Effective action and vacuum expectations in nonlinear $\sigma$ model

B. A. Fayzullaev

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arXiv · 1510.07367

Effective action and vacuum expectations in nonlinear $\sigma$ model

B. A. Fayzullaev

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Abstract

The equations for effective action for nonlinear $\sigma$ model are derived using DeWitt method in two forms - for generator of vertex parts $\Gamma$ and for generator of weakly connected parts $W$. Loop-expansion solutions to these equations are found. It is shown that vacuum expectation values for various quantities including divergence of a N\"{o}ther current, trace of the energy-momentum tensor and so on, can be calculated by this method. Also it is shown that vacuum expectation to the sigma-field is determined by an explicit combination of tree Green function and classical solution. It is shown that the limit when coupling constant tends to zero is singular one.

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B. A. Fayzullaev. 2015-10-26. Effective action and vacuum expectations in nonlinear $\sigma$ model. https://arxiv.org/abs/1510.07367

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