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REPRESENTATION OF STATE PROPERTY SYSTEMS D. AERTS AND S. PULMANNOVA
 

Summary: REPRESENTATION OF STATE PROPERTY SYSTEMS
D. AERTS AND S. PULMANNOVA
Abstract. A `state property system' is the mathematical structure which
models an arbitrary physical system by means of its set of states, its set of
properties, and a relation of `actuality of a certain property for a certain state'.
We work out a new axiomatization for standard quantum mechanics, starting
with the basic notion of state property system, and making use of a general-
ization of the standard quantum mechanical notion of `superposition' for state
property systems.
1. Introduction
In standard quantum mechanics a state pc of a quantum entity S is represented by
the one dimensional subspace or the ray c of a separable complex Hilbert space H.
An experiment eA testing an observable A is represented by a self adjoint operator
A on H, and the set of outcomes of this experiment eA is the spectrum spec(A) of
this self-adjoint operator A. Measurable subsets B spec(A) represent the events
(in the sense of probability theory) of outcomes. The interaction of the experiment
eA with the physical entity being in state pc is described in the following way: (1)
the probability for a specific event B spec(A) to occur if the entity is in a specific
state pc is given by c, PB(c) , where PB is the spectral projection corresponding to
B, c is the unit vector in the ray c representing state pc, and , is the inproduct

  

Source: Aerts, Diederik - Leo Apostel Centre, Vrije Universiteit Brussel

 

Collections: Multidisciplinary Databases and Resources; Physics