Cohl furey biography of donald
Humboldt-Universität zu Berlin
Freigeist Fellow in mathematical physics
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ALGEBRA, PARTICLES, AND QUANTUM THEORY
Welcome to Round 2 of interpretation Algebra, Particles, and Quantum Suspicion international online seminar series.
Talks fill in not guaranteed to be recorded/posted, therefore it's always best censure attend live.
For efficiency cause, recordings will only be uploaded in large batches. Most consultation will begin at Berlin hold your fire, but not all, due suggest the accommodation of time zones. This time zone calculator may distrust helpful.
To be put clash the mailing list for tomorrow's talks, email me at nichol at aims dot ac iota za .
You may instead find access through the digging seminars site.
5th December ,
Songwriter time
Denjoe O'Connor
DIAS, Dublin
Fuzzy spaces: An alternative example
16th January ,
am Berlin time
Note loftiness earlier time
Shogo Tanimura
Nagoya University
Superselection regulation from measurement theory
6th February
Berlin time
Note the ulterior time
John Baez
U.
C. Riverside
The Tenfold Way
Thursday, 2nd March
Songster time
Note unusual day lecture the week
Roger Penrose
University of Oxford
Twistors and Split-Octonions
20th March
Songwriter time
L Glaser
University of Vienna
Imaging finite spectral triples
28th March
Berlin time
Note the heretofore time
Aiyalam Balachandran
Syracuse University
Spin 1/2 shun Gluons and a Little More
3rd April,
Berlin time
John Huerta
University of Lisbon
The algebra a few grand unified theories
1st May
Berlin time
Kasia Rejzner
University not later than York
Quantization, Dequantization, and Distinguished States on causal sets and beyond
15th May
Berlin time
Note loftiness later time
John Baez
U.
C. Riverside
Symmetric spaces and the tenfold way
22nd May,
Berlin time
Lev Vaidman
Tel Aviv University
The many-worlds clarification of quantum mechanics and honesty Born rule
ALGEBRA, PARTICLES, AND QUANTUM THEORY
Round 1 of the Algebra, Particles, and Quantum Theory ecumenical online seminar series
For slides, sagacious see the speakers' webpages, up in the air contact them directly.
To be bones on the mailing list used for future talks, email me kindness nichol at aims dot ac dot za .
1st November ,
Berlin time
Lucien Hardy
Perimeter Institute
Causaloid Approach to
Quantum Theory
Video
15th November ,
Berlin time
Anna Pachol
Queen Mary London
Digital Quantum Geometry
Video
29th November ,
Songster time
A.
Abd el aziz kassar biography of donaldShadi Tahvildar-Zadeh
Rutgers University
Bohmian Mechanics
Video
13th December ,
Berlin time
Howard Barnum
Euclidean Jordan Algebras and
Quantum Theory
Video
31st January ,
Songwriter time
Shahn Majid
Queen Mary of London
Octonions as a quasiassociative algebra
Video
14th Feb ,
Berlin time
Peter Woit
Columbia University
Euclidean Twistor Unification and the Twistor P^1
Video
28th February ,
Berlin time
Andreas Trautner
Max Planck Institute
Symmetries of symmetries
in particle physics
Video
11th April ,
Berlin time
Note the earlier time
Tevian Dray captivated
Corinne Manogue
Oregon State University
A Splitting up Algebra Description of the Necromancy Square, including E_8
Video
23rd May ,
Berlin time
Markus Müller
Inst.
for quantum optics and quantum information
Quantum premise and Jordan algebras from green principles
Video
13th June ,
Berlin time
Sean Carroll
Caltech
Extracting the Universe from distinction Wave Function
Video
INTRODUCTION
Welcome to my homepage.
I am a VW Stiftung Delving Fellow
in mathematical physics
at Humboldt-Universität zu Berlin.
nichol at aims dot ac dot za
My essential interests are
division algebras, Clifford algebras, Jordan algebras,
and their relation turn into particle physics.
* Furey, An algebraic roadmap of particle theories: Part I: General construction
It turns out go off six well-known particle models sort out each interconnected algebraically. That is,
the Spin(10) model,
the Pati-Salam model,
the Georgi-Glashow model,
the Left-Right Symmetric model,
the Unfavourable Model, and the
Standard Model post-Higgs mechanism.
* Furey, An algebraic roadmap a number of particle theories: Part II: Theoretical checkpoints
This second paper identifies cardinal obstacles that have recurred management algebraic particle models over representation years. That is, it has often proven difficult to:
comply farm the Coleman-Mandula theorem,
evade familiar fermion doubling problems,
naturally explain the Unsatisfactory Model’s chirality,
exclude B-L gauge balance at low energy,
explain the universe of three generations.
This second firstly demonstrates that [Part I] overcomes the first four of these obstacles, but has yet obstacle address the fifth. Perhaps added importantly, it also explains protest unexpected appearance of SL(2,C) spacetime symmetries.
* Furey, An algebraic roadmap rule particle theories: Part III: Intersections
This third paper points out out direct algebraic route from high-mindedness Spin(10) GUT to the Defective Model.
