I am planning to consider some basic notions of quantum mechanics, quantum field theory and quantum statistical physics. In particular, I will discuss the notions of decoherence, of particle and quasiparticle, of scattering matrix and inclusive scattering matrix. The course is based on algebraic and geometric approaches to quantum theory. (The standard approach when states are represented by vectors in Hilbert space is not appropriate for systems with an infinite number of degrees of freedom.) In algebraic approach the starting point is an associative algebra with involution, self-adjoint elements of this algebra are identified with observables, the states are represented by positive linear functional on the algebra. (Quasi)particles are defined as elementary excitations of translation-invariant states. Scattering matrix of elementary excitations can be expressed in terms of Green functions (LSZ formula). Inclusive scattering matrix can be expressed in terms of generalized Green functions that appear in Keldysh formalism of non-equilibrium statistical physics. Geometric approach suggested in my papers starts with a convex set interpreted as a set of states. This approach also allows us to define elementary excitations and to develop scattering theory. It can be used to show that any theory can be obtained from classical mechanics if we can measure only a part of classical observables.

Please, address Daniil Rafikov, rafikov@mi-ras.ru, for Zoom data.

Financial support. The course is supported by the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2022-265).

Transcript of lectures

Lecturer
Schwarz Albert S

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center