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Direct Calculation of Retarded/Advanced Green Function and Bremsstrahlung in Thermal QED

Author: Xiao
Tutor: WangEnKe
School: Central China Normal University
Course: Theoretical Physics
Keywords: temperature-field theory thermal QED Advanced/Retarded Green function bremsstrahlung radiation infrared divergence coherent state
CLC: O572.3
Type: Master's thesis
Year: 2002
Downloads: 70
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Abstract


The Finite-Temperature Field Theory is widely used to investigate the property of quark-gluon plasma. Basing on this theory, in this paper, a new Feyn-man rule for directly calculating the retarded, advanced Green functions and the bremsstrahlung in thermal QED are discussed.We first recall the Closed-Time Path Formalism in real-time finite-temperature field theory and introduce two kinds of representations: single-time representation and physical representation. The physical field, ghost field and matrix propagator are defined in the single-time representation. Type-1 vertex is identical with the physical field vertex, type-2 vertex is different with a opposite sign, external particle line (physical leg) is only connect with the type-1 vertex. In physical representation, the non-vanish components of matrix are retarded, advanced Green function and the matrix component related with the thermal distribution function. Using the Keldysh transformation, we deduce a new Feynman rule in <^3 theory. The advantage is that it can be used to directly calculate the real physics quantities in an economic way. In this way, we needn’t perform the analytical continuation from the result in the ITF. This new rule has the following property; the vertex is only related with the coupling constant and independent of the orientation of the momenta, one half of the vertex components vanish. The 2-pointself-energy and 3-point vertex correction in <j)3 theory are calculated in this rule, and the Fluctuation-Dissipation theorem for 3-point nonlinear response function is verified.With the run of RHIC, how to find the signals of QGP from the final hadrons state has become the sensitive topics in high energy heavy ion collision. In particular, because the electromagnetic signal can penetrate the medium without further strong interaction with others, this signal is considered to be the clearest one. So the study of bremsstrahlung in equilibrium will be helpful to understand the collective effects and thermodynamic property of QGP. In this thesis, we investigates the bremsstrahlung processes in thermal QED and its relation with coherent state. In the QED perturbative calculation, the infrared divergences of soft photons can be cancelled by virtual contribution. For a particle in thermal bath , except for the logarithmic divergence in zero temperature, it also has a new infrared divergence (linear divergence) from finite temperature effect. It is assumed the particle isn’t thermalized when passing through the plasma in equilibrium, so the electron propagator is independent of temperature. By calculating the Feynman diagram in RTF, we find that when taking into account both the thermal photon emission, absorption and the virtual photon exchange processes, the infrared divergences at zero and finite temperature can be cancelled at the same time. The full quantum calculation results for soft photon radiation coincide completely with the Poisson distribution obtained in the semiclassical approximation (the coupling of the classical current and quantized field). In the framework of thermofied dