2025/08/11 by Sia, Bik Soon
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2508.11688
A connection between the completion of quantum mechanics featuring events and the theory of emergent spacetime in quantum gravity where von Neumann algebra plays a vital role is established. In thermal equilibrium, we show that the Principle of Diminishing Potentialities (PDP) holds for the large N algebra of N=4 Super Yang-Mills (SYM) theory with gauge group SU(N) when the temperature is higher than Hawking-Page temperature. Below Hawking-Page transition and for the case of zero temperature, PDP does not hold. Since the centralizer of thermofield double state on the large N algebra of N=4 SYM theory coincides with the center of the large N algebra which is trivial, we extend the large N algebra by performing crossed product by the maximal abelian subgroup H of the compact symmetry group G of the two-sided eternal black hole. In this case, the centralizer of an extension of thermofield double state is non-trivial and it is given by the action of the maximal abelian subgroup H on the Hilbert space HTFD ⊗ L2 (H). This centralizer is by itself commutative and it coincides with its own center. This implies that the first actual event that initiate the ``Events-Trees-Histories'' dynamical evolution in this framework is given by the spectral projectors associated to the action of the Cartan subalgebra \mathfrakh of the Lie algebra \mathfrakg associated to the group G on the Hilbert space HTFD ⊗ L2 (H).