Strong C P phase and parity in the Hamiltonian formalism
Year: 2025
Type: article
Abstract: We show using the Hamiltonian formalism that if parity is a good symmetry of QCD, then the strong C P phase θ ¯ must be 0 or π . We find that for P to be a physical symmetry, it must leave the Hilbert space H θ associated with the θ -vacuum invariant ( P : H θ → H θ ), which is possible only for θ = 0 or π . We also show that forming linear combinations of states from different θ sectors produces only classical statistical mixtures, consistent with superselection rules, confirming that H θ is the most general Hilbert space for the quantum theory. Furthermore, we demonstrate that requiring [ P , Ω ] = 0 —where Ω is the generator of large gauge transformations—independently enforces θ ¯ = 0 (mod π ), and that for complex quark mass matrix M , if a generalized parity operator P is a symmetry, then the value of θ gets determined so that it exactly cancels A r g D e t M , again giving θ ¯ = 0 ( mod π ) . These results establish the equivalence of the Hamiltonian and Lagrangian approaches to the strong C P problem.
DOI: 10.1103/bl6j-dt75
Author: Ravi Kuchimanchi
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4415295538