L-functionals: Applications to QED, Gravity and Disordered Systems

Quantizing classical systems we consider Hilbert spaces equipped with representations of canonical commutation relations (CCR).  In the case of an infinite number of degrees of freedom it is necessary to consider representations of  CCR that are not equivalent to the standard Fock representation (for example in QED the "photon cloud" dressing an electron does not belong to Fock space). In this case it  is convenient to represent states by  some functionals (L-functionals) that are well defined for every vector or density matrix in any representation of CCR or CAR. The formalism of L-functionals is as convenient as the formalism based on Hilbert spaces (and sometimes more convenient). In particular, the scattering matrix in this formalism (inclusive scattering matrix) is closely related to inclusive cross sections.

I'll explain how the formalism of L-functionals  can be applied to systems with quenched disorder, to infrared problem in quantum electrodynamics and to similar problem in linearized gravity.