Closed-form expressions for thermal Green's functions in field theories

Almeida, Alisson Pinto de; Frenkel, Jacob A.; Taylor, John

doi:10.1103/physrevd.45.2081

Cited by 5 publications

(9 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In thermal quantum field theory the 1PI contributions to the graviton 2-point function are in general dependent on the parametrization of the graviton fields. However, as shown in the second work of reference [12], the traceless quantity: However for contributions from thermal matter, which are characterized by the presence of massive particles,Π µν, αβ is no longer independent of the graviton field parametrization at finite temperatures. Our task is to generalize (5.1) in such a way that the corresponding quantity should represent a physical graviton self-energy at all temperatures.…”

Section: The Graviton Self-energy At Finite Temperaturementioning

confidence: 98%

“…Hence, the effective graviton propagator can be written in the form:D in the second paper of Ref. [12]]. Considering for definiteness the high-temperature limit, it is then straightforward to verify that Eq.…”

Section: The Effective Graviton Propagatormentioning

confidence: 99%

“…This can always be achieved by a further rescaling of the h ′ fields in (5.3) [see ref. [12]]. Furthermore, we shall consider for simplicity the class of parametrizations characterized by the conditions a b − a c + 2 b d = 0;…”

Section: The Graviton Self-energy At Finite Temperaturementioning

confidence: 99%

See 2 more Smart Citations

Thermal matter and radiation in a gravitational field

1994

Self Cite

View full text Add to dashboard Cite

We study the one-loop contributions of matter and radiation to the gravitational polarization tensor at finite temperatures. Using the analytically continued imaginary-time formalism, the contribution of matter is explicitly given to next-to-leading ($T^2$) order. We obtain an exact form for the contribution of radiation fields, expressed in terms of generalized Riemann zeta functions. A general expression is derived for the physical polarization tensor, which is independent of the parametrization of graviton fields. We investigate the effective thermal masses associated with the normal modes of the corresponding graviton self-energy.Comment: 32 pages, IFUSP/P-107

show abstract

Section: The Graviton Self-energy At Finite Temperaturementioning

confidence: 98%

Section: The Effective Graviton Propagatormentioning

confidence: 99%

See 1 more Smart Citation

Thermal matter and radiation in a gravitational field

1994

Self Cite

View full text Add to dashboard Cite

show abstract

“…We will discuss here, for definiteness, the retarded thermal self-energy of the gluon, which is obtained by the analytic continuation k 0 → k 0 + iǫ. (A rather similar analysis can be made in the case of the time-ordered self-energy, following the approach presented in reference [11]). In order to illustrate in a simple way the mechanism of the cancellation of the log(−k 2 ) contributions, let us first consider the special case of the Feynman gauge, where Π C vanishes even at finite temperature.…”

Section: Tl µνmentioning

confidence: 99%

“…As we have seen, only such contributions would give rise, after the K-integration, to individual log(−k 2 ) terms. It is possible to evaluate exactly all other temperature-dependent contributions to I 1 , in terms of logarithmic functions and of Riemann's zeta functions with arguments (1 + K ± /T ), which are analytic when K ± → 0 [11]. Since the complete expression is rather involved, we indicate here, for simplicity, only the logarithmic temperature-dependent contributions to I 1 :…”

mentioning

confidence: 99%

Behavior of logarithmic branch cuts in the self-energy of gluons at finite temperature

Brandt

Frenkel

1999

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We give a simple argument for the cancellation of the log(−k 2 ) terms (k is the gluon momentum) between the zero-temperature and the temperature-dependent parts of the thermal self-energy.There have been many studies of thermal Green functions in gauge field theories [1][2][3][4][5][6][7], which show that their behavior at finite temperature is rather different from the one at zero temperature. In particular, it was recently pointed out by Weldon [8] that in QED, the logarithmic branch cut singularities cancel to one loop-order, in the thermal self-energy of the electron.The purpose of this note is to show that in the Yang-Mills theory, a somewhat similar behavior occurs in the full gluon self-energy, which includes finite temperature effects. Of course, in this theory, the massless gluons are quite modified by these effects and the gluon propagator requires the Braaten-Pisarski resummation. Nevertheless, it is interesting to remark that, even before such a procedure is carried out, the one-loop log(−k 2 ) terms cancel in the sum of the T = 0 and the T = 0 contributions to the gluon self-energy. As we shall see, this happens because the log(−k 2 ) terms appear in the thermal part of the self-energy only in the combination log(−k 2 /T 2 ). But one can show that the log(T 2 ) contributions have the same structure as the ultraviolet divergent terms which occur at zero temperature [9]. Consequently, the log(−k 2 /T 2 ) terms combine directly with the log(−k 2 /µ 2 ) contributions which occur at T = 0 (µ is the renormalization scale), so that the log(−k 2 ) terms cancel in a simple way in the thermal self-energy of the gluon. The branch cut in the log(−k 2 ) contribution at T = 0 is associated with the imaginary part of the self-energy, which gives the rate of decay of a time-like virtual gluon into two real gluons. Although this contribution cancels at T = 0, there appear then additional, temperature-dependent logarithmic branch points. These singularities indicate processes not available at zero temperature, where particles decay or are created through scattering in the thermal bath.To one-loop order, the thermal self-energy of gluons generally depends on three structure functions, Π T , Π L andwhere the projection operators P T,L µνare transverse with respect to the external four-momentum k µ and satisfy: 6,7]. The non-trnsverse projection operator P C µν can be written in the plasma rest frame as follows [10]Although Π C vanishes at T = 0 because of the Slavnov-Taylor identity, it is in general a non-vanishing function of the temperature, so that k µ Π µν = 0 for the exact self-energy. We will discuss here, for definiteness, the retarded thermal self-energy of the gluon, which is obtained by the analytic continuation k 0 → k 0 + iǫ.(A rather similar analysis can be made in the case of the time-ordered self-energy, following the approach presented in reference [11]). In order to illustrate in a simple way the mechanism of the cancellation of the log(−k 2 ) contributions, let us first consider the special case of...

show abstract