Uhlhorn theorem
WebBy the Uhlhorn theorem (which generalized the famous Wigner theorem; see, e.g., [18]), the or-thogonality structure of the projective space of H also determines its Hilbert space structure up to unitary or anti-unitary if dimH ≥ 3 (see, e.g., [19, Corol-lary 2.2.2]). In the case when the (complex) linear structure of the Hilbert space WebA result that has been proved to be true (using operations and facts that were already known). Example: The "Pythagoras Theorem" proved that a2 + b2 = c2 for a right angled triangle. Other examples: • Intermediate Value Theorem • Binomial Theorem • Fundamental Theorem of Arithmetic • Fundamental Theorem of Algebra Lots more!
Uhlhorn theorem
Did you know?
WebThis theorem has since been generalized under the name of Uhlhorn’s theorem [2]. The latter is based on a less restrictive assumption: it is su cient to request that h 1j 2i= 0 ()hT 1jT 2i= 0 (6) to ensure that T is either unitary or anti-unitary. In any case, the conclusion is the same: a symmetry operator is necessarily unitary or anti-unitary. Web20 Jan 2024 · Based on the fundamental theorem of projective geometry, U. Uhlhorn established a version of Wigner’s famous theorem on the structure of quantum …
Web6 Sep 2002 · We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. Web7 Dec 2024 · Here, we extend this result by showing that an essential one among these hypotheses—the need of unitary transforms to relate different contexts—can be removed and is better seen as a necessary consequence of Uhlhorn’s theorem. View Full-Text Keywords: quantum mechanics; contextuality; Gleason’s theorem; Uhlhorn’s theorem
Webversion’’ of the fundamental theorem of projective geometry. This result enablesustouseoperatoralgebraictoolstoattacktheproblem.Wenote that this kind of … Web22 Dec 2004 · Wigner's theorem states that a symmetry operation of a quantum system is induced by a unitary or an anti‐unitary transformation. This note presents a detailed proof …
WebThe Wigner theorem, in its Uhlhorn’s formulation, states that a bijective transformation of the set of all one-dimensional linear subspaces of a complex Hilbert space which …
WebPreservers of matrix pairs with a fixed inner product value internet service providers near 30078WebWe present an operator algebraic approach to Wigner's unitary-antiunitary theorem using some classical results from ring theory. To show how effective this approach is, we prove … newcrest annual report 2021WebWe present an analogue of Uhlhorn’s version of Wigner’s theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. internet service providers near 32818WebB_IV Uhlhorn-Wigner Theorem 1 Real Space 2 Complex Space V Representations of the Galileo and Poincaré Groups: Mass, Spin and Energy A Galileo Group B Poincaré Group A_V Some Properties of the Operators S and W_2 1 Operator S 2 Eigenvalues of the Operator W_2 B_V Geometric Displacement Group newcrest apartmentsWeb26 Jul 2010 · As a partial generalisation of the Uhlhorn theorem to Hilbert -modules, we show in this article that the module structure and the orthogonality structure of a Hilbert -module determine its Hilbert -module structure. In fact, we have a more general result as follows. Let be a -algebra, and be Hilbert -modules, and be the ideal of generated by . newcrest bidWebLinear orthogonality preservers of Hilbert C ∗ -modules over general C ∗ -algebras newcrest base game save fileWeb1 Oct 2002 · Abstract. We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This … internet service providers near 32828