Spin projection operators in quantum field theory and representations of the Brauer algebra
Seminars
Seminar “Modern Mathematical Physics”
Date and Time: Monday, 4 October 2021, at 1:00 PM
Venue: Online conference on Zoom, Bogoliubov Laboratory of Theoretical Physics
Seminar topic: “Spin projection operators in quantum field theory and representations of the Brauer algebra” (based on PhD thesis)
Speaker: M.A. Podoinitsyn
Abstract:
On the basis of the Wigner unitary representations of the covering group ISL(2,C) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. These wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-tensors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal operators).
With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal operators) and then find relativistic spin projection operators for half integer spins. These spin projection operators determine the numerators in the propagators of fields of relativistic particles. We deduce generalizations of the fully symmetric Behrends-Fronsdal operators for arbitrary space-time dimensions D>2.
A new class of representations of the Brauer algebra that centralizes the action of orthogonal and symplectic groups in tensor spaces is found. These representations make it possible to apply the technique of building primitive orthogonal idempotents of the Brauer algebra to the construction of integer spin Behrends-Fronsdal type projectors of an rbitrary type of symmetries.