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pro vyhledávání: '"Bruce, Andrew James"'
Autor:
Bruce, Andrew James
Publikováno v:
Acta Phys. Pol. B 55, 8-A1 (2024)
We propose a very simple toy model of a $\mathbb{Z}_2^2$-supersymmetric quantum system and show, via Klein's construction, how to understand the system as being an $N=2$ supersymmetric system with an extra $\mathbb{Z}_2^2$-grading. That is, the commu
Externí odkaz:
http://arxiv.org/abs/2406.19103
Autor:
Bruce, Andrew James
Publikováno v:
Symmetry 2024, 16(6), 725
We examine the heap of linear connections on anchored vector bundles and Lie algebroids. Naturally, this covers the example of affine connections on a manifold. We present some new interpretations of classical results via this ternary structure of co
Externí odkaz:
http://arxiv.org/abs/2303.13327
Autor:
Bruce, Andrew James
Publikováno v:
Archivum Mathematicum, vol. 60 (2024), issue 2, pp. 101-124
We introduce the notion of a Lie semiheap as a smooth manifold equipped with a para-associative ternary product. For a particular class of Lie semiheaps we establish the existence of left-invariant vector fields. Furthermore, we show how such manifol
Externí odkaz:
http://arxiv.org/abs/2208.03224
Autor:
Bruce, Andrew James
Publikováno v:
International Journal of Geometric Methods in Modern Physics 2022
We examine the bundle structure of the field of nowhere vanishing null vector fields on a (time-oriented) Lorentzian manifold. Sections of what we refer to as the null tangent, are by definition nowhere vanishing null vector fields. It is shown that
Externí odkaz:
http://arxiv.org/abs/2204.11645
Autor:
BRUCE, ANDREW JAMES ndrewjamesbruce@googlemail.com
Publikováno v:
Acta Physica Polonica B. 2024, Vol. 55 Issue 8, p1-11. 11p.
Autor:
Bruce, Andrew James
Publikováno v:
Universe 2022, 8(1), 56
We re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. In particular, we review the construction of a semiheap on a Hilbert space and the set of bounded operators on a Hilbert space. The new aspect of
Externí odkaz:
http://arxiv.org/abs/2111.13369
Autor:
Bruce, Andrew James
We examine the question of the integrability of the recently defined $\mathbb{Z}_2\times \mathbb{Z}_2$-graded sine-Gordon model, which is a natural generalisation of the supersymmetric sine-Gordon equation. We do this via appropriate auto-B\"{a}cklun
Externí odkaz:
http://arxiv.org/abs/2106.06372
Autor:
Bruce, Andrew James, Grabowski, Janusz
Publikováno v:
Journal of Geometric Mechanics, 2021
Roughly speaking, $\mathbb{Z}_2^n$-manifolds are `manifolds' equipped with $\mathbb{Z}_2^n$-graded commutative coordinates with the sign rule being determined by the scalar product of their $\mathbb{Z}_2^n$-degrees. We examine the notion of a symplec
Externí odkaz:
http://arxiv.org/abs/2103.00249
Autor:
Bruce, Andrew James1 (AUTHOR) andrewjamesbruce@googlemail.com
Publikováno v:
Symmetry (20738994). Jun2024, Vol. 16 Issue 6, p725. 12p.
Publikováno v:
SIGMA 17 (2021), 060, 58 pages
We establish the representability of the general linear ${\mathbb Z}_2^n$-group and use the restricted functor of points - whose test category is the category of ${\mathbb Z}_2^n$-manifolds over a single topological point - to define its smooth linea
Externí odkaz:
http://arxiv.org/abs/2011.01012