AG Mathematische Physik, Carmine de Rosa (Trento): Achronal Localization and Representation of the Causal Logic from Conserved Currents
Carmine de Rosa (Trento)
Achronal Localization and Representation of the Causal Logic
from Conserved Currents
Abstract:
In this seminar, I will present and discuss recent achievements [1, 2, 3, 4] concerning the theory of achronal localization derived from conserved currents, as well as the representation theory of the Causal Logic of Minkowski spacetime. Due to the one-to-one correspondence between (covariant) achronal localizations and (covariant) representations of the causal logic thus, apparently for the first time, a
covariant representation of the causal logic for an elementary relativistic quantum mechanical system has been achieved. Localizations are gained out of covariant conserved currents computing their flux passing through achronal surfaces. This general method applies to the probability density currents with causal kernel regarding the massive scalar boson. Similarly one derives the covariant family of representations of the causal logic related to the stress energy tensor of the massive scalar boson. To prove these results, it is necessary to develop certain techniques of geometric measure theory concerning sets with almost Lipschitz boundaries.
References
[1] Moretti, V. (2023), On the relativistic spatial localization for massive real scalar Klein–Gordon quan-
tum particles. Letters in Mathematical Physics 113, 66
[2] De Rosa C., Moretti V. (2024), Quantum particle localization observables on Cauchy surfaces of
Minkowski spacetime and their causal properties Letters in Mathematical Physics 114, 24
[3] Catrigiano D.P.L., De Rosa C., Moretti V. (2025), Achronal localization and representation of the
causal logic from conserved current, application to massive scalar boson arXiv:2501.12699
[4] Castrigiano D.P.L. (2025), Achronal localization, representations of the causal logic for massive sys-
tems. Lett Math Phys 115, 25 .
∗University of Trento, Italy and INFN-TIFPA; e-mail: carmine.derosa@unitn.it