Joint BCAM-UPV/EHU Analysis and PDE seminar: Positron Position Operators

Abstract
I address the question of what kind of position operators should accompany the free standard quantized Dirac field. I propose a POVM on a configuration space of particle positions of two kinds of point particles, positrons and electrons, acting on the Hilbert space of the quantized Dirac field. It is supposed to serve in several roles of position operators: (i) characterizing what an ideal detector sees, (ii) clarifying how probabilities of macroscopic configurations are provided by the quantum state, and (iii) defining the distribution of Bohmian particles. The existence of this POVM, which I call P_natural, depends on a mathematical conjecture which at present I can neither prove nor disprove; in the talk I explore consequences of the conjecture. P_natural is different from the obvious POVM that one would guess from the wave function representation (as in Thaller's book) of Fock space vectors; several considerations make P_natural seem more physically plausible than P_obvious. I will also explain what the corresponding Bohmian trajectories look like, how P_natural avoids Malament's no-go theorem, how it arises naturally as a limiting object from taking the Dirac sea literally, and how it is expected to extend to the cases with external fields, curved space-time, and interaction.



Link to the session: 
">https://us06web.zoom.us/j/99649860282?pwd=SE0vemtYMFlwbFBNTXQyOTBONG0vZz09


More info at https://sites.google.com/view/apdebilbao/home