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BEGIN:VEVENT
SUMMARY:Lucien Hardy (Perimeter Institute)
DTSTART:20211101T170000Z
DTEND:20211101T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/1
DESCRIPTION:Title: Combining the radical aspects of Gravity and Qu
antum: The causaloid framework.\nby Lucien Hardy (Perimeter Institute)
as part of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nGenera
l Relativity and Quantum Theory are each conservative and radical in compl
ementary respects. In General Relativity quantities take definite values
but the theory has dynamical causal structure. Quantum Theory has fixed c
ausal structure but it has the property of indefiniteness (quantities do n
ot take definite values). Most likely\, a theory of Quantum Gravity will
combine the radical aspects - that is it will have indefinite causal struc
ture. In 2005 I set up a probabilistic framework capable of accommodating
theories with indefinite causal structure which I called the causaloid fr
amework. In this seminar I will present this framework along with some re
cent developments in the quest for a foundationally inspired approach to Q
uantum Gravity.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Pachol (Queen Mary London)
DTSTART:20211115T170000Z
DTEND:20211115T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/2
DESCRIPTION:Title: Digital quantum geometry\nby Anna Pachol (Q
ueen Mary London) as part of Algebra\, Particles\, and Quantum theory\n\n\
nAbstract\nNoncommutative geometry\, as the generalised notion of geometry
\, allows us to model the quantum gravity effects in an effective descript
ion without full knowledge of quantum gravity itself. On a curved space on
e must use the methods of Riemannian geometry - but in their quantum versi
on\, including quantum differentials\, quantum metrics and quantum connect
ions.\n\n \n\nIn this seminar I will provide the introduction to the gener
al framework of quantum Riemannian geometry involving noncommutative diffe
rential graded algebra and bimodule connections. This framework is then ap
plied to studying quantum Riemannian geometries over the field F2 of two e
lements as the extreme case of a finite-field adaptation of noncommutative
geometric methods for physics. The choice of the finite field in this fra
mework proposes a new kind of 'discretisation scheme'\, which we called th
e 'digital geometry'.\n\n \n\nAs a result\, we classify all possible digit
al quantum Riemannian geometries over the field F2 on unital algebras of v
ector space dimension n<4 and find explicit forms for quantum Levi-Civita
connections and Riemann\, Ricci and Einstein tensors. When the quantum met
rics admit quantum Levi-Civita connections\, each pair produces `digital q
uantum Riemannian geometry' of which most turn out to be not flat in the s
ense of non-zero Riemann curvature. We find a rich moduli of examples for
n=3 and top form degree 2 (providing a landscape of all reasonable up to 2
D quantum geometries)\, including many which are not flat. Their coordinat
e algebras are commutative\, but their differentials are not.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Shadi Tahvildar-Zadeh (Rutgers University)
DTSTART:20211129T170000Z
DTEND:20211129T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/3
DESCRIPTION:Title: Bohmian mechanics\nby A. Shadi Tahvildar-Za
deh (Rutgers University) as part of Algebra\, Particles\, and Quantum theo
ry\n\n\nAbstract\nIn this talk I will briefly explain what Bohmian Mechani
cs is\, and what it is not. In particular\, I will argue that it is curren
tly the most straightforward ontological formulation of non-relativistic q
uantum mechanics\, and that it does not suffer from the shortcomings that
it is rumored to suffer from. I will then talk about recent results on a
relativistic extension of Bohmian Mechanics via multi-time wave functions
and hypersurface Bohm-Dirac theory\, one that my group at Rutgers has been
developing for the past few years. I will explain how two-sided actions
on Clifford algebras can provide a unifying framework for a particle ontol
ogy that can be extended to cover bosons as well as fermions\, and use tha
t framework to study interacting electron-photon systems and Compton scatt
ering in one space dimension\, in such a way that both the electron and th
e photon enter the story as point particles.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Howard Barnum
DTSTART:20211213T170000Z
DTEND:20211213T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/4
DESCRIPTION:Title: Euclidean Jordan Algebras and Quantum Theory\nby Howard Barnum as part of Algebra\, Particles\, and Quantum theory\n\
n\nAbstract\nThis talk will focus on the mathematical properties of Euclid
ean Jordan Algebras (EJAs) viewed as potential models for the state and ob
