This week I have been reading about and working on operators other than the volume operator. One paper I particularly enjoyed was by Seth. A. Major who is an interesting physicist. Not only does he do a lot of work in the area of quantum gravity but he is one of the leading physicists exploring the idea of the universe as a computer. In this paper he develops a phenomenology for the deep spatial geometry of loop quantum gravity. In the context of a simple model – an atom of space, he is shows how combinatorial structures can affect physical observations. The angle operator is used to develop a model of angular corrections to local, continuum flat-space 3-geometries. This is similar to the work of Roger Penrose described in an earlier post: Angular momentum: An approach to combinatorial space-time by Roger Penrose. The physical effects reply on the combinatorics of SU(2) recoupling. Bhabha scattering, that is, electron-positron scattering is used as an example of how these effects might be observed.

**The Angle operator**

The angle operator acts on nodes and the spectrum may be expressed in terms of the SU(2) representations of the intertwiner at a single node.

The angle operator may also be defined in terms of the electric flux variables and the usual embedded graphs of LQG. I have also been working on a sagemath program to calculate the angle operator eigenvalues for given J1, J2, J3 and J4.

###### Related articles

- Quantum steps towards the Big Bang (tracingknowledge.wordpress.com)
- Physicists Discover Geometry Underlying Particle Physics | Simons Foundation (simonsfoundation.org)
- Theoretical physics: The origins of space and time (kielarowski.wordpress.com)
- Loop Quantum Gravity – wiki.sagemath.org/ (quantumtetrahedron.wordpress.com)

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