Mon père F.A. Berezin

The groupoid of bifractional transformations

“…The Berezin formalism [15][16][17][18] represents an operator Θ with the analytic function L(z, w * ; θ 1 , θ 2 |Θ) defined below. It shows that the L(z, z * ; θ 1 , θ 2 |Θ 1 Θ 2 ) of the product of two operators Θ 1 Θ 2 , can be expanded as a Taylor series, where the first term is the product L(z, z * ; θ 1 , θ 2 |Θ 1 )L(z, z * ; θ 1 , θ 2 |Θ 2 ) (which is classical in the sense that it is commutative), and the other terms are quantum corrections (and go to zero in the limit → 0).…”

Point perturbations in constant curvature spaces

“…where the coupling constant ε should be considered as infinitely small [12,14,18,19]. More precisely, adding a point perturbation potential εδ q (x) is equivalent to a boundary condition at the point q [12,20,21].…”

“…[12]). It should be mentioned that the first correct mathematical description of the model in the framework of the theory of a self-adjoint extensions of symmetric operators was given in [14]. We use Krein's technique to construct self-adjoint extension which gives us the model in question.…”

The equations of motion for a classical color particle in background non-Abelian bosonic and fermionic fields

“…The account for the spin degree of freedom in the general dynamics of the particle will be considered in our next paper [13]. In particular, there it will be shown how one can connect the c -number spinorsψ α and ψ α with the pseudovector and pseudoscalar dynamical variables ξ µ , µ = 0, 1, 2, 3 and ξ 5 commonly used in a description of the spin degree of freedom of massive spinning particles, and which in turn are elements of the Grassmann algebra [14,15].…”