Quasi-spaces an the foundation of quantum mechanics

Domenech, Graciela and Holik, Federico and Krause, Décio (2008) Quasi-spaces an the foundation of quantum mechanics.

Abstract

Our aim in this paper is to take quite seriously Heinz
Post's claim that the non-individuality and the indiscernibility of
quantum objects should be introduced right at the start, and
not made a posteriori by introducing symmetry conditions. Using a
different mathematical framework, namely, quasi-set theory, we avoid
working within a label-tensor-product-vector-space-formalism, to use
Redhead and Teller's words, and get a more intuitive way of dealing
with the formalism of quantum mechanics, although the underlying
logic should be modified. Thus, this paper can be regarded as a
tentative to follow and enlarge Heinsenberg's suggestion that new
phenomena require the formation of a new ``closed" (that is,
axiomatic) theory, coping also with the physical theory's underlying
logic and mathematics.