Division algebraic symmetry breaking

Furey, Nichol; Hughes, M. J.

doi:10.1016/j.physletb.2022.137186

Cited by 15 publications

(18 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With this choice, the combined weak Cartan element which forms part of the charge operator, is R z = D iℓ,jℓ • ι. Similarly to the analysis above for spin, in order for a Dirac spinor, satisfying (20), to have a well-defined weak eigenvalue, that is, be an eigenstate of R z , two of the mass components must vanish, namely m b = 0 for b = iℓ, jℓ.…”

Section: Spinors and The Dirac Equationmentioning

confidence: 98%

“…We seek Dirac spinors that combine two Weyl spinors with the same physical properties. Our ability to achieve this goal is constrained by (20). If ψ R is an eigenvector of a particular Cartan element, does ψ L have the same eigenvalue?…”

Section: Spinors and The Dirac Equationmentioning

confidence: 99%

“…We must first deal with the potential complication that the complex structure anticommutes with Q, that is, with both P and M . Nonetheless, the complex structure commutes with the combination P • M that appears in (20), thus ensuring that solutions of the Dirac equation are complex, that is, if ψ satisfies (16) for given Q, so does ι(ψ).…”

Section: Spinors and The Dirac Equationmentioning

confidence: 99%

“…8,9], as well as [10][11][12][13][14][15]. More recently, Lisi [16] attempted to fit the Standard Model into E 8 , while Furey [17][18][19][20][21], building on earlier work of Dixon [22], uses products of division algebras to explain particle properties, and there has been other recent work along similar lines [e.g. 23,24].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Octions: An $E_8$ description of the Standard Model

Manogue¹,

Dray²,

Wilson³

2022

Preprint

View full text Add to dashboard Cite

We interpret the elements of the exceptional Lie algebra e 8(−24) as objects in the Standard Model, including lepton and quark spinors with the usual properties, the Standard Model Lie algebra su(3) + su(2) + u(1), and the Lorentz Lie algebra so(3, 1). The resulting model naturally contains GUTs based on SO(10) (Georgi-Glashow), SU(5) (Georgi), and SU(4)×SU( 2)×SU(2) (Pati-Salam). We then briefly speculate on the role of the remaining elements of e8, and propose a mechanism leading to exactly three generations of particles.

show abstract

Section: Spinors and The Dirac Equationmentioning

confidence: 98%

Section: Spinors and The Dirac Equationmentioning

confidence: 99%

Section: Spinors and The Dirac Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Octions: An $E_8$ description of the Standard Model

Manogue¹,

Dray²,

Wilson³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Moreover, it has been suggested that the division algebra "R ⊗ C ⊗ H ⊗ O" including real, complex, quaternionic, and octonionic ones may be treated as a gateway to explaining some features of the SM like symmetry breaking [5] and one generation of SM Weyl representations [6]. Conclusively, these stories of using algebraic structures imply that what physical information we can excavate depends on what mathematical language we use for physical reasoning.…”

Section: Introductionmentioning

confidence: 99%

Gauge Theory on Fiber Bundle of Hypercomplex Algebras

Jang¹

2023

Preprint

View full text Add to dashboard Cite

I introduce a way of constructing a fiber bundle whose fibers are given by hypercomplex algebras and woven by appropriate structure group, and present that a novel gauge theory can be built on the hypercomplex fiber bundle. In this work, I aim to answer a question about how nature selects one preferred vacuum among degenerate physical vacua, called vacuum selection problem. In the end, I found presence of the impenetrable domain wall that prohibits phase transition between the two vacua. To be specific, I found that in this theory, one particular vacuum between two degenerate physical vacua for Higgs-like scalar potential can be dynamically chosen with priority due to intrinsic even parity of both a scalar field and its vacuum under a Z 2 symmetry, even though its scalar potential is given to be Z 2 -symmetric under both odd-and even-parity transformations of the scalar field. This means that the vacuum selection problem can be resolved in this gauge theory. I suggest that this work may be a gateway to addressing the theoretical origin of the true physical vacuum that nature takes.

show abstract

The Mass Gap of the Space‐time and its Shape

Ali

2024

Fortschritte der Physik

View full text Add to dashboard Cite

Snyder's quantum space‐time which is Lorentz invariant is investigated. It is found that the quanta of space‐time have a positive mass that is interpreted as a positive real mass gap of space‐time. This mass gap is related to the minimal length of measurement which is provided by Snyder's algebra. Several reasons to consider the space‐time quanta as a 24‐cell are discussed. Geometric reasons include its self‐duality property and its 24 vertices that may represent the standard model of elementary particles. The 24‐cell symmetry group is the Weyl/Coxeter group of the group which was found recently to generate the gauge group of the standard model. It is found that 24‐cell may provide a geometric interpretation of the mass generation, Avogadro number, color confinement, and the flatness of the observable universe. The phenomenology and consistency with measurements is discussed.

show abstract

Division algebraic symmetry breaking

Cited by 15 publications

References 20 publications

Octions: An $E_8$ description of the Standard Model

Octions: An $E_8$ description of the Standard Model

Gauge Theory on Fiber Bundle of Hypercomplex Algebras

The Mass Gap of the Space‐time and its Shape

Contact Info

Product

Resources

About