University of Wisconsin Colleges, USA
Title: New mathematics for classical and quantum physics
Biography: Alexey Kryukov
A recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory will be presented. In the framework, states of a classical particle are identified with Dirac deltas. The classical space is "made" of these functions and becomes a sub-manifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space sub-manifold) yields the Born rule for transitions between arbitrary quantum states.