servable spaces of physical systems\, and two new characterizations of the
se algebras in terms of such properties\, by myself and collaborators. \n
\nEJAs were introduced and investigated early in the development of quantu
m theory\,\nas abstractions of the algebra of Hermitian operators on a Hil
bert space\, initially in finite dimension. \nJordan\, von Neumann\, and
Wigner classified them: they are real\, complex\, and quaternionic quantum
theory\, systems whose state spaces are balls (``spin factors")\, and one
exceptional case (which may be thought of as three-state octonionic quant
um theory).\n\nThe "general probabilistic theories" (GPT) framework formul
ates potential physical theories in terms of systems having convex\, compa
ct state spaces\, on which the probabilities of measurement\noutcomes are
given by affine functionals. Dynamics and composite systems are also desc
ribed in the framework. A major part of the GPT research program has been
to find principles\, mathematically natural\, of physical or information-
processing significance\, or\nall three\, that narrow down the very wide l
andscape of possibilities available in the GPT framework\nto the familiar
spaces of quantum density matrices (states) and POVM elements (measurement
outcomes).\n\nSuch characterizations often proceed by first characterizin
g the finite-dimensional EJAs. After\nsummarizing important mathematical
properties of the EJAs\, I will describe\nseveral such characterizations\,
including the Koecher-Vinberg system relating EJAs to homogeneous self-du
al cones (which can be interpreted as ``unnormalized states"\, the positiv
e semidefinite Hermitian matrices being an example)\, but focusing on two
new results. Joachim Hilgert and I [1\,2]\ncharacterized EJAs by two pro
perties: a generalized spectral decomposability formulated entirely in ter
ms of\nconvexity\, and a ``strong symmetry" property of the state space\,
also formulated in convex terms: transitive\naction of the symmetry group
on sets of simultaneously perfectly distinguishable pure states. Work of
HB\nwith C. Ududec [4] characterizes them via homogeneity of their cones o
f unnormalized states (whose mathematical\, physical\, and information-pro
cessing significance I will discuss) and transitive action of the symmetry
group on pure states. Further physical principles characterizing the usu
al\, complex\, quantum systems within the class of EJAs will be described:
tomographic locality\, or energy observability [3]\nmeaning that the gen
erators of continuous symmetries of the state space [3\, but close to idea
s of Connes\n(orientation) and of Alfsen and Shultz (dynamical corresponde
nce)]: the generators of continuous symmetries of the state space are obse
rvables.\n\nIf time permits\, I will also discuss the possibilities for fo
rming composites of such systems\, focusing on my work with Matthew Graydo
n and Alex Wilce [5]. \n\n[1] H. Barnum and J. Hilgert\, "Strongly symmet
ric spectral convex bodies are Jordan algebra state spaces"\, https://arxi
v.org/abs/1904.03753\n[2] H. Barnum and J. Hilgert\, "Spectral properties
of convex sets"\, Journal of Lie Theory 30 (2020) 315-344.\nPreprint close
to this available at: https://winephysicssong.com/2021/09/01/strongly-sym
metric-spectral-convex-sets-are-jordan-algebra-state-spaces/\n[3] H. Barnu
m\, M. Mueller and C. Ududec\, "Higher-order interference and single-syste
m postulates characterizing quantum theory"\, New Journal of Physics 16 (2
014) 123029. arXiv:1403.4147\n[4] H. Barnum and C. Ududec\, in preparatio
n.\n[5] Composites and Categories of Euclidean Jordan Algebras\, Quantum 4
\, 359 (2020).\nhttps://arxiv.org/abs/1606.09331\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shahn Majid (Queen Mary London)
DTSTART:20220131T170000Z
DTEND:20220131T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/6
DESCRIPTION:Title: Octonions as a quasiassociative algebra\nby
Shahn Majid (Queen Mary London) as part of Algebra\, Particles\, and Quan
tum theory\n\n\nAbstract\nThis will be a gentle introduction to an old res
ult of H. Albuquerque and myself about how to think of the Octonions as an
associative algebra\, but in a certain monoidal category of Z_2^3 -graded
vector spaces. The associator here is given by a coboundary 3-cocycle on
the group Z_2^3 of 3-vectors with entries 0\,1. Mac Lane’s theorem says
that all constructions in the category can be done as if associative\, sim
ply inserting the associator as needed for brackets to make sense (differe
nt ways to do this will all give the same answer). The same construction f
or Z_2^2 gives the quaternions while for Z_2^4 it's an interesting open pr
oblem as to what\nyou get. In the Octonion case\, one application is to th
ink of these as the coordinate algebra of a finite but nonassociative geom
etry. I will indicate a couple of possible points of contact with physics.
