Mathematics Colloquia and Seminars

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In algebraic approach to quantum theory the main object is an associative algebra with involution and the states are positive linear functionals on this algebra. I show that one can give another formulation of quantum theory where the main object is the cone of states. This formulation is based on the derivation of probabilities in quantum theory from the interaction with environment (from decoherence). It allows us to construct new models, in particular, in the language of Jordan algebras closely related to homogeneous cones.

I show also how one can analyze collisions of particles and quasiparticles in algebraic and geometric approach. This analysis is based on the notion of inclusive scattering matrix that will be discussed also from different viewpoint in my talk in Physics Dept ( Monday, April 29, 1:30 PM, room 432).