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.
- 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)