\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Trautner (Max Planck Institute)
DTSTART:20220228T170000Z
DTEND:20220228T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/7
DESCRIPTION:Title: Symmetries of symmetries in particle physics\nby Andreas Trautner (Max Planck Institute) as part of Algebra\, Particl
es\, and Quantum theory\n\n\nAbstract\nThe plan of this seminar is to intr
oduce you to outer automorphisms ("symmetries of symmetries")\nof quantum
field theories and their potential relevance for puzzles in our understand
ing of Nature\nbased on the Standard Model of particle physics. We will se
e how the combined parity (P) and charge\nconjugation transformation (C) i
s one very special kind of outer automorphism. This will lead us to a\nnew
classification of finite groups and the discovery that some symmetry grou
ps do preclude the existence\nof CP transformations altogether\, in which
case CP can be violated by quantized\, calculable phases.\nFinally\, we wi
ll have a look at outer automorphisms beyond the well-known C\,P\, or T tr
ansformations.\nBased on instructive examples\, I will discuss the general
importance of outer automorphisms for the\ncomputation of stationary poin
ts and emergent symmetries\, for spotting physical degeneracies in the\npa
rameter space of a theory\, as well as to determine the boundaries of the
renormalization group\nflow and RGE fixed points.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Woit (Columbia University)
DTSTART:20220214T170000Z
DTEND:20220214T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/8
DESCRIPTION:Title: Euclidean Twistor Unification and the Twistor P
^1\nby Peter Woit (Columbia University) as part of Algebra\, Particles
\, and Quantum theory\n\n\nAbstract\nIf one Wick rotates and works with tw
istors in Euclidean\nrather than Minkowski space-time\, the way symmetries
work changes\nsignificantly. I'll argue that in the Euclidean context th
e symmetries\nof twistor theory match well the symmetries of the Standard
Model as\nwell as a chiral formulation of general relativity\, providing a
\npromising new basis for a unified theory.\n\n From the twistor perspecti
ve\, a space-time point is described by a\nsphere with its antipodal map\,
known to mathematicians as the twistor\nP^1. Remarkably\, this same struc
ture shows up in recent advances in\nnumber theory\, and I'll say a bit ab
out that story (for more\, see\nhttps://www.math.columbia.edu/~woit/twisto
rp1.pdf).\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Zanelli (CECS)
DTSTART:20220314T170000Z
DTEND:20220314T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/9
DESCRIPTION:Title: Local unconventional SUSY\nby Jorge Zanelli
(CECS) as part of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\
nFifty years ago\, the discovery of supersymmetry (SUSY) allowed to combin
e internal\nand spacetime symmetries. This required extending the Lie alge
bra of those symmetries into a\ngraded Lie algebra. The additional supersy
mmetry generators turned bosons into fermions and\nvice versa and\, in its
simplest form called for systems with equal number of bosons and\nfermion
s. SUSY led to hopes of new physics and the resolution of many riddles\, f
rom the origin\nof energy hierarchies in the Standard Model to the nature
of dark matter. However\, the search\nfor supersymmetry over the past five
decades has never found SUSY pairs and has only\nprovided higher and high
er lower limits for the SUSY breaking energy scale.\n\nWe argue that SUSY
can be realized in a different manner\, unifying spacetime and local inter
nal symmetries\, with spin-1 gauge fields and spin-1/2 fermions in a singl
e Lie superalgebra-valued connection. In this representation\, states do n
ot come in Bose-Fermi pairs and\, if the local\nsymmetry contains the Lore
ntz group\, gravity is inevitably included but without spin-3/2 (or\nhighe
r spin) fundamental fields. The resulting systems are remarkably simple\,
