of particle physics trying to tell us Latham Boyle Perimeter Institute builds on work of Barrett Bizi Brouder Besnard Chamseddine Connes DAndrea Dabrowski ID: 811890
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Slide1
What is the standard model of particle physics trying to tell us?
Latham Boyle (Perimeter Institute)
builds on work of
Barrett,
Bizi
,
Brouder
,
Besnard
,
Chamseddine
,
Connes
,
D’Andrea
,
Dabrowski
, Dubois-Violette,
Kerner
,
Krajewski
,
Landi
,
Lizzi
, Lott,
Madore
,
Marcolli
,
Martinetti
,
Schucker
, van
Suijlekom
based on arXiv:1604.00847 w/ S.
Farnsworth
(and another in preparation)
Slide2Slide3Slide4The EFT perspective: the basic input
Slide5The EFT perspective: the basic input
Slide6The EFT perspective: the basic input
Slide7The EFT perspective: the basic input
Slide8The EFT perspective: the basic input
Slide9The EFT perspective: the basic input
Slide10The EFT perspective: the basic input
Slide11The EFT perspective: the basic input
Slide12The EFT perspective: the basic input
Slide13The EFT perspective: the basic input
Slide14The EFT perspective: the basic input
Slide15The EFT perspective: the basic input
Slide16The EFT perspective: the basic input
Slide17The EFT perspective: the basic input
Slide18The EFT perspective: the basic input
Slide19The EFT perspective: the basic input
Slide20The EFT perspective: the basic input
Slide21The EFT perspective: the basic input
Slide22The EFT perspective: the basic input
Slide23The NCG perspective: an initial thought
Slide24The NCG perspective: an initial thought
Slide25The NCG perspective: an initial thought
Slide26The NCG perspective: an initial thought
Slide27Quick reminder: what is an algebra?
Example 1: smooth functions f(x): Infinite dimensionalCommutativeExample 2:
nxn
complex matrices:
Finite dimensional
Non-commutative
Example 3
:
Quaternions:
Slide28Quick reminder: what is an algebra?
Example 1: smooth functions f(x): Infinite dimensionalCommutativeExample 2:
nxn
complex matrices:
Finite dimensional
Non-commutative
Example 3
:
Quaternions:
Slide29Quick reminder: what is an algebra?
Example 1: smooth functions f(x): Infinite dimensionalCommutative (and associative)Example 2:
nxn
complex matrices:
Finite dimensional
Non-commutative
Example 3
:
Quaternions:
Slide30Quick reminder: what is an algebra?
Example 1: smooth functions f(x): Infinite dimensionalCommutative (and associative)Example 2:
nxn
complex matrices:
Finite dimensional
Non-commutative
Example 3
:
Quaternions:
Slide31Quick reminder: what is an algebra?
Example 1: smooth functions f(x): Infinite dimensionalCommutative (and associative)Example 2:
nxn
complex matrices:
Finite dimensional
Non-commutative (and associative)
Example 3
:
Quaternions:
Slide32Quick reminder: what is an algebra?
Example 1: smooth functions f(x): Infinite dimensionalCommutative (and associative)Example 2:
nxn
complex matrices:
Finite dimensional
Non-commutative (and associative)
Example 3
:
Quaternions:
Slide33Quick reminder: what is an algebra?
Example 1: smooth functions f(x): Infinite dimensionalCommutative (and associative)Example 2:
nxn
complex matrices:
Finite dimensional
Non-commutative (and associative)
Example 3
:
Quaternions:
Slide34Quick reminder: what is an algebra?
Example 1: smooth functions f(x): Infinite dimensionalCommutative (and associative)Example 2:
nxn
complex matrices:
Finite dimensional
Non-commutative (and associative)
Example 3
:
Quaternions:
Slide35Quick reminder: what is an algebra?
Example 1: smooth functions f(x): Infinite dimensionalCommutative (and associative)Example 2:
nxn
complex matrices:
Finite dimensional
Non-commutative (and associative)
Example 3
:
Quaternions:
Slide36Slide37Slide38Slide39Slide40Slide41Slide42???
Slide43Gauge
and Higgs bosons from covariance of D
Slide44Slide45Slide46?
Slide47Slide48Slide49Slide50Slide51Slide52Slide53Slide54?
Slide55Slide56Slide57Slide58Slide59Slide60Slide61Gauge
and Higgs bosons from covariance of D
Slide62Gauge
and Higgs bosons from covariance of D
Slide63Gauge
and Higgs bosons from covariance of D
Slide64Slide65Slide66Slide67Slide68Slide69Slide70Slide71Slide72Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide73Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide74Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide75Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide76Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide77Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide78Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide79Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide80Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide81Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Associative
Jordan!
Slide82Filling in the back story: briefly!
Riemann: Connes:Eilenberg:arXiv:1604.00847
Unify nearly all NCG axioms & assumptions!
New constraints: fix ! (more restrictive)
Physical symmetries are
automorphisms
of B!
Inner
automorphisms
: standard model
Outer
automorphisms
: gravity and U(1)_{B-L}
Recently: Non-Commutative
Jordan!
Slide83Some topics for the future
A better bosonic action (F^2?)Relation to fine-tuning problems in SMRelation to grand unification
Relation to exceptional Jordan algebra