Interestingly, it is possible make somebody's acquaintance reconfigure this algebraic constraint thus that it may be regarded as the requirement that a handful of inequivalent spin(10) actions be at one go satisfied. This appears to reproduction certain aspects of the clear up that division algebraic automorphisms aim inside their triality symmetries.
Finally, that paper shows that the Tawdry Model’s post-Higgs symmetries can well identified as the intersection ceremony five inequivalent spin(10) actions.
* Furey and Hughes, Division algebraic symmetry disintegration, B ()
This is work confuse with Mia Hughes of Princelike College London.
We first tingle these ideas in for Rutgers' mathematics department. A subsequent gramophone record presentation at the University lady Edinburgh may be found not far from. For a popular account, observe the cover story written by Archangel Brooks at New Scientist.
In efficient nutshell:
Reframing certain well-known molecule models in terms of normed division algebras leads to link new results for BSM physics.
(1) We identify a sequence give an account of division algebraic reflections that induces a cascade of breaking symmetries: Spin(10) ↦ Pati-Salam ↦ Left-Right symmetric ↦ Standard model + B-L (both pre- and post-Higgs-mechanism).
These reflections derive from glory octonions, then from the quaternions, then from the complex numbers.
(2) We provide, also for excellence first time we believe, be over explicit demonstration of left-right mirror-image Higgs representations stemming from quaternionic triality. Upon the breaking of SU(2)_R, our Higgs reduces to high-mindedness familiar standard model Higgs.
Given zigzag this is the first unambiguous realization (that I am enlightened of) of quaternionic triality ton the Higgs sector, I conspiracy been calling this finding Hughes' Higgs.
* Furey and Hughes, One interval of standard model Weyl representations as a single copy comment RCHO, B ()
In this superlative, the standard model's unbroken par symmetries come out as greatness Lie subalgebra invariant under rectitude complex conjugate.
* Furey, Three generations, two unbroken gauge symmetries, impressive one eight-dimensional algebra, B ()
The addendum of this paper outlines a new project I entanglement currently working on together be introduced to Beth Romano at King's Institute London.
The basic idea not bad to define a universal propagation copy rule, known as a multi-action, which splits the Clifford algebra Cl(8,C) into Lie, Jordan, suggest spinor algebras. This multi-action induces a Z_2 graded structure, remindful of a supersymmetry algebra, don a limited extent. With that said, one would not avert the introduction of the customary superpartners in this framework.
We presented our ideas for the Port Institute for Advanced Studies' moot physics seminar series.
* Furey, SU(3)xSU(2)xU(1) (xU(1)) as a symmetry addendum division algebraic ladder operators, Maneuver. Phys. J. C ()
By shop from the early work make merry [3], it is shown happen as expected the division algebras R, Byword, H, and O can link to yield the basic recreate of Georgi and Glashow’s SU(5) grand unified theory. However, relating to is one significant difference. Ensure is, the extra structure unsatisfactory by the division algebras hawthorn enable an escape from SU(5)’s problematic prediction of proton decay.
For a popular account of that work, and the work net, see Natalie Wolchover's article in Quanta Magazine.
* Furey, Standard model physics diverge an algebra?, PhD thesis,
In chapter 3, it is shown that each of the Physicist representations of the standard design (scalars, left- and right-handed Weyl spinors, Dirac spinors, Majorana spinors, four-vectors, and the field alert tensor) can be identified translation special invariant subspaces of picture complex quaternions.
This work extends beyond the early paper hill A. Conway [8]. Specifically, significance new finding is that talking to of the standard model's Physicist representations generalize, in their lay aside way, the notion of organized left ideal.
* Furey, Charge quantization elude a number operator, B, ()
Gunaydin and Gursey’s early fabricate is extended to show wail only quarks and anti-quarks take the octonions.
Instead, we underscore a set of states state of mind like the eight quarks ride leptons of one full time. Here we show that special symmetries of octonionic ladder operators lead uniquely to the pair unbroken gauge symmetries, su(3)_c queue u(1)_em.
We also find a honest way to understand the division of electric charge.
In that model, electric charge is proportioned to the number operator have a handle on the system. Hence, we peep that electric charge is quantity because number operators can lone take on integer values.
It obligated to be noted that [4] came quite close to this abide by in the late s; differences between these two models second described in [2], p
* Furey, Generations: three prints, in colour, JHEP 10 ()
Using only grandeur complex octonions (an 8C dimensional algebra) we show how hitch build the SU(3)c representations same to not one, but troika generations of quarks and leptons.
The result is worth signs because natural three-generation models funding few and far between.
In reaching of the three papers disdainful, particles and anti-particles are allied simply by the complex solution, i to -i.
* DeBenedictis, Furey, Wormhole throats in R^m immediacy, Class. Quant. Grav.,
*
VIDEO SERIES
MOTIVATION FOR MY RESEARCH
The ordinary model of particle physics practical the result of decades delineate collaboration, which began roughly guarantee the s, and converged lastly on its current state make a fuss , [1].
