Working Seminar on Wednesdays / Spring2024


Working Seminar on Mathematical Physics
of HSE University and Skoltech Igor Krichever Center for Advanced Studies
on Wednesdays at 16.20 at aud. 110 of the Faculty of Mathematics [ + zoom ]

February 7, 2024 / Nikita Belousov (Steklov Inst., St.Petersburg)
= = Quantum Toda-Calogero-Ruijsenaars systems
February 14, 2024 / Anton Rarovskii (Skoltech, HSE Univ.)
= = Frobenius structures and orbifold equivalence for quasihomogeneous singularities (1/2)
February 21, 2024 / Anton Rarovskii (Skoltech, HSE Univ.)
= = Frobenius structures and orbifold equivalence for quasihomogeneous singularities (2/2)
February 28, 2024 / Leonid Cherepanov (HSE Univ.)
= = Ruijsenaars system, Macdonald operators and limiting procedures (1/2)
March 6, 2024 / Alexander Belavin (Landau Inst.)
= = Conformal bootstrap and heterotic string Gepner models
March 13, 2024 / Leonid Cherepanov (HSE Univ.)
= = Ruijsenaars system, Macdonald operators and limiting procedures (2/2)
March 20, 2024 / Artem Sidorenko (HSE Univ.)
= = Rod structure of some solutions of Einstein’s equations in vacuum
March 27, 2024 / Anton Il’yn (Lebedev Inst., HSE Univ.), Alexey Kopyev (Lebedev Inst.)
= = Fundamentals of the K41 theory
April 10, 2024 / Gleb Ananiev (HSE Univ.)
= = Three-dimensional gravity
April 17, 2024 / Daniil Lopatin (Skoltech, MIPT)
= = Local quench within the Keldysh technique


April 24, 2024
Alexander Savchenko
(Skoltech, HSE Univ.)
Linearity of actions and bilinear relations for multicomponent fermionic operators

We start with an intro to fermionic operators and their correspondent vacuum states – the ‘Dirac Sea’. Using their algebraic (anticommuting) relations, we prove a linearity of an algebraic and group-like adjoint actions – going through simple cases to more general.
As a result, we get concrete expressions of adjoint actions in the multi-component case. For example, showing that for a row and column consisting of fermions, the actions turn out to be an opposite of each other.
This fact induces the bilinear relation for fermionic operators, satisfied by group-like elements made up from fermions, which completes the report

[ link to access the Seminar – zoom 84806604382, ID 848 0660 4382, Code 1]
arXiv