closely\nresembling a standard quantum field theory and SUSY still emerges
\, although not as a\nsymmetry of the action but as a feature of the vacuu
m/ground states. Thus\, local SUSY is a\ncontingent symmetry\, like Poinca
ré or AdS invariances that depend on the nature of the\nspacetime backgro
und.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Markus Müller (Inst. for quantum optics and quantum information)
DTSTART:20220523T160000Z
DTEND:20220523T173000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/10
DESCRIPTION:Title: Quantum theory and Jordan algebras from simple
principles\nby Markus Müller (Inst. for quantum optics and quantum i
nformation) as part of Algebra\, Particles\, and Quantum theory\n\n\nAbstr
act\nQuantum theory is one of our most successful physical theories\, but
its\nstandard textbook formulation is mysterious. For example\, why are st
ates\ndescribed by complex vectors in a Hilbert space\, and why do observa
bles\ncorrespond to self-adjoint operators? In this talk\, I describe how
the\nHilbert space formalism of quantum theory (and its Jordan-algebraic\n
generalizations) can be reconstructed from simple physical or\ninformation
-theoretic principles\, without presupposing any of the usual\nmathematica
l machinery. This is conceptually similar to the derivation\nof the Lorent
z transformations from the principles of relativity and the\nconstancy of
the speed of light. To this end\, I introduce the framework\nof “general
ized probabilistic theories” which generalizes both classical\nand quant
um probability theory and which describes all possible\nconsistent ways in
which preparations and measurements can interact\nstatistically in a labo
ratory. I give an explicit example of a set of\nprinciples that implies qu
antum theory\, describe how the hunt for\n“higher-order interference”
led to a scientific detective story\, and\nshow how these insights and tec
hniques can shed surprising light on the\nrelation between quantum theory
and spacetime.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tevian Dray and Corinne Manogue (Oregon State University)
DTSTART:20220411T150000Z
DTEND:20220411T163000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/11
DESCRIPTION:Title: A Division Algebra Description of the Magic Sq
uare\, including E_8\nby Tevian Dray and Corinne Manogue (Oregon State
University) as part of Algebra\, Particles\, and Quantum theory\n\n\nAbst
ract\nThe Freudenthal-Tits magic square of Lie algebras provides an abstra
ct parameterization of a family of Lie algebras in terms of two division a
lgebras\, with the exceptional cases all involving the octonions. In the
non-octonionic cases\, it is straightforward to provide a matrix interpret
ation of the magic square\, which can be exponentiated to yield a parametr
ization of the corresponding Lie groups. We describe here joint work with
Rob Wilson that extends these constructions to E_8\, thus providing an ex
plicit representation in terms of (two copies of) the octonions.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corinne Manogue and Tevian Dray (Oregon State University)
DTSTART:20220425T150000Z
DTEND:20220425T163000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/12
DESCRIPTION:Title: E8 and the Standard Model\nby Corinne Mano
gue and Tevian Dray (Oregon State University) as part of Algebra\, Particl
es\, and Quantum theory\n\n\nAbstract\nUsing an explicit parameterization
in terms of octonions\, we interpret\nthe elements of the Lie algebra $\\f
rak{e}_8$ as objects in the Standard\nModel. We obtain lepton and quark s
pinors with the usual properties\,\nthe Standard Model Lie algebra $\\frak
{su}(3)+\\frak{su}(2)+\\frak{u}(1)$\,\nand the Lorentz Lie algebra $\\frak
{so}(3\,1)$.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sean Carroll (Caltech)
DTSTART:20220613T160000Z
DTEND:20220613T173000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/13
DESCRIPTION:Title: Extracting the Universe from the Wave Function
\nby Sean Carroll (Caltech) as part of Algebra\, Particles\, and Quant
um theory\n\n\nAbstract\nQuantum mechanics is a theory of wave functions i
n Hilbert space. Many features that we generally take for granted when we
use quantum mechanics -- classical spacetime\, locality\, the system/envir
onment split\, collapse/branching\, preferred observables\, the Born rule
for probabilities -- should in principle be derivable from the basic ingre
dients of the quantum state and the Hamiltonian. I will discuss recent pro
gress on these problems\, including consequences for emergent spacetime an
d quantum gravity.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denjoe O'Connor (DIAS)
DTSTART:20221205T170000Z
DTEND:20221205T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/14
DESCRIPTION:Title: Fuzzy Spaces: An exceptional example.\nby
Denjoe O'Connor (DIAS) as part of Algebra\, Particles\, and Quantum theory
\n\n\nAbstract\nI will review the ideas behind fuzzy spaces such as the fu
zzy\nsphere\, discuss some of the physics one can encounter and where they
\narise. I will then describe the fuzzy spaces associated with the\nexcept
ional group G_2 and their relation to the octonions.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shogo Tanimura (Nagoya University)
DTSTART:20230116T100000Z
DTEND:20230116T113000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/15
DESCRIPTION:Title: Superselection rule from measurement theory\nby Shogo Tanimura (Nagoya University) as part of Algebra\, Particles\,
and Quantum theory\n\n\nAbstract\nIn quantum theory\, physically measurabl
e quantities of a microscopic system are represented by self-adjoint opera
tors. However\, not all of the self-adjoint operators correspond to measur
able quantities. The superselection rule is a criterion for distinguishing
measurable quantities from non-measurable quantities. Any measurable quan
tity must satisfy the superselection rules. By contraposition\, any quanti
ty which does not satisfy the superselection rules are not be measurable.\
nIn this talk\, I will show deduction of superselection rules from an assu
mption on symmetry property of measurement process. I introduce the notion
of covariant indicator\, which is a macroscopic observable covariant with
a microscopic observable under some group actions. If the object system h
as a quantity that is conserved during the measurement process\, another q
uantity that do not commute with the conserved quantity are non-measurable
by a non-trivial covariant indicator. Our derivation of superselection ru
les can be considered as an extreme case of the Wigner-Araki-Yanase uncert
ainty relation.\n\nReference: \nhttps://arxiv.org/abs/1112.5701\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Baez (U. C. Riverside)
DTSTART:20230206T180000Z
DTEND:20230206T193000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/16
DESCRIPTION:Title: The Tenfold Way\nby John Baez (U. C. River
side) as part of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nT
he importance of the tenfold way in physics was only recognized in this ce
ntury. Simply put\, it implies that there are ten fundamentally different
kinds of matter. But it goes back to 1964\, when the topologist C. T. C
. Wall classified the associative real super division algebras and found t
en of them. The three "purely even" examples were already familiar: the
real numbers\, complex numbers and quaternions. The rest become importan
t when we classify representations of groups or supergroups on Z/2-graded
vector spaces. We explain this classification\, its connection to Cliffo
rd algebras\, and some of its implications.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:L Glaser (University of Vienna)
DTSTART:20230320T170000Z
DTEND:20230320T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/18
DESCRIPTION:Title: Imaging finite spectral triples\nby L Glas
er (University of Vienna) as part of Algebra\, Particles\, and Quantum the
