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M. Khandoga , V. Skalozub. Gluon Polarization Tensor in external field in SU(3) theory. New Physics and Quantim Chromodynamics at External Conditions 2011 May 5 Dnipropetrovsk. Introduction.
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New Physics and Quantim Chromodynamics at External Conditions 2011
- QCD Lagrangian
Field potential А(х) is divided into external field B(x)andquantum fluctuations Q(x):
External field is chosen in the following form:
Lagrangian in background gauge:
Since external field is directed along 3rd axis in the color space, it is convenient to introduce the following basis, which is called charged:
Spatial structure remains unchanged
Now we have 8 degrees of freedom instead of 3 which results in 8 gauge particles.
One more external field is added, it has same spatial orientation and directed along 8th axis in color space.
- SU(3) group structure constants.
Let’s switch to charged basis:
Neutral gluons do not interact with each other. We can write interaction Lagrangians of both neutral gluons as a combination of SU(2)-like Lagrangians:
Every interaction Lagrangian has a structure, identical to SU(2) case.
Thus the polarization operator of neutral gluons in SU(3) theory can be brought to SU(2) case, already researched by M.Bordag, V. Skalozub, Phys. Rev. D 75, 125003 (2007)
Spontaneous generation of magnetic fields at high temperature
But after reaching some temperature only one field remains:
Hence the behavior of field-dependant quantities differs significantly at high temperature. Let’s illustrate it on Debye mass.
If electrical potential is surrounded by plasma, it has a limited reach:
Sometimes it is convenient to use an inverted quantity:
In QFT Debye screening is caused by vacuum polarization. Debye mass can be obtained from polarization operator:
In finite-temperature QCD there is a well-known result:
O. Kalashnikov (1984)
Debye mass slightly grows at high temperature:
In SU(3) theory charged gluons do interact with each other:
SU(2) case was researched in paper by M. Bordag and V. Skalozub Phys. Rev. D 77, 105013 (2008)
For polarization operators of charged gluons we get
Expressions for Debye mass:
Dependence on temperature: