منابع مشابه
Statistical Geometry in Quantum Mechanics
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the space of all square-integrable functions. More precisely, by consideration of the square-root density function we can regard M as a ...
متن کاملQuantum Statistical Mechanics, L-series and Anabelian Geometry
It is known that two number fields with the same Dedekind zeta function are not necessarily isomorphic. The zeta function of a number field can be interpreted as the partition function of an associated quantum statistical mechanical system, which is a C-algebra with a one parameter group of automorphisms, built from Artin reciprocity. In the first part of this paper, we prove that isomorphism o...
متن کاملQuantum Mechanics of Geometry
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate students in physics. As an illustrative application, I indicate how some of the detailed features of the micro-structure of geometry can be tested using black h...
متن کاملGeometry and Quantum Mechanics
Attempts for a geometrical interpretation of Quantum Theory were made, notably the deBroglie-Bohm formulation. This was further refined by Santamato who invoked Weyl's geometry. However these attempts left a number of unanswered questions. In the present paper we return to these two formulations, in the context of recent studies invoking fuzzy spacetime and noncom-mutative geometry. We argue th...
متن کاملQuantum Mechanics_ Quantum statistical mechanics
Quantum statistical mechanics is statistical mechanics applied to quantum mechanical systems. In quantum mechanics a statistical ensemble (probability distribution over possiblequantum states) is described by a density operatorS, which is a nonnegative, self-adjoint, trace-classoperator of trace 1 on the Hilbert space Hdescribing the quantum system. This can be shown under various mathematical ...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
سال: 1998
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.1998.0266