...ted by a given braided vectorspace. They appear as quantum Borel part of [[quantum group]]s and often (e.g. when finite or over an abelian group) possess an [ [[Category:Quantum groups]] ...

...athematical field of [[knot theory]], a '''quantum knot invariant''' or '''quantum invariant''' of a [[knot (mathematics)|knot]] or link is a linear sum of [[ ...l|author1-link= Gail Letzter |title = Invariant differential operators for quantum symmetric spaces, II|year = 2004}}</ref> ...

..., and there exists an exterior derivative. Correspondingly, a first order quantum differential calculus means at least the following: ...dge product]] and often denoted <math>\wedge</math>. The noncommutative or quantum [[de Rham cohomology]] is defined as the cohomology of this complex. ...

...e=1 Nov 2013|class=math.QA|eprint=1311.0278}}</ref> a concept related to [[quantum group]]s and [[Hopf algebra]]s. ...

...d to construct [[Configuration state function]]s (CSFs) in computational [[quantum chemistry]]. As reflected in its name, the method uses the mathematical pro ...year=1978| last1=Shavitt| first1=Isaiah| journal=International Journal of Quantum Chemistry| volume=14| pages=5–32}}</ref> introduced the graphical aspect (G ...

...|url=https://doi.org/10.1093/oso/9780198886723.001.0001 |title=Topological Quantum |date=2023-09-29 |publisher=Oxford University PressOxford |isbn=0-19-888672 ...1-06-10 |title=Composite particle construction of the Fibonacci fractional quantum Hall state |url=https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103. ...

...ies and modular tensor categories to the [[algebraic theory of topological quantum information]], this theorem has found various uses within [[mathematical ph == Interpretation in terms of topological quantum field theory == ...

...ries can be used to define projective representations of the mapping class groups of all closed surfaces. ...mathcal{C}</math>, where in both these formulas <math>d_{A}</math> are the quantum dimensions of the simple objects. ...

...example is the [[Toric code|toric code model]], which is a special case of quantum double model by setting input group as cyclic group <math>\mathbb{Z}_2</mat == Kitaev quantum double model == ...

...ermine which one it is. This assumption distinguishes such techniques from quantum tomography, which does not impose additional requirements on the state of t ...this deficiency. With exceptions, these techniques can be divided into two groups, namely those based on error minimization and then those that allow the sta ...

...r spherically symmetric potentials. The [[representation theory]] of these groups leads to [[irreducible representation]]s, which for SO(3) gives the angular ...inear map|antilinear]], and including these in the symmetry group leads to groups including both unitary and antiunitary operators. ...

...ns]] in Warsaw and gave a talk titled ''Integrable models in classical and quantum field theory''. * {{cite journal|title=Quantum inverse problem method I|journal=Theoretical and Mathematical Physics|volum ...

{{Short description|Method used to solve integrable many-body quantum systems}} ...|last1=Takhtadzhan |first1=L A |last2=Faddeev |first2=Lyudvig D |title=The Quantum Method of the Inverse Problem and the Heisenberg Xyz Model |journal=Russian ...

...an mathematician known for her research in [[representation theory]] and [[quantum logic gate]]s. Formerly a professor of mathematics at [[Pennsylvania State ...and, characterizing [[Quantum logic gate#Universal quantum gates|universal quantum logic gates]].{{r|zkg}}{{ran|UQG}} ...

...">{{cite book|last=C.Cohen Tannoudji|author2=B.Diu |author3=F.Laloe |title=Quantum mechanics|publisher=Wiley|year=1999|isbn=978-0-471-56952-7}}</ref> ...1 (\text{except } J=0 \rightarrow J=0)</math> (J: [[total angular momentum quantum number]]) ...

...nd 2000s, his research dealt with [[knot theory]] (and its algebras) and [[quantum group]]s. ...Invited Speaker with talk ''Geometric representation theory of compact Lie groups'' at the [[International Congress of Mathematicians|ICM]] in [[Berkeley, Ca ...

...nalog of the classical correspondence between analytic local groups ([[Lie groups]]) and [[Lie algebra]]s. ...E.+Tarasov+Quantum+Mechanics+of+Non-Hamiltonian+and+Dissipative+Systems. ''Quantum Mechanics of Non-Hamiltonian and Dissipative Systems.'' Elsevier Science, A ...