Vacuum diagrams in light-front field theory
Seminars
Seminar “Hadron Physics”
Date and Time: Friday, 21 June 2019, at 11:00 AM
Venue: Blokhintsev Hall (4th floor), Bogoliubov Laboratory of Theoretical Physics
Seminar topic: “Vacuum diagrams in light-front field theory”
Speaker: L. Martinovic (BLTP JINR & Institute of Physics SAS, Bratislava)
Abstract:
We demonstrate that vacuum diagrams in light front field theory are non-zero, contrary to the prevailing opinion. Using the light-front Hamiltonian (time-ordered) perturbation theory, the vacuum amplitudes in self-interacting scalar λφ3 and λφ4 models are obtained as p = 0 limit of the associated self-energy diagrams, where p is the external momentum. They behave as C(λ/μ)2 in D = 2, with μ being the scalar-field mass, or diverge in D = 4, in agreement with the usual “equal-time” form of field theory, and with the same value of the constant C. The simplest case of the vacuum bubble with two internal lines is analyzed in detail. It is shown that, surprisingly, the light-front diagrams are nonvanishing not due to the zero-mode contribution. This is made explicit using the DLCQ method — the discretized (finite-volume) version of the theory, where the light-front zero modes are manifestly absent, but the vacuum amplitudes still converge to their continuum-theory values with the increasing “harmonic resolution” K. Finally, a few open (and a bit puzzling) questions will be discussed.