What are the applications of matrix theory
Matrix theory as an alternative to string theory?
Even after the spectacular discovery of the Higgs boson in 2012 at CERN, the search for a comprehensive theory of the fundamental interactions remains one of the great unsolved problems in theoretical physics. The merging of quantum mechanics and gravitation presents particular difficulties.
Physicists working with Harold Steinacker from the University of Vienna are using so-called matrix models to investigate an alternative approach to the favored string theory. To this end, they recently published in the journal “Progress of Theoretical and Experimental Physics”.
String theory provides a far-reaching approach for the connection between quantum mechanics and gravity, but in its conventional formulation leads to an unmanageable variety of possibilities. This severely limits the predictive power of the theory. This is where the FWF-funded project by Harold Steinacker, theoretical physicist at the University of Vienna, comes in.
“The so-called matrix models we use are remarkably simple. All physical objects and their dynamics are coded and described in a few matrices, especially space-time and its geometry, "says Steinacker:" The models allow deep-seated questions, for example about the quantum structure of space-time or the number of dimensions of our space-time examine ".
The scope of this approach is, however, controversial: In particular, it was not yet clear whether a realistic description of the elementary particles and their interactions is even possible with it. The crux of the matter here is an essential property of the standard model of elementary particles, the so-called chirality. It was not clear whether and how this property could be realized in matrix models.
Chirality as a key property
In the work that has now been published, Harold Steinacker and Jochen Zahn were able to show that the chiral properties of the standard model can also be realized within the framework of the matrix models. For the first time, they found a configuration in the matrix model that comes close to the standard model of elementary particles, at least in essentials. The approach leads to an expansion in particular of the Higgs sector of the standard model, which is assigned a geometric role, albeit in a currently still speculative form.
The basis for this are new mathematical techniques of quantum geometry, which have been developed and adapted in recent years, especially at the University of Vienna. The physical properties of the models can be described and understood through such quantum geometries in additional dimensions. "Access via matrix models makes it possible to take up ideas from string theory while avoiding the associated problems," explains Steinacker.
These developments open up a remarkably simple approach to the search for a unified theory of fundamental interactions, in which quantum physics also determines the structure of spacetime. The physicist concludes that there is still a long unexplored road to a sufficient understanding of these matrix models and their viability as a fundamental theory.
An extended standard model and its Higgs geometry from the matrix model: Harold C. Steinacker, Jochen Zahn. In: Progress of Theoretical and Experimental Physics 2014;
Doi: 10.1093 / ptep / ptu111
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