Dr. Nichol Furey
Profil
Forschungsthemen1
In-Depth Study Into the Algebraic Structure of Elementary Particle Physics
Quelle ↗Förderer: Volkswagen Stiftung Zeitraum: 02/2020 - 12/2028 Projektleitung: Dr. Nichol Furey
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Stand: 26.4.2026, 19:48:44 (Top-K=20, Min-Cosine=0.4)
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Publikationen16
Top 25 nach Zitationen — Quelle: OpenAlex (BAAI/bge-m3 embedded für Matching).
Physics Letters B · 80 Zitationen · DOI
A considerable amount of the standard model's three-generation structure can be realised from just the 8C-dimensional algebra of the complex octonions. Indeed, it is a little-known fact that the complex octonions can generate on their own a 64C-dimensional space. Here we identify an su(3)⊕u(1) action which splits this 64C-dimensional space into complexified generators of SU(3), together with 48 states. These 48 states exhibit the behaviour of exactly three generations of quarks and leptons under the standard model's two unbroken gauge symmetries. This article builds on a previous one, [1], by incorporating electric charge.
Physics Letters B · 43 Zitationen · DOI
We explain how an unexpected algebraic structure, the division algebras, can be seen to underlie a generation of quarks and leptons. From this new vantage point, electrons and quarks are simply excitations from the neutrino, which formally plays the role of a vacuum state. Using the ladder operators which exist within the system, we build a number operator in the usual way. It turns out that this number operator, divided by 3, mirrors the behaviour of electric charge. As a result, we see that electric charge is quantized because number operators can only take on integer values. Finally, we show that a simple hermitian form, built from these ladder operators, results uniquely in the nine generators of SUc(3) and Uem(1). This gives a direct route to the two unbroken gauge symmetries of the standard model.
Apollo (University of Cambridge) · 27 Zitationen · DOI
This thesis constitutes a first attempt to derive aspects of standard model particle physics from little more than an algebra. Here, we argue that physical concepts such as particles, causality, and irreversible time may result from the algebra acting on itself. We then focus on a special case by considering the algebra $\mathbb{R}\otimes\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$. Using nothing more than $\mathbb{R}\otimes\mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$ acting on itself, we set out to find standard model particle representations. From the complex quaternionic portion of the algebra, we find generalized ideals, and show that they describe concisely all of the Lorentz representations of the standard model. From the complex octonionic portion of the algebra, we find minimal left ideals, and show that they mirror the behaviour of a generation of quarks and leptons under $su(3)_c$ and $u(1)_{em}$. We then demonstrate a rudimentary electroweak model which yields a straightforward explanation as to why $SU(2)_L$ acts only on left-handed states. This holds in the case of leptons. Finally, we demonstrate how $\mathbb{C}\otimes\mathbb{O}$ can generate a 64-$\mathbb{C}$-dimensional algebra, wherein we find the $SU(3)_c$ irreducible representations corresponding to three generations of quarks and leptons. We then conclude by showing how to arrive at all 48 electric charges.
International Journal of Modern Physics A · 27 Zitationen · DOI
We bring to light an electroweak model which has been reappearing in the literature under various guises.[Formula: see text] In this model, weak isospin is shown to act automatically on states of only a single chirality (left). This is achieved by building the model exclusively from the raising and lowering operators of the Clifford algebra [Formula: see text]. That is, states constructed from these ladder operators mimic the behaviour of left- and right-handed electrons and neutrinos under unitary ladder operator symmetry. This ladder operator symmetry is found to be generated uniquely by [Formula: see text] and [Formula: see text]. Crucially, the model demonstrates how parity can be maximally violated, without the usual step of introducing extra gauge and extra Higgs bosons, or ad hoc projectors.
Physics Letters B · 25 Zitationen · DOI
Reframing certain well-known particle models in terms of normed division algebras leads to two new results for BSM physics. (1) We identify a sequence of complex structures which induces a cascade of breaking symmetries: Spin(10) ↦ Pati-Salam ↦ Left-Right symmetric ↦ Standard model + B-L (both pre- and post-Higgs-mechanism). These complex structures derive from the octonions, then from the quaternions, then from the complex numbers. (2) We provide, also for the first time we believe, an explicit demonstration of left-right symmetric Higgs representations stemming from quaternionic triality, tri(H). Upon the breaking of su(2)R, our Higgs reduces to the familiar standard model Higgs.
Physics Letters B · 16 Zitationen · DOI
Peering in from the outside, A:=R⊗C⊗H⊗O looks to be an ideal mathematical structure for particle physics. It is 32 C-dimensional: exactly the size of one full generation of fermions. Furthermore, as alluded to earlier in [1], it supplies a richer algebraic structure, which can be used, for example, to replace SU(5) with the SU(3)×SU(2)×U(1)/Z6 symmetry of the standard model. However, this line of research has been weighted down by a difficulty known as the fermion doubling problem. That is, a satisfactory description of SL(2,C) symmetries has so far only been achieved by taking two copies of the algebra, instead of one. Arguably, this doubling of states betrays much of A's original appeal. In this article, we solve the fermion doubling problem in the context of A. Furthermore, we give an explicit description of the standard model symmetries, , its gauge bosons, Higgs, and a generation of fermions, each in the compact language of this 32 C-dimensional algebra. Most importantly, we seek out the subalgebra of which is invariant under the complex conjugate - and find that it is given by su(3)C⊕u(1)EM. Could this new result provide a clue as to why the standard model symmetries break in the way that they do?
arXiv (Cornell University) · 3 Zitationen · DOI
An optimal algebraic model of particle physics has a number of checkpoints to pass. As a minimum, models should $\langle 1 \rangle$ conform to the Coleman-Mandula theorem (or establish a loophole), $\langle 2 \rangle$ evade familiar fermion doubling problems, $\langle 3 \rangle$ naturally explain the Standard Model's chirality, $\langle 4 \rangle$ exclude B-L gauge symmetry at low energy, and $\langle 5 \rangle$ explain the existence of three generations. We demonstrate how the model introduced in [1] passes checkpoints $\langle 1 \rangle, \langle 2 \rangle, \langle 3 \rangle, \langle 4 \rangle$, and has yet to cross $\langle 5 \rangle$. We close by elucidating an unexpected appearance of spacetime symmetries.
arXiv (Cornell University) · 2 Zitationen · DOI
Expanding the results of [1], [2], [3], we demonstrate a network of algebraic connections between six well-known particle theories. These are the Spin(10) model, the Georgi-Glashow model, the Pati-Salam model, the Left-Right Symmetric model, the Standard Model both pre- and post-Higgs mechanism. A new inclusion of a quaternionic reflection within the network further differentiates $W^{\pm}$ bosons from the $Z^0$ boson in comparison to the Standard Model. It may introduce subtle new considerations for the phenomenology of electroweak symmetry breaking.
arXiv (Cornell University) · 2 Zitationen · DOI
In this article, we bypass the detailed symmetry breaking pathways established in [1]. Instead, a direct route from the Spin(10) model to the Standard Model is enabled via a single algebraic constraint. This single constraint, however, may be reconfigured as a requirement that three $\mathfrak{so}(10)$ actions coincide on a fixed space of multi-vector fermions. This $\mathfrak{so}(10) \mapsto \mathfrak{su}(3)_{C} \oplus \mathfrak{su}(2)_{L} \oplus{u}(1)_{Y}$ breaking (from a three-way intersection) mirrors, in certain ways, the $\mathfrak{so}(8) \mapsto \mathfrak{g}_2$ breaking (from a three-way intersection) in the context of octonionic triality. By extending this result to include quaternions and complex numbers, we find that a five-way intersection breaks $\mathfrak{so}(10) \mapsto \mathfrak{su}(3)_{C} \oplus \mathfrak{u}(1)_{Q}$. These are the Standard Model's unbroken gauge symmetries, post-Higgs-mechanism.
Physics Letters B · 1 Zitationen · DOI
We identify the Standard Model's su(3)⊕su(2)⊕u(1) internal symmetries within the triality symmetries tri(C)⊕tri(H)⊕tri(O). From here, the corresponding Standard Model group action is applied to the triality triple (Ψ+,Ψ−,V) for Ψ+,Ψ−,V∈C⊗H⊗O. Together, Ψ+ and Ψ− provide the correct irreducible representations for two generations. Owing to a certain Cartan factorization, which we define, V provides the irreducible representations for a third generation. Said more explicitly in another way, division algebraic multiplication merges a third generation of spinor representations into a set of scalar bosons. This set of scalar bosons includes the familiar Standard Model Higgs representation.
arXiv (Cornell University) · 1 Zitationen · DOI
We identify the Standard Model's $\mathfrak{su}(3)\oplus \mathfrak{su}(2)\oplus \mathfrak{u}(1)$ internal symmetries within the triality symmetries $\mathfrak{tri}(\mathbb{C}) \oplus \mathfrak{tri}(\mathbb{H}) \oplus \mathfrak{tri}(\mathbb{O})$. From here, the corresponding Standard Model group action is applied to the triality triple $\left( Ψ_+, Ψ_-,V\right)$ for $Ψ_+, Ψ_-, V \in \mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}$. Together, $Ψ_+$ and $Ψ_-$ provide the correct irreducible representations for two generations. Owing to a certain Cartan Factorization, which we define, $V$ provides the irreducible representations for a third generation. Said more explicitly in another way, division algebraic multiplication merges a third generation of spinor representations into a set of scalar bosons. This set of scalar bosons includes the familiar Standard Model Higgs representation.
Annalen der Physik · DOI
Abstract It is demonstrated how a set of particle representations, familiar from the Standard Model, collectively form a superalgebra. Those representations mirroring the behavior of the Standard Model's gauge bosons, and three generations of fermions, are each included in this algebra, with exception only to those irreps involving the top quark. This superalgebra is isomorphic to the Euclidean Jordan algebra of hermitian matrices, , and is generated by division algebras. The division algebraic substructure enables a natural factorization between internal and spacetime symmetries. It also allows for the definition of a grading on the algebra. Those internal symmetries respecting this substructure are found to be , in addition to four iterations of . For spatial symmetries, one finds multiple copies of . Given its Jordan algebraic foundation, and its apparent non‐relativistic character, the model may supply a bridge between particle physics and quantum computing. We close by describing how this article fits into the larger picture of Bott Periodic Particle Physics, first introduced in 2014, 2021, 2023.
Annalen der Physik · DOI
Abstract Expanding the results of previous research, a network of algebraic connections is demonstrated between six well‐known particle theories . These are the Spin(10) model, the Georgi–Glashow model, the Pati–Salam model, the Left–Right Symmetric model, the Standard Model both pre‐ and post‐Higgs mechanism. A new inclusion of a quaternionic reflection within the network further differentiates bosons from the boson in comparison to the Standard Model. It may introduce subtle new considerations for the phenomenology of electroweak symmetry breaking.
Annalen der Physik · DOI
Abstract In this study, the detailed symmetry breaking pathways established in Furey et al. (2024) are bypassed. Instead, a direct route from the Spin(10) model to the Standard Model is enabled via a single algebraic constraint. This single constraint, however, may be reconfigured as a requirement that three actions coincide on a fixed space of multi‐vector fermions. This breaking (from a three‐way intersection) mirrors, in certain ways, the breaking (from a three‐way intersection) in the context of octonionic triality. By extending this result to include quaternions and complex numbers, we find that a five‐way intersection breaks . These are the Standard Model's unbroken gauge symmetries, post‐Higgs‐mechanism.
Annalen der Physik · DOI
Abstract An optimal algebraic framework of particle physics has a number of checkpoints to pass. As a minimum, models should conform to the Coleman‐Mandula theorem (or establish a loophole), evade familiar fermion doubling problems, naturally explain the Standard Model's chirality, exclude B‐L gauge symmetry at low energy, and explain the existence of three generations. The framework introduced in ref. [1] is shown to passes checkpoints , and has yet to cross . The discussion is concluded by elucidating an unexpected appearance of spacetime symmetries.
Apollo (University of Cambridge) · DOI
We explain how an unexpected algebraic structure, the division algebras, can be seen to underlie a generation of quarks and leptons. From this new vantage point, electrons and quarks are simply excitations from the neutrino, which formally plays the role of a vacuum state. Using the ladder operators which exist within the system, we build a number operator in the usual way. It turns out that this number operator, divided by 3, mirrors the behaviour of electric charge. As a result, we see that electric charge is quantized because number operators can only take on integer values. Finally, we show that a simple hermitian form, built from these ladder operators, results uniquely in the nine generators of $SU(3)_c$ and $U(1)_{em}$. This gives a direct route to the two unbroken gauge symmetries of the standard model.
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Identität, Organisation und Kontakt aus HU-FIS.
- Name
- Dr. Nichol Furey
- Titel
- Dr.
- Fakultät
- Mathematisch-Naturwissenschaftliche Fakultät
- Institut
- Institut für Physik
- Arbeitsgruppe
- Theoretische Physik (Quantenfeldtheorie jenseits des Standardmodells und Stringtheorie)
- Telefon
- +49 30 2093-66385
- HU-FIS-Profil
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- 26.4.2026, 01:04:58