Results 21 to 30 of about 5,272 (123)

Efficient Gaussian Simulations of Fermionic Open Quantum Systems

Advanced Quantum Technologies, Volume 9, Issue 4, April 2026.
Building upon Bravyi's fundamental theoretical framework, efficient classical simulation methods are reviewed and further developed for general fermionic Gaussian processes. The emphasis remains on a unified approach applicable to generic fermionic Gaussian operations.
Yinan Fang, Hyesung Choi, Minchul Lee, Mahn‐Soo Choi   +3 more
wiley   +1 more source

Constrained generalized supersymmetries and superparticles with tensorial central charges. A classification

, 2005
We classify the admissible types of constraint (hermitian, holomorphic, with reality conditions on the bosonic sectors, etc.) for generalized supersymmetries in the presence of complex spinors.
A.A. Zheltukhin, A.A. Zheltukhin, C. Fronsdal, D. Sorokin, F. Toppan, Francesco Toppan, H.L. Carrion, I.R. Porteous, K.S. Stelle, K.S. Stelle, M.F. Atiyah, P.C. West, P.K. Townsend, R. D'Auria, Zhanna Kuznetsova   +14 more
core   +1 more source

Noncommutative polygonal cluster algebras

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of Θ$\Theta$‐positivity for the groups Spin(p,q)$\mathrm{Spin}(p,q)$.
Zachary Greenberg, Dani Kaufman, Merik Niemeyer, Anna Wienhard   +3 more
wiley   +1 more source

An Algebraic Roadmap of Particle Theories

Annalen der Physik, Volume 537, Issue 4, April 2025.
The SO(10) grand unified theory, the Georgi–Glashow SU(5) grand unified theory, the Pati–Salam model, the Left–Right Symmetric model, and the Standard model have been studied extensively since the 1970s. Recasting these models in a division algebraic language elucidates how they are each in fact connected.
Nichol Furey
wiley   +2 more sources

Analyzing the Free States of one Quantum Resource Theory as Resource States of Another

Advanced Quantum Technologies, Volume 9, Issue 2, February 2026.
The article investigates how free states in one quantum resource theory can become highly resourceful in another. It systematically studies multipartite entanglement, fermionic non‐Gaussianity, imaginarity, realness, spin coherence, Clifford non‐stabilizerness, Sn‐equivariance, and non‐uniform entanglement, combining rigorous analytical tools and ...
Andrew E. Deneris, Paolo Braccia, Pablo Bermejo, N. L. Diaz, Antonio A. Mele, M. Cerezo   +5 more
wiley   +1 more source

A geometric construction of the exceptional Lie algebras F4 and E8

, 2007
We present a geometric construction of the exceptional Lie algebras F4 and E8 starting from the round 8- and 15-spheres, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background.
C. Bär, F. Harvey, H. Lawson, J.M. Figueroa-O’Farrill, J.M. Figueroa-O’Farrill, J.M. Figueroa-O’Farrill, José Figueroa-O’Farrill, M. Green, M. Wang, M.A.A. van Leeuwen, M.F. Atiyah, S. Gallot, Y. Kosmann   +12 more
core   +1 more source

Bilinear covariants and spinor fields duality in quantum Clifford algebras [PDF]

Journal of Mathematical Physics, 2014
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime
Abłamowicz, Rafał, Gonçalves, Icaro, da Rocha, Roldão   +2 more
openaire   +2 more sources

Derangements in intransitive groups

Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.
Abstract Let G$G$ be a nontrivial permutation group of degree n$n$. If G$G$ is transitive, then a theorem of Jordan states that G$G$ has a derangement. Equivalently, a finite group is never the union of conjugates of a proper subgroup. If G$G$ is intransitive, then G$G$ may fail to have a derangement, and this can happen even if G$G$ has only two ...
David Ellis, Scott Harper
wiley   +1 more source

Clifford Algebras and Liquid Crystalline Fermions

Physical Review X
We show that Clifford algebras provide a natural language to describe the physics of liquid crystal defects in 3D. This framework shows that most of these defects have fermionic nature, as the director field profile on a 2D cross section can ...
N. Johnson, L. C. Head, O. D. Lavrentovich, A. N. Morozov, G. Negro, E. Orlandini, C. A. Smith, G. M. Vasil, D. Marenduzzo   +8 more
doaj   +1 more source

Further investigation of mass dimension one fermionic duals

, 2019
In this paper we proceed into the next step of formalization of a consistent dual theory for mass dimension one spinors. This task is developed approaching the two different and complementary aspects of such duals, clarifying its algebraic structure and ...
Cavalcanti, R. T., da Silvaa, J. M. Hoff
core   +2 more sources