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On some algebraic formulations within universal enveloping algebras related to superintegrability
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
We report on some recent purely algebraic approaches to superintegrable systems from the perspective of subspaces of commuting polynomials in the enveloping algebras of Lie algebras that generate quadratic (and eventually ...
A note on entanglement classification for tripartite mixed states
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
We study the classification of entanglement in tripartite systems by using Bell-type inequalities and principal basis. By using Bell unctions and the generalized three dimensional Pauli operators, we present a set of Bell ...
On generalized Heun equation with some mathematical properties
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
We study the analytic solutions of the generalized Heun equation, (α0 + α1 r + α2 r2 + α3 r3) y′′ + (β0 + β1 r + β2 r2) y′ + (ε0 + ε1 r) y = 0, where |α3| + |β2|≠ 0, and {αi}3i=0, {βi}2i=0, {εi}1i=0 are real parameters. ...
Maxwell-Chern-Simons-Higgs theory
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
We consider the three dimensional electrodynamics described by a complex scalar field coupled with the U(1) gauge field in the presence of a Maxwell term, a Chern-Simons term and the Higgs potential. The Chern-Simons term ...
On the Wess-Zumino Model: a supersymmetric field theory
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
We consider the free massless Wess-Zumino Model in 4D which describes a supersymmetric field theory that is invariant under the rigid or global supersymmetry transformations where the transformation parameter ϵ (or ϵ ) ...
Swanson Hamiltonian revisited through the complex scaling method
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
In this work, we study the non-hermitian PT-symmetry Swanson Hamiltonian in the framework of the Complex Scaling Method. We show that by applying this method we can work with eigenfunctions that are square-integrable both ...
Complex topological soliton with real energy in particle physics
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
We summarise the procedure used to find the classical masses of Higgs particle, massive gauge boson and t’Hooft-Polyakov monopole in non-Hermitian gauge field theory. Their physical regions are explored, and the mechanism ...
Conserved quantities in non-hermitian systems via vectorization method
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time (PT) symmetry that are best understood as systems ...
How to understand the structure of beta functions in six-derivative Quantum Gravity?
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
We extensively motivate the studies of higher-derivative gravities, and in particular we emphasize which new quantum features theories with six derivatives in their definitions possess. Next, we discuss the mathematical ...
Rational extension of many particle systems
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
In this talk, we briefly review the rational extension of many particle systems, and is based on a couple of our recent works. In the first model, the rational extension of the truncated Calogero-Sutherland (TCS) model is ...