Thursday, May 23, 2013

1305.5244 (Newton da Costa et al.)

A formal framework for the study of the notion of undefined particle
number in quantum mechanics

Newton da Costa, Federico Holik
It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position -supported by E. Schrodinger- asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an unde?ned particle number. In this work we present a set theoretical framework for the description of unde?ned particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions.
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