SU(2) × SU(2) Algebras and the Lorentz Group O(3,3)
نویسندگان
چکیده
منابع مشابه
q-FUZZY SPHERES AND QUANTUM DIFFERENTIALS ON Bq[SU2] AND Uq(su2)
We show that the 2-parameter Podles sphere is a q-fuzzy sphere precisely interpolating between the fuzzy sphere as quotient of the angular momentum algebra U(su2) and the standard q-sphere Cq [S] as subalgebra of the quantum group Cq [SU2]. Whereas the classical sphere as CP 1 can be defined as the algebra generated by the matrix entries of a projector e with trace(e) = 1, the fuzzy-sphere is d...
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The algebra su 2 is derived from two commuting quon algebras for which the parameter q is a root of unity. This leads to a polar decomposition of the shift operators J + and J − of the group SU 2 (with J + = J † − = HUr where H is Hermitean and Ur unitary). The Wigner-Racah algebra of SU 2 is developed in a new basis arising from the simultanenous diagonalization of the commuting operators J 2 ...
متن کاملThe Quantum Double as Quantum Mechanics
We introduce ∗-structures on braided groups and braided matrices. Using this, we show that the quantum double D(Uq(su2)) can be viewed as the quantum algebra of observables of a quantum particle moving on a hyperboloid in q-Minkowski space (a three-sphere in the Lorentz metric), and with the role of angular momentum played by Uq(su2). This provides a new example of a quantum system whose algebr...
متن کامل2 00 2 Operator representations of cross product algebras of Podles ’ quantum spheres
Operator representations of the cross product ∗-algebra O(S2 qc)⋊Uq(su2) of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(S2 qc) of Podles’ spheres are studied. Two classes of representations are described by explicit formulas for the actions of the generators.
متن کاملA ] 2 1 Ju l 2 00 3 Representations of cross product algebras of Podleś quantum spheres
Hilbert space representations of the cross product ∗-algebras of the Hopf ∗-algebra Uq(su2) and its module ∗-algebras O(Sqr) of Podleś spheres are investigated and classified by describing the action of generators. The representations are analyzed within two approaches. It is shown that the Hopf ∗-algebra O(SUq(2)) of the quantum group SUq(2) decomposes into an orthogonal sum of projective Hopf...
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ژورنال
عنوان ژورنال: Symmetry
سال: 2020
ISSN: 2073-8994
DOI: 10.3390/sym12050817