The Stabilized Poincare–heisenberg Algebra: A Clifford Algebra Viewpoint

Gresnigt, Niels G.; Renaud, Peter; Butler, P. H.

doi:10.1142/s0218271807010857

Cited by 11 publications

(7 citation statements)

References 21 publications

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“…These are just one type of algebraic deformation that can be considered [28,29]. Lie-type deformations (those that deform a Lie algebra) have proven very useful in generalizing spacetime symmetries [30][31][32][33]. q-Deformation on the other hand seem to have particular applications in generalized descriptions of internal and gauge symmetries [10,34,35].…”

Section: Octet-decuplet Mass Relationmentioning

confidence: 99%

Charge specific baryon mass relations with deformed SUq(3) flavor symmetry

Gresnigt

2016

Eur. Phys. J. A

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The quantum group SUq(3) = Uq(su (3)) is taken as a baryon flavor symmetry. Accounting for electromagnetic contributions to baryons masses to zeroth order, new charge specific q-deformed octet and decuplet baryon mass formulas are obtained. These new mass relations have errors of only 0.02% and 0.08% respectively; a factor of 20 reduction compared to the standard Gell-Mann-Okubo mass formulas. A new relation between the octet and decuplet baryon masses that is accurate to 1.2% is derived. An explicit formula for the Cabibbo angle, taken to be π 14 , in terms of the deformation parameter q and spin parity J P of the baryons is obtained.

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Section: Octet-decuplet Mass Relationmentioning

confidence: 99%

Charge specific baryon mass relations with deformed SUq(3) flavor symmetry

Gresnigt

2016

Eur. Phys. J. A

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“…Clifford algebras are the result of an attempt by William Clifford in 1876 to generalize the quaternions to higher dimensions and since then they have found many applications in physics [21][22][23][24][25]. They appear whenever spinors do, suggesting they likely play an important role in describing SM fermions.…”

Section: Clifford Algebrasmentioning

confidence: 99%

Braids, normed division algebras, and Standard Model symmetries

Gresnigt¹

2018

Physics Letters B

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This paper represents a first attempt at unifying two promising attempts to understand the origin of the internal symmetries of leptons and quarks. It is shown that each of the four normed division algebras over the reals admits a representation of a circular braid group. For the complex numbers and the quaternions, the represented circular braid groups are B 2 and B c 3 , precisely those used to construct leptons and quarks as framed braids in the Helon model of Bilson-Thompson. It is then shown that these framed braids coincide with the states that span the minimal left ideals of the complex (chained) octonions, shown by Furey to describe one generation of leptons and quarks with unbroken SU (3) c and U (1) em symmetry.The identification of basis states of minimal ideals with certain framed braids is possible because the braiding in B 2 and B c 3 in the Helon model are interchangeable. It is shown that the framed braids in the Helon model can be written as pure braid words in B c 3 with trivial braiding in B 2 , something which is not possible for framed braids in general.

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“…The importance of Lie-algebraic stability was first promoted by Mendes [3]. Since then, several others have similarly argued that the stability of a physically relevant Lie algebra should be considered a physical principle [4][5][6][7][8].…”

Section: Lie-type Deformations and The Importance Of Stabilitymentioning

confidence: 99%

Deformations of spacetime and internal symmetries

Gresnigt¹,

Gillard²

2017

EPJ Web Conf.

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Abstract. Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both spacetime and internal symmetries are discussed. As a specific example we demonstrate how deforming the classical flavor group S U(3) to the quantum group S U q (3) ≡ U q (su(3)) (a Hopf algebra) and taking into account electromagnetic mass splitting within isospin multiplets leads to new and exceptionally accurate baryon mass sum rules that agree perfectly with experimental data.

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The Stabilized Poincare–heisenberg Algebra: A Clifford Algebra Viewpoint

Cited by 11 publications

References 21 publications

Charge specific baryon mass relations with deformed SUq(3) flavor symmetry

Charge specific baryon mass relations with deformed SUq(3) flavor symmetry

Braids, normed division algebras, and Standard Model symmetries

Deformations of spacetime and internal symmetries

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