If you really want your head to spin, I recommend Phys. Rev. Lett. 94, 011602 (2005), “Spontaneous Symmetry Breaking Origin for the Difference Between Time and Space” by C. Wetterich:
In this Letter we pursue the perhaps radical idea that the difference between time and space arises as a consequence of the ‘‘dynamics’’ of the theory rather than being put in by hand. More precisely, we will discuss a model where the ‘‘classical’’ or ‘‘microscopic’’ action does not make any difference between time and space. The time-space asymmetry is generated only as a property of the ground state and can be associated to spontaneous symmetry breaking.
I think this is the first time I have ever seen anyone use SO(128,C).
Indeed headspinning but a very interesting paper… I love the approach it is trying to take. I also freaked out at the specific groups mentioned!