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
   [PDF]

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.
View original: http://arxiv.org/abs/1305.5244

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