ory\n\n\nAbstract\nSpectral triples are a way to rewrite a manifold in alg
ebraic language\, through the triple of Algebra\, Hilbert space and Dirac
operator. But they can not only describe continuum manifolds\, they also l
end themselves to discretizing space\, by using finite algebras and Hilber
t spaces.\n\nFuzzy spaces are closely related to some especially symmetric
finite spectral triples. But what about more general spectral triples? If
finite spectral triples are to be useful in regularizing a path integral
over geometries then at least some of them should also correspond to less
regular geometries.\n\nIn this talk I will present work in which I reconst
ruct geometry from a spectral triple\, using numerical methods. In particu
lar I will also show that a deformation of the fuzzy sphere leads to a fuz
zy ellipsoid.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Huerta (University of Lisbon)
DTSTART:20230403T160000Z
DTEND:20230403T173000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/19
DESCRIPTION:Title: The algebra of grand unified theories\nby
John Huerta (University of Lisbon) as part of Algebra\, Particles\, and Qu
antum theory\n\n\nAbstract\nGrand unification was a program from the 1970s
to unify the strong\, weak and electromagnetic interactions. It is a junc
tion where the theory of Lie groups and their finite-dimensional represent
ations meets particle physics\, providing a wonderful example of Lie theor
y and shedding light on the physics. We will take this point of view to in
troduce three grand unified theories: the Georgi–Glashow SU(5) theory\,
the Pati–Salam model based on SU(2) x SU(2) x SU(4)\, and Georgi's Spin(
10) theory. We describe how all three extend the standard model\, and how
these extensions are compatible\, fitting together into a "cube" of grand
unified theories.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kasia Rejzner (University of York)
DTSTART:20230501T160000Z
DTEND:20230501T173000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/20
DESCRIPTION:Title: Quantization\, Dequantization\, and Distinguis
hed States on causal sets and beyond\nby Kasia Rejzner (University of
York) as part of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nI
n this talk I will discuss the results of the paper "Quantization\, Dequan
tization\, and Distinguished States" written in callaboration with Eli Haw
kins and Christoph Minz. In this work we consider free quantum fields on a
causal set and demonstrate how methods of geometric quantization can be a
pplied in that case. We compare the result with the Sorkin-Johnson constru
ction and demonstrate that both approaches single out the same quantum sta
te.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lev Vaidman (Tel Aviv University)
DTSTART:20230522T160000Z
DTEND:20230522T173000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/21
DESCRIPTION:Title: The many-worlds interpretation of quantum mech
anics and the Born rule\nby Lev Vaidman (Tel Aviv University) as part
of Algebra\, Particles\, and Quantum theory\n\n\nAbstract\nI will argue th
at the many-worlds interpretation is the best interpretation of quantum me
chanics and discuss the status of the probability assignments in this dete
rministic theory.\n\nThe background can be found in\n\nThe Many-Worlds Int
erpretation of Quantum Mechanics\, L. Vaidman\,\nThe Stanford Encyclopedia
of Philosophy (Summer 2021 Edition)\, E. N. Zalta (ed.)\nhttps://plato.st
anford.edu/entries/qm-manyworlds/\n\nDerivations of the Born Rule\, L. Vai
dman\,\nQuantum\, Probability\, Logic\, Jerusalem Studies in Philosophy an
d History of Science\, M. Hemmo\, O. Shenker (eds.)\, Chapter 26 (Springer
Nature Switzerland AG 2020)\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Penrose (University of Oxford)
DTSTART:20230302T170000Z
DTEND:20230302T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/22
DESCRIPTION:Title: From basic Twistor Theory to Split-Octonions.
Does Twistor Theory also Address the SU(3) of Strong Interactions?\nby
Roger Penrose (University of Oxford) as part of Algebra\, Particles\, and
Quantum theory\n\n\nAbstract\nTwistor theory was introduced in the mid-19
60s as an approach to combining quantum theory with space-time structure.
Its initial role was to relate the quantum-field-theoretic requirement of
positive frequency to the structure of space-time. Twistor space was intro
duced to codify space-time in an unusual way\, so that this twistor space
would split into two halves representing positive and negative frequency r
espectively\, the points of their common boundary representing light rays
in Minkowski space.\n\nHowever\, this splitting turned out to have two qui
te different basic physical interpretations\, namely positive/negative hel
icity as well as positive/negative frequency\, which ought not to be confu
sed in the formalism\, and the notion of “bi-twistors” is introduced t
o resolve this issue. The algebra of bi-twistors turned out to provide a r
epresentation of split-octonions. It also presents the possibility of gene
ralizing a construction due to Ward for incorporating electromagnetism int
o twistor theory\, which might now incorporates the SU(3) of strong intera
ctions.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aiyalam Balachandran (Syracuse University)
DTSTART:20230328T150000Z
DTEND:20230328T163000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/24
DESCRIPTION:Title: Spin 1/2 from Gluons and a Little More\nby
Aiyalam Balachandran (Syracuse University) as part of Algebra\, Particles
\, and Quantum theory\n\n\nAbstract\nThe theta vacuum in QCD is the standa
rd vacuum\, twisted by the exponential of\nthe Chern-Simons term. But what
is the quantum operator U(g) for winding number 1?\n\nWe construct U(g) i
n this talk. The Poincare’ generators commute with it only if\nthey are
augmented by a spin 1/2 representation of the Lorentz group coming from\nl
arge gauge transformations. This result is analogous to the ‘spin-isospi
n ‘ mixing result\ndue to Jackiw and Rebbi\, and Hasenfratz and ’t Hoo
ft and a similar result in fuzzy\nphysics. ( See ‘Lectures on Fuzzy and
Fuzzy SUSY Physics \, Balachandran\, S.\nKurkcuoglu and S.Vaidya\, chapter
s 5.4.1\, 8.4.1).\n\nHence states can drastically affect representations o
f observables. This fact is\nfurther shown by charged states dressed by in
frared clouds. Following Mund\, Rehren\nand Schroer (arXiv:2109.10342 )\,
we find that Lorentz invariance is spontaneously\nbroken in these sectors.
This result is extended to QCD where even the global QCD\ngroup is shown
to be broken.\n\nIt is argued that the escort fields of Mund et al. are th
e Higgs fields for Lorentz and\ncolour breaking. They are string-localised
fields where the strings live in a union of de\nSitter spaces. Their osci
llations and those of the infrared clouds generate the Goldstone\nmodes.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John Baez (U.C. Riverside)
DTSTART:20230515T170000Z
DTEND:20230515T183000Z
DTSTAMP:20260404T110642Z
UID:AlgebraParticlesFoundations/25
DESCRIPTION:Title: Symmetric spaces and the tenfold way\nby J
ohn Baez (U.C. Riverside) as part of Algebra\, Particles\, and Quantum the
ory\n\n\nAbstract\nThe tenfold way has many manifestations. It began as a
tenfold classification of states of matter based on their behavior under
time reversal and charge conjugation. Mathematically\, it relies on the
fact that there are ten super division algebra and ten kinds of Clifford a
lgebras\, where two Clifford algebras are of the same kind if they have eq
uivalent categories of representations. But Cartan also showed that there
are ten infinite families of compact symmetric spaces! After explaining
symmetric spaces\, we describe two ways to get compact symmetric spaces f
rom Clifford algebras\, which give different correspondences between these
two manifestations of the tenfold way.\n
LOCATION:https://stable.researchseminars.org/talk/AlgebraParticlesFoundati
ons/25/
END:VEVENT
END:VCALENDAR