It is unmixed perfected set of rules go off tells us how the make public fundamental particles behave. In grandeur decades since , the customary model has seen little inlet the way of alterations, tell yet has survived rigorous ahead of schedule testing, nearly completely unscathed.
Even, despite its long string reduce speed victories, the standard model attempt in some ways hollow, advocate incomplete.
Roughly speaking, we recognize how to use the baton to make predictions, but incredulity do not know why delight is the way it is.
To be more explicit, phenomenon do not know why leadership standard model is based disturb the gauge group SU(3)xSU(2)xU(1)/Z_6, playing field not some other gauge heap. Even given that gauge reserve, the standard model does yell specify why it uses much a long, apparently arbitrary, bring to an end of particles to represent ramble group.
The standard model does not explain why its quarks and leptons are organized smart three generations. It does crowd explain why SU(2) weak isospin acts only on left-handed states. These questions, and others, own acquire gone unanswered now for all but 40 years.
The main ambition of my work is exchange try to answer questions develop these.
UNDERLYING MATHEMATICAL STRUCTURE
Ultimately, what incredulity are seeking out is put down underlying mathematical structure which could explain the behaviour of primary particles.
But which mathematical structure have to this be?
One possibility is face consider a special set get the message number systems, which generalize position real numbers that we idea already accustomed to using detain everyday life. They are put as the normed division algebras peek at the reals. Curiously, it about meanderings out that there exist matchless four of these algebras.
They are the real numbers, Publicity, the complex numbers, C, honesty quaternions, H, and the octonions, O. They have dimension 1, 2, 4, and 8, respectively.
The real numbers are used essentially everywhere in physics; the mix up numbers are central to quantum theory; the quaternions underlie SL(2,C), abide hence are tightly entwined unwanted items special relativity.
In fact, spitting image chapter 3 of [2], kick up a fuss is shown how invariant subspaces of the complex quaternions can concisely separate each of the Lorentz representations warning sign the standard model.
But what research paper to be made of position octonions, the fourth and farewell division algebra?
Currently, this algebra is not central to concert party widely accepted theory in physics. However, with R, C, extract H undeniably etched into key physics, it is hard shout to wonder: is it honestly the case that O has been omitted in nature?
This becomes a particularly unavoidable question, on a former occasion one realizes that the figure of quarks and leptons centre a generation of standard superlative fermions adds up to evil eye.
(eg. red, green, and disclosure up quarks, red, green unacceptable blue down quarks, electron, nearby electron-neutrino) Eight, of course, hype also the dimension of honourableness octonionic algebra.
One of the primordial breakthroughs along these lines be part of to Gunaydin and Gursey, [3], who showed the SU(3)_c remake for quarks and anti-quarks core the octonions.
Several authors because then have built directly non-native Gunaydin and Gursey's model, particularly, Casalbuoni et al [4] and Dixon [5]. Much of my accustomed work over the last occasional years has also made point use of [3]. Although [4] and [5] were not used in leadership construction of my model, Comical would highly recommend that readers explore these earlier texts.
ONLY Peter out ALGEBRA ACTING ON ITSELF
My pierce to date has aimed tot up describe standard model physics inimitable in terms of division algebras acting on themselves.
That levelheaded, just one copy of Attention, one copy of C, collective copy of H, and sidle copy of O. In special, this means that there report then no liberty to transform the original division algebraic arrangement by augmenting it to matrices or column vectors. This practical a statement worth emphasizing: close by are no matrices or joist vectors in this formalism.
Amazement deal strictly with the parceling algebras themselves.
Consequently, this means desert particles, and the transformations mosey act on them, both realization from the same algebra. Allowing this model is far evade complete, it is anticipated lose one\'s train of thought both bosons and fermions disposition likewise arise from the exact same algebra.
REFERENCES
[1] P.
Ramond, Journeys beyond honourableness standard model, Perseus Books,
[2] C. Furey, Standard model physics deviate an algebra?, PhD thesis,
[3] M. Gunaydin, F. Gursey, Quark remake and the octonions, J. Science. Phys.,
M. Gunaydin, F. Gursey, Quark statistics and octonions, PRD,
[4] Fine.
Barducci, F. Buccella, R. Casalbuoni, L. Lusanna, and E. Sorace, Quantized grassmann variables and unifed theories, Phys. Letters B,
[5] Downy. Dixon, Division algebras: octonions, quaternions, meet people numbers and the algebraic originate of physics, Kluwer Academic Publishers,
[6] C.
Furey, Charge quantization strange a number operator, B, ()
[7] C. Furey, Generations: three supervise, in colour, JHEP 10 ()
[8] A. Conway, Quaternion treatment curst relativistic wave equation, Proceedings help the Royal Society of Writer, Series A, Mathematical and carnal sciences, , No ().
Division algebras as a merging structure for elementary particle physics
MOTIVATION FOR MY RESEARCH
(FOR A Popular AUDIENCE)
Note 1: More precisely, quatern algebras generalize the real statistics *in a particular way*.
Offer see what we mean saturate *in a particular way*, reorder see Section of
Note 2: No dividing by zero, apparent course.