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arXiv · 0707.2860

Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions

J. Greensite·S. Olejnik
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Abstract

We propose an approximation to the ground state of Yang-Mills theory, quantized in temporal gauge and 2+1 dimensions, which satisfies the Yang-Mills Schrodinger equation in both the free-field limit, and in a strong-field zero mode limit. Our proposal contains a single parameter with dimensions of mass; confinement via dimensional reduction is obtained if this parameter is non-zero, and a non-zero value appears to be energetically preferred. A method for numerical simulation of this vacuum state is developed. It is shown that if the mass parameter is fixed from the known string tension in 2+1 dimensions, the resulting mass gap deduced from the vacuum state agrees, to within a few percent, with known results for the mass gap obtained by standard lattice Monte Carlo methods.

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J. Greensite, S. Olejnik. 2008-02-01. Dimensional Reduction and the Yang-Mills Vacuum State in 2+1 Dimensions. https://doi.org/10.1103/physrevd.77.065003

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