NDLI: Dynamics and Potentials

Content Provider	Springer Nature Link
Author	Araki, Huzihiro
Copyright Year	2007
Abstract	For a system of spins and Fermions (satisfying graded commutation relations) on a lattice, a C-dynamics can be associated with a potential, which has a natural convergence property and a very convenient standardness property. The existence and the uniqueness of the potential with the required properties for any C-dynamics under consideration, the form of the convergence property and the standardness property are all new results, for which the only assumption for the dynamics is that any strictly localized operator has the time derivative, a condition minimally necessary for the description of a dynamics in terms of a potential. The standardness brings about the unique choice of the potential (out of multitudes of equivalent potentials) by distinguishing the genuine n-body potential from mingled k-body potentials with k < n. An energy estimate is shown as a simple and yet non-trivial example of effectiveness of the standardness property, with an aid of non-commutative conditional expectations – an important tool of this entire analysis. The key point in the above analysis is a bijective correspondence of a linear space of -derivations and that of standard potentials, where the -derivations considered are the restriction of the generators of the dynamics to strictly local operators.
Ending Page	306
Page Count	10
Starting Page	297
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	2-3
Volume Number	82
Language	English
Publisher	Springer Netherlands
Publisher Date	2007-11-27
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	spin algebra Applications of selfadjoint operator algebras to physics Mathematical and Computational Physics Fermion algebra standardness equilibrium statistical mechanics C-dynamics Geometry graded commutation relations Quantum equilibrium statistical mechanics (general) convergence condition non-commutative conditional expectation Group Theory and Generalizations potential Statistical Physics -derivation
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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