arXiv subjects
Publications and source records attributed to Igor Frolov.
It is well known that the inclusive cross section in QED is infrared finite. In the standard diagram techniques this result follows from cancellation of infrared divergences. We construct a new diagram technique where the diagrams for inclusive cross sections (and, more generally, for inclusive scattering matrix) do not contain infrared divergences.
In quantum mechanics, one can express the evolution operator and other quantities in terms of functional integrals. The main goal of this paper is to prove corresponding results in the geometric approach to quantum theory. We apply these results to the formalism of L-functionals.
This is a non-standard exposition of the main notions of quantum mechanics and quantum field theory including some recent results. It is based on the algebraic approach where the starting point is a star-algebra and on the geometric approach where the starting point is a convex set of states. Standard formulas for quantum probabilities are derived from decoherence. This derivation allows us to go beyond quantum theory in the geometric approach. Particles are defined as elementary excitations of the ground state (and quasiparticles as elementary excitations of any translation invariant state). The conventional scattering matrix does not work for quasiparticles (and even for particles if the theory does not have particle interpretation). The analysis of scattering in these cases is based on the notion of inclusive scattering matrix, closely related to inclusive cross-sections. It is proven that the conventional scattering matrix can be expressed in terms of Green functions (LSZ formula) and the inclusive scattering matrix can be expressed in terms of generalized Green functions that appear in the Keldysh formalism of non-equilibrium statistical physics. The derivation of the expression of the evolution operator and other physical quantities in terms of functional integrals is based on the notion of the symbol of an operator; these arguments can be applied also in the geometric approach. The notion of inclusive scattering matrix makes sense in the geometric approach (but it seems that one cannot give a definition of the conventional scattering matrix in this situation). The geometric approach is used to show that quantum mechanics and its generalizations can be considered as classical theories where our devices can measure only a part of observables.