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Confinement Models at Finite Temperature and Density · Around

2009

Confinement Models at Finite Temperature and Density

Lo, Pok Man, Swanson, Eric S.

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In-medium chiral symmetry breaking in confining potential models of QCD is examined.

Past attempts to analyse these models have been hampered by infrared divergences that appear at non-zero temperature.
We argue that previous attempts to circumvent this problem are not satisfactory and demonstrate a simple resolution.
We also show that the expectation that confining models do not exhibit a chiral phase transition is incorrect.

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A simple example is the following: the integral ∫ d 3 r r exp ( − r 2 / 2 ) \int d^{3}r\,r\exp(-r^{2}/2) is well-defined; however its momentum space equivalent is ∫ d 3 k / ( 2 π ) 3 ( − 8 π / k 4 ) ( 2 π ) 3 / 2 exp ( − k 2 / 2 ) \int d^{3}k/(2\pi)^{3}(-8\pi/k^{4})(2\pi)^{3/2}\exp(-k^{2}/2) which is infrared divergent. The problem, of course, can be traced to the naive expression for the Fourier transform of a linear potential

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