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Thermal one- and two-graviton Green's functions in the temporal gauge

F. T. Brandt·B. Cuadros-Melgar·F. R. Machado
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Abstract

The thermal one- and two-graviton Green's function are computed using a temporal gauge. In order to handle the extra poles which are present in the propagator, we employ an ambiguity-free technique in the imaginary-time formalism. For temperatures T high compared with the external momentum, we obtain the leading T^4 as well as the subleading T^2 and log(T) contributions to the graviton self-energy. The gauge fixing independence of the leading T^4 terms as well as the Ward identity relating the self-energy with the one-point function are explicitly verified. We also verify the 't Hooft identities for the subleading T^2 terms and show that the logarithmic part has the same structure as the residue of the ultraviolet pole of the zero temperature graviton self-energy. We explicitly compute the extra terms generated by the prescription poles and verify that they do not change the behavior of the leading and sub-leading contributions from the hard thermal loop region. We discuss the modification of the solutions of the dispersion relations in the graviton plasma induced by the subleading T^2 contributions.

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F. T. Brandt, B. Cuadros-Melgar, F. R. Machado. 2003-04-23. Thermal one- and two-graviton Green's functions in the temporal gauge. https://doi.org/10.1103/physrevd.67.125006

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