Multiple solutions for the fermion mass function in QED3

Theories that support dynamical generation of a fermion mass gap are of widespread interest. The phenomenon is often studied via the Dyson-Schwinger equation for the fermion self-energy, i.e., the gap equation. When the rainbow truncation of that equation supports dynamical mass generation, it typically also possesses a countable infinity of simultaneous solutions for the dressed-fermion mass function, solutions which may be ordered by the number of zeros they exhibit. These features can be understood via the theory of nonlinear Hammerstein integral equations. Using QED3 as an example, we demonstrate the existence of a large class of gap-equation truncations that possess solutions with damped oscillations. We suggest that there is a larger class, quite probably including the exact theory, which does not. The structure of the dressed fermion–gauge boson vertex is an important factor in deciding the issue.

Note:

8 pages, 6 figures. To appear in Phys. Rev. D

11.15.Tk
11.30.Rd
12.20.-m
12.38.Aw
fermion: mass
fermion: propagator
gap equation
Dyson-Schwinger equation
integral equations: nonlinear
mass generation

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