Waiting for new data at 13 TeV, staying tuned to the Higgs

(... because spectralized Higgs data may show more interesting results than the sonified one to the physicists who know that spinors can hear the forces of spacetime :-)

Here are a few abstracts for the talks that will take place this week at Radboud University Nijmegen which hosts the Gauge theory and Noncommutative Geometry Conference 


Nadir Bizi: The noncommutative standard model. 

Lorentzian signature and noncommutative differential forms. We first show how non-commutative differential forms can be used to refine the non-commutative standard model. We then redefine spectral triples using Krein spaces instead of the usual Hilbert spaces. By drawing a parallel with Clifford algebras, we show that the representation space of spectral triples should be an indefinite inner product space later turned into a positive definite one, and not the other way around. We study the properties of indefinite inner product spaces relevant to spectral triples.

Latham Boyle: The standard model as a differential graded super-algebra*.

I will describe how the basic data {A, H, D, γ, J} in the spectral triple formulation of NCG may be naturally repackaged into an “Eilenberg algebra” B (a particularly simple type of superalgebra). From the simple requirement that B is a differential graded star-algebra (or ∗-DGA), one then recovers nearly all of the traditional axioms governing the spectral triple, as well as a few novel constraints. When we apply our formalism to the spectral triple traditionally used to describe the standard model of particle physics, we find that these new constraints each correspond to a physically meaningful and phenomenologically correct constraint on the geometry. I will explain how this formalism is related to, but greatly improves upon, a proposal we made in 2014.

Ali Chamseddine: Unification of gravity and gauge interactions.

The tangent group of the four dimensional space-time does not need to have the same number of dimensions as the base manifold. Considering a higher-dimensional Lorentz group as the symmetry of the tangent space, we unify gravity and gauge interactions in a natural way. The spin connection of the gauged Lorentz group is then responsible for both gravity and gauge fields, and the action for the gauged fields becomes part of the spin curvature squared. The realistic group which unifies all known particles and interactions is the SO(1,13) Lorentz group whose gauge part leads to SO(10) grand unified theory. I briefly discuss the Brout-Englert-Higgs mechanism which breaks the SO(1,13) symmetry first to SO(1,3)×SU(3)×SU(2)×U(1) and further to SO(1,3)×SU(3)×U(1). The spectral action associated with the Dirac operator is also discussed. 

Koen van den Dungen: The fermionic action.

I will discuss the Lorentzian version of the fermionic action in non-commutative geometry, which is based on the use of Krein spaces instead of Hilbert spaces. This fermionic action correctly recovers the fermionic Lagrangians for standard examples of gauge theories, including the full Standard Model of particle physics. The description of these examples does not require a real structure (or charge conjugation), unless one includes Majorana masses for right-handed neutrinos, in which case the internal spaces also exhibit a Krein space structure. This talk is based on arXiv:1505.01939.

José Gracia-Bondia: Light-like string localized quantum fields. 

As gravitational waves provide a post-modern Sidereus Nuncius to scour the heavens, it is useful to reflect on the status of our perception of it. Non-commutative geometry has been termed spectral geometry, since its empirical root is the acknowledgment that we only sense the universe through very narrow light-fronts. Now, Einstein used to say that those who think they understand the light quantum are fooling themselves. Indeed there are few experiences more embarrassing to physicists writing textbooks that trying to sort out the clash between the relativity principle and the apparatus of quantum mechanics; a clash made much worse in the world of gluons and massive vector bosons. Surely, each science requires and engenders its own technologies, be they concrete or abstract tools: to deal with that clash we got the exotic herd of ghost fields, anti-fields, Nakanishi-Lautrup Lagrange multipliers, S-operators and whatnot, replacing the hapless Gupta-Bleuler ‘formalism’. But tools can (and should) evolve even where there is little progress in basic understanding. In the talk I exhibit a new version of a recent technology for quantum field theory, preempting the clash without calling up the ghosts and opening new vistas in the elementary particle realm. In its framework the very concept of gauge transformation dissolves. 

Fedele Lizzi: Wick rotation, fermion doubling and Lorentz symmetry for the spectralaction.

We deal with two features of the spectral action approach to the Standard Model: the fact that the model requires a Wick rotation to Lorentzian space and that it shows a quadrupling of the fermionic degrees of freedom. We show how the two issues are intimately related. We give a precise prescription to Wick rotate the Euclidean theory to the Lorentzian one and eliminate the extra degrees of freedom. This requires not only a projecting out of mirror fermions but also the elimination of remaining extra degrees of freedom. The remaining doubling has to be removed in order to recover the correct Fock space of the physical (Lorentzian) theory. To have a Spin(4)-invariant Euclidean theory and a Spin(1,3)-invariant Lorentzian theory, such an elimination must be performed after the Wick rotation. Some connections with Clifford symmetries will be mentioned at the end, time permitting.  

//last edit on April 6, 2016:  *A new algebraic structure in the standard model of particle physics 
//new edit on April 12, 2016 : links added to the different talks