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Notes on algebraic invariants for non-commutative dynamical systems [PDF]
Communications in Mathematical Physics, 1979 We consider an algebraic invariant for non-commutative dynamical systems naturally arising as the spectrum of the modular operator associated to an invariant state, provided certain conditions of mixing type are present. This invariant turns out to be exactly the annihilator of the invariantT of Connes.
openaire +3 more sources
Dynamical noncommutativity [PDF]
, 2002 We present a model of Moyal-type noncommutativity with time-depending noncommutativity parameter and the exact gauge invariant action for the U(1) noncommutative gauge theory.
A. Sitarz +5 more
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On a Trivial Family of Noncommutative Integrable Systems [PDF]
, 2013 We discuss trivial deformations of the canonical Poisson brackets associated with the Toda lattices, relativistic Toda lattices, Henon-Heiles, rational Calogero-Moser and Ruijsenaars-Schneider systems and apply one of these deformations to construct a ...
Tsiganov, Andrey V.
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A Variational Formulation of Symplectic Noncommutative Mechanics
, 2007 The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space.
Anderson I. +5 more
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Bergelson's Theorem for weakly mixing C*-dynamical systems
, 2006 We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khintchine's recurrence theorem obtained by Bergelson in the measure theoretic case.
Duvenhage, Rocco
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From Noncommutative Sphere to Nonrelativistic Spin [PDF]
, 2010 Reparametrization invariant dynamics on a sphere, being parameterized by angular momentum coordinates, represents an example of noncommutative theory.
Deriglazov, Alexei A.
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(Pre)-Inflationary Dynamics with Starobinsky Potential in Noncommutative Effective LQC
UniverseIn this work, we investigate the (pre)-inflationary dynamics of a flat, homogeneous, and isotropic universe governed by the Starobinsky potential within the framework of noncommutative effective loop quantum cosmology.
Luis Rey Díaz-Barrón +3 more
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A Geometric Approach to Noncommutative Principal Torus Bundles
, 2012 A (smooth) dynamical system with transformation group $\mathbb{T}^n$ is a triple $(A,\mathbb{T}^n,\alpha)$, consisting of a unital locally convex algebra $A$, the $n$-torus $\mathbb{T}^n$ and a group homomorphism $\alpha:\mathbb{T}^n\rightarrow\Aut(A ...
Wagner, Stefan
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Quantum Probability Theory [PDF]
, 2005 The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von Neumann in ...
Redei, Miklos, Summers, Stephen J.
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A Non-Canonical Classical Mechanics
AppliedMathBased on noncommutative relations and the Dirac canonical dequantization scheme, I generalize the canonical Poisson bracket to a deformed Poisson bracket and develop a non-canonical formulation of the Poisson, Hamilton, and Lagrange equations in the ...
Shi-Dong Liang
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