Zobrazeno 1 - 10
of 550
pro vyhledávání: '"Van der Jeugt, J."'
Autor:
Stoilova, N. I., Van der Jeugt, J.
Publikováno v:
J. Phys. A: Math. Theor. 57 (2024) 395206 (17pp)
We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commu
Externí odkaz:
http://arxiv.org/abs/2409.14789
Autor:
Stoilova, N. I., Van der Jeugt, J.
A ${\mathbb Z}_2\times{\mathbb Z}_2$-graded Lie algebra $\mathfrak g$ is a ${\mathbb Z}_2\times{\mathbb Z}_2$-graded algebra $\mathfrak g$ with a bracket $[|. , . |]$ that satisfies certain graded versions of the symmetry and Jacobi identity. In part
Externí odkaz:
http://arxiv.org/abs/2408.09274
Autor:
Stoilova, N. I., Van der Jeugt, J.
Publikováno v:
J. Phys. A: Math. Theor. 57 095202 (2024)
A $Z_2\times Z_2$-graded Lie superalgebra $g$ is a $Z_2\times Z_2$-graded algebra with a bracket $[.,.]$ that satisfies certain graded versions of the symmetry and Jacobi identity. In particular, despite the common terminology, $g$ is not a Lie super
Externí odkaz:
http://arxiv.org/abs/2402.11952
Autor:
Stoilova, N. I., Van der Jeugt, J.
Publikováno v:
J. Math. Phys. 64, 061702 (2023)
We construct classes of $Z_2 \times Z_2$-graded Lie algebras corresponding to the classical Lie algebras, in terms of their defining matrices. For the $Z_2 \times Z_2$-graded Lie algebra of type $A$, the construction coincides with the previously kno
Externí odkaz:
http://arxiv.org/abs/2305.18604
Autor:
Stoilova, N. I., Van der Jeugt, J.
Publikováno v:
Journal of Lie Theory 33 (2023), No. 4, 1005--1008
In this short communication we show how the Lie algebra $\mathfrak{g}_2$ can easily be described as a free Lie algebra on 3 generators, subject to some simple quadruple relations for these generators.
Externí odkaz:
http://arxiv.org/abs/2212.04131
Autor:
Stoilova, N. I., Van der Jeugt, J.
Publikováno v:
Springer Proceedings in Mathematics & Statistics, 396, 263 (2022)
It has been known for a long time that there are two non-trivial possibilities for the relative commutation relations between a set of $m$ parafermions and a set of $n$ parabosons. These two choices are known as ``relative parafermion type'' and ``re
Externí odkaz:
http://arxiv.org/abs/2112.14118
Autor:
Stoilova, N. I., Van der Jeugt, J.
Publikováno v:
J. Phys. A: Math. Theor. 55 045201 (2022)
The parastatistics Fock spaces of order $p$ corresponding to an infinite number of parafermions and parabosons with relative paraboson relations are constructed. The Fock spaces are lowest weight representations of the $Z_2 \times Z_2$-graded Lie sup
Externí odkaz:
http://arxiv.org/abs/2112.12811
Publikováno v:
J. Phys. A: Math. Theor. 53 (2020) 485301
We present an exact solution of a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent on the position. The free Hamiltonian of the proposed model has the form of the Ben
Externí odkaz:
http://arxiv.org/abs/2010.04477
Autor:
Stoilova, N. I., Van der Jeugt, J.
Publikováno v:
Phys. Lett. A 384, 126421 (2020)
New formulas are given for the grand partition function of paraboson systems of order p with n orbitals and parafermion systems of order p with m orbitals. These formulas allow the computation of statistical and thermodynamic functions for such syste
Externí odkaz:
http://arxiv.org/abs/2005.03704
Autor:
Stoilova, N. I., Van der Jeugt, J.
Publikováno v:
J. Phys. A: Math. Theor. 52, 135201 (28pp) (2019)
The algebraic structure generated by the creation and annihilation operators of a system of m parafermions and n parabosons, satisfying the mutual parafermion relations, is known to be the Lie superalgebra osp(2m+1|2n). The Fock spaces of such system
Externí odkaz:
http://arxiv.org/abs/1904.00061