Some Analytical Aspects in Field Theories with Dynamical Mass Generation

The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski solution is looking for. The examples are reviewed and studied for several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence of propagator pole goes hand by hand with the nontrivial solution for mass function. The consequences are discussed.