Causal set approach, discrete quantum gravity, quantum sequential growth process
A discrete quantum gravity model given by a quantum sequential growth process (QSGP) is considered. The QSGP describes the growth of causal sets (causets) one element at a time in discrete steps. It is shown that the set P of causets can be partitioned into three subsets P = (ANT) ∪ (MIX) ∪ (MAT) where ANT is the set of pure antimatter causets, MAT the set of pure matter causets and MIX the set of mixed matter-antimatter causets. We observe that there is an asymmetry between ANT and MAT which may explain the matter-antimatter asymmetry of our physical universe. This classification of causets extends to the set of paths Ω in P to obtain Ω = ΩANT ∪ Ω MIX ∪ Ω MAT. We introduce a further classification Ω MIX = ΩMIX M ∪ Ω MIX A into matter-antimatter parts. Approximate classical probabilities and quantum propensities for these various classifications are considered. Some conjectures and unsolved problems are presented.
Gudder, S., "A Matter of Matter and Antimatter" (2012). Mathematics Preprint Series. Paper 31.