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Effective potential for »Ж4 theory at finite temperature in R x SD-1 and R x HD-1 // Tomsk State Pedagogical University Bulletin. 2004. Issue 7 (44). P. 99-109

We calculate the explicit expression of the effective potential in а »Ж4 theory at finite temperature in a static universe for arbitrary spacetime dimensions (2dDin R x SD-1 and R x HD-1. The phase structure of a »Ж4 theory is found by observing the minimum of the effective potential with varying temperature and scale factor. All the ring diagrams are resummed for De4 to improve the loop expansion at high temperature. For a conformaily coupled and a minimally coupled scalar field it is shown that temperature and positive curvature suppress the symmetry breaking, while negative curvature enhances it. The conformaily coupled scalar has larger curvature effects than the minimally coupled one.

REGULARIZATION PARAMETER INDEPENDENT APPROACH IN A FOUR FERMION INTERACTION MODEL // Tomsk State Pedagogical University Bulletin. 2012. Issue 13 (128). P. 66-69

In QCD a non-perturbative effect is essential in low energy phenomena. A usual perturbative procedure loses its validity. A four-fermion interaction model is used to evaluate the low energy phenomena for quarks and gluons. Since the four-fermion interaction is nonrenormalizable, the results depend on the regularization parameter in four spacetime dimensions. Here we show the possibility to eliminate the regularization parameter dependence for some of physical observables.

Keywords: four-fermion interaction, dimensional regularization

SCHWINGER-DYSON ANALYSIS OF 1+2 DIMENSIONAL QED // Tomsk State Pedagogical University Bulletin. 2014. Issue 12 (153). P. 100-102

The QED ground state is studied for a four component Dirac fermion with the topological Chern-Simons term in 1+2 dimension. The Lagrangian for a massless Dirac fermion has the parity and the chiral symmetries. Spontaneous breaking of these symmetries can be found by evaluating the vacuum expectation values for fermion and anti-fermion pairs. We introduce approximate vertex functions and calculate the expectation values by solving the Schwinger-Dyson equation. We observe a smaller gauge dependence for the Ball-Chiu vertex function.

Keywords: 1+2 dimensional QED, Schwinger-Dyson equation, Chern-Simons term