Unstable Particles in Quantum Field Theory

Abstract

In honor of Dave Roper's 90th birthday, I present a pedagogical introduction to our modern understanding of unstable particles in Quantum Field Theory, based on the analytic structure of the propagator, with occasional remarks on the Roper resonance. I discuss the mass and decay rate of unstable particles, Breit-Wigner resonance formulae and width, poles and branch cuts, and pole trajectories.

Figures (7)

• Figure 1: Self-energy corrections to the propagator.
• Figure 2: Evaluating the Fourier transform of the propagator by closing the contour in the lower-half energy plane (for $t>0)$.
• Figure 3: Analytic structure of the propagator in the complex $p^2$ plane. The poles lie on the second sheet.
• Figure 4: Analytic structure of the propagator in the complex energy plane. The poles lie on the second sheet. The integration contour for the Fourier transform is also shown.
• Figure 5: Evaluating the Fourier transform of the propagator by closing the contour in the lower-half energy plane (for $t>0)$ on the first sheet.