The authors quantize the Abelian and nonAbelian Chern-Simons theories in (2+1) dimensions by the Dirac quantization formulation. Gauge theories with a topological mass term in both the Abelian and nonAbelian cases are also quantized by the same method.
Besides the * theory, the 6 model and the * + 3 model are aiso useful in physics. Some specific types of solutions of them can be obtained from the solutions of * model. The important solutions previously known are the special examples of ours. The dissipation equations of these models are also studied. The results indicate that the friction effects spread the singular solutions with velocity v = 1 (Heaviside function) of the undamped equations such that they are nonsingular and their velocities are lower than one.
By means of Gaussian effective potential method, we investigate two models with and coupling in 3+1 dimensions respectively. While the fermion effect through Yukawa coupling makes the autonomous λϕ4 theory more stable, it is shown that there are three different autonomous phases for model. The temperature dependences of these two models are similar to those in pure λϕ4 autonomous theory.
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