BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Clifford algebra of the Standard Model
DTSTART;VALUE=DATE-TIME:20210322T160000Z
DTEND;VALUE=DATE-TIME:20210322T170000Z
DTSTAMP;VALUE=DATE-TIME:20220518T234624Z
UID:indico-contribution-62@events.perimeterinstitute.ca
DESCRIPTION:Speakers: Ivan Todorov (Bulgarian Academy of Sciences\, Instit
ute for Nuclear Research)\nWe explore the Z2 graded product C`10 = C`4⊗
ˆC`6 (introduced by Furey) as a finite quantum algebra of the Standard Mo
del of particle physics. The gamma matrices generating C`10 are expressed
in terms of left multiplication by the imaginary octonion units and the Pa
uli matrices. The subgroup of Spin(10) that fixes an imaginary unit (and t
hus allows to write O = C⊗C 3 expressing the quark-lepton splitting) is
the Pati-Salam group GP S = Spin(4) × Spin(6)/Z2 ⊂ Spin(10). If we iden
tify the preserved imaginary unit with the C`6 pseudoscalar ω6 = γ1...γ
6\, ω2 6 = −1 (cf. the talk of Furey and Hughes)\, then Pex = 1 2 (1
− iω6) will play the role of the projector on the extended particle sub
space including the right-handed (sterile) neutrino. We express the genera
tors of C`4 and C`6 in terms of fermionic oscillators aα\, a∗ α\, α =
1\, 2 and bj \, b∗ j \, j = 1\, 2\, 3 describing flavour and colour\, r
espectively. The internal space observable algebra (an analog of the algeb
ra of real functions on space-time) is then defined as the Jordan subalgeb
ra of hermitian elements of the complexified Clifford algebra C ⊗ C`10 t
hat commute with the weak hypercharge 1 2 Y = 1 3 P3 j=1 b ∗ j bj − 1
2 P2 α=1 a ∗ αaα. We only distinguish particles from antiparticles if
they have different eigenvalues of Y . Thus the sterile neutrino and anti
neutrino (with Y = 0) are allowed to mix into Majorana neutrinos. Restrict
ing C`10 to the particle subspace which consists of leptons with Y < 0 and
quarks with Y > 0 allows a natural definition of the Higgs field Φ\, the
scalar of Quillen’s superconnection\, as an element of C`1 4\, the odd
part of the first factor in C`10. As an application we express the ratio m
H mW of the Higgs and the W-boson masses in terms of the cosine of the the
oretical Weinberg angle.\nThe talk is based on the paper arXiv:2010.15621v
3\n\nhttps://events.perimeterinstitute.ca/event/5/contributions/62/
LOCATION:
URL:https://events.perimeterinstitute.ca/event/5/contributions/62/
END:VEVENT
END:VCALENDAR