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81.
Recent development brings new results on the interplay of states on operator algebras and axiomatics of quantum mechanics.
Neither hidden space in the sense of Kochen and Specker nor approximate hidden variables exist on von Neumann algebras. Tracial
properties of states are connected with dispersions. The axioms on composite systems simplify to state extension properties. 相似文献
82.
Anna?AvalloneEmail author Paolo?Vitolo 《International Journal of Theoretical Physics》2005,44(7):793-806
Let L be a lattice ordered effect algebra. We prove that the lattice uniformities on L which make uniformly continuous the operations − and + of L are uniquely determined by their system of neighborhoods of 0 and form a distributive lattice. Moreover we prove that every
such uniformity is generated by a family of weakly subadditive [0,+∞]-valued functions on L. 相似文献
83.
Carlos Castro 《Foundations of Physics》2005,35(6):971-1041
We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford ClC (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale
. Previous work led us to show from first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship
, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl (1, 7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit. 相似文献
84.
We summarize and deepen existing results on systems of orthogonal pure states in the context of Jordan–Banach (JB) algebras
and C* algebras. Especially, we focus on noncommutative generalizations of some principles of topology of locally compact
spaces such as exposing points by continuous functions, separating sets by continuous functions, and multiplicativity of pure
states. 相似文献
85.
86.
In this paper we consider two von Neumann subalgebras and of a type II1 factor . For a map φ on , we define
87.
Continuity of Effect Algebra Operations in the Interval Topology 总被引:1,自引:0,他引:1
We study the continuity of and of effect algebras in the interval topology, and present several examples of effect algebras with interesting properties. 相似文献
88.
Ideal Topology on Effect Algebras 总被引:2,自引:0,他引:2
The ideals of effect algebras induce a topology on effect algebras. The operations and of effect algebras are continuous with respect to this topology. 相似文献
89.
R.M. Green 《Journal of Algebraic Combinatorics》2004,19(2):173-196
Heaps of pieces were introduced by Viennot and have applications to algebraic combinatorics, theoretical computer science and statistical physics. In this paper, we show how certain combinatorial properties of heaps studied by Fan and by Stembridge are closely related to the properties of a certain linear map
E
associated to a heap E. We examine the relationship between
E
and
F
when F is a subheap of E. This approach allows neat statements and proofs of results on certain associative algebras (generalized Temperley–Lieb algebras) that are otherwise tricky to prove. The key to the proof is to interpret the structure constants of the aforementioned algebras in terms of the maps . 相似文献
90.
Karin Erdmann Miles Holloway Rachel Taillefer Nicole Snashall Øyvind Solberg 《K-Theory》2004,33(1):67-87
Support varieties for any finite dimensional algebra over a field were introduced in (Proc. London Math. Soc. 88 (3) (2004) 705–732) using graded subalgebras of the Hochschild cohomology ring. We mainly study these varieties for selfinjective algebras under appropriate finite generation hypotheses. Then many of the standard results from the theory of support varieties for finite groups generalize to this situation. In particular, the complexity of the module equals the dimension of its corresponding variety, all closed homogeneous varieties occur as the variety of some module, the variety of an indecomposable module is connected, the variety of periodic modules are lines and for symmetric algebras a generalization of Webbs theorem is true. As a corollary of a more general result we show that Webbs theorem generalizes to finite dimensional cocommutative Hopf algebras.Received November 2003Mathematics Subject Classifications (2000) Primary: 16E40, 16G10, 16P10, 16P20; Secondary: 16G70. 相似文献