Clifford algebras, Fourier transforms, and quantum mechanics
H De Bie - Mathematical Methods in the Applied Sciences, 2012 - Wiley Online Library
In this review, we give an overview of several recent generalizations of the Fourier transform,
related to either the Lie algebra or the Lie superalgebra. In the former case, one obtains …
related to either the Lie algebra or the Lie superalgebra. In the former case, one obtains …
[HTML][HTML] Divergence theorems and the supersphere
J Groeger - Journal of Geometry and Physics, 2014 - Elsevier
The transformation formula of the Berezin integral holds, in the non-compact case, only up to
boundary integrals, which have recently been quantified by Alldridge–Hilgert–Palzer. We …
boundary integrals, which have recently been quantified by Alldridge–Hilgert–Palzer. We …
The orthosymplectic supergroup in harmonic analysis
K Coulembier - arXiv preprint arXiv:1202.0668, 2012 - arxiv.org
The orthosymplectic supergroup OSp (m| 2n) is introduced as the supergroup of isometries
of flat Riemannian superspace R^{m| 2n} which stabilize the origin. It also corresponds to …
of flat Riemannian superspace R^{m| 2n} which stabilize the origin. It also corresponds to …
Conformal symmetries of the super Dirac operator
K Coulembier, H De Bie - Revista matemática iberoamericana, 2015 - ems.press
Conformal symmetries of the super Dirac operator Page 1 Rev. Mat. Iberoam. 31 (2015), no. 2,
373–410 doi 10.4171/rmi/838 c European Mathematical Society Conformal symmetries of the …
373–410 doi 10.4171/rmi/838 c European Mathematical Society Conformal symmetries of the …
Introductory clifford analysis
H De Schepper, F Sommen - Operator theory, 2015 - biblio.ugent.be
In this chapter an introduction is given to Clifford analysis and the underlying Clifford
algebras. The functions under consideration are defined on Euclidean space and take …
algebras. The functions under consideration are defined on Euclidean space and take …
-model and Vertex-Reinforced Jump Process the Regular Trees: Infinite-Order Transition and an Intermediate Phase
P Wildemann, R Poudevigne - arXiv preprint arXiv:2309.01221, 2023 - arxiv.org
We explore the supercritical phase of the vertex-reinforced jump process (VRJP) and the
$\mathbb {H}^{2| 2} $-model on rooted regular trees. The VRJP is a random walk, which is …
$\mathbb {H}^{2| 2} $-model on rooted regular trees. The VRJP is a random walk, which is …
A Fock Model and the Segal-Bargmann Transform for the Minimal Representation of the Orthosymplectic Lie Superalgebra
The minimal representation of a semisimple Lie group is a'small'infinite-dimensional
irreducible unitary representation. It is thought to correspond to the minimal nilpotent …
irreducible unitary representation. It is thought to correspond to the minimal nilpotent …
A minimal representation of the orthosymplectic Lie supergroup
We construct a minimal representation of the orthosymplectic Lie supergroup for even,
generalizing the Schrödinger model of the minimal representation of to the super case. The …
generalizing the Schrödinger model of the minimal representation of to the super case. The …
Fischer decomposition for polynomials on superspace
R Lávička, D Šmíd - Journal of Mathematical Physics, 2015 - pubs.aip.org
Recently, the Fischer decomposition for polynomials on superspace ℝ m| 2n (that is,
polynomials in m commuting and 2n anti-commuting variables) has been obtained unless …
polynomials in m commuting and 2n anti-commuting variables) has been obtained unless …
Generalized Cauchy–Kovalevskaya extension and plane wave decompositions in superspace
A Guzmán Adán - Annali di Matematica Pura ed Applicata (1923-), 2021 - Springer
The aim of this paper is to obtain a generalized CK-extension theorem in superspace for the
biaxial Dirac operator ∂ _ x+ ∂ _ y∂ x+∂ y. In the classical commuting case, this result can …
biaxial Dirac operator ∂ _ x+ ∂ _ y∂ x+∂ y. In the classical commuting case, this result can …