QUANTUM
STRUCTURE of
SPACETIME and
GRAVITY
2016
Panorama of Belgrade
AUGUST 21-28 2016
BELGRADE, SERBIA
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Harold Steinacker: Fuzzy spaces and applications

The lectures on fuzzy spaces will be structured as follows:

Lecture 1 with provide the basics of fuzzy spaces (i.e. quantized embedded symplectic spaces). This will cover the 2-dimensional fuzzy sphere, the fuzzy torus, fuzzy CP^n, and more generally quantized coadjoint orbits.

Lecture 2 will discuss some further structures on fuzzy spaces, in particular coherent states, string states & the separation of UV / IR regimes, and Laplace- and Dirac operators. Furthermore, the 4-dimensional fuzzy sphere will be briefly introduced.

In Lecture 3 some physical applications will be discussed, in particular noncommutative field theory and gauge theory as described by matrix models. The phenomenon of UV/IR mixing will be explained. If time permits & depending on the interests, either fuzzy extra dimensions in Yang-Mills gauge theory or emergent gravity on fuzzy S^4 will be briefly discussed.

Reading material:

  1. "Measuring finite Quantum Geometries via Quasi-Coherent States"
    Lukas Schneiderbauer, Harold C. Steinacker, J. Phys. A 49 (2016) no.28, 285301, arXiv:1601.08007 (sections 1-6)
  2. "Non-commutative geometry and matrix models"
    Harold Steinacker, arXiv:1109.5521 (mainly sections 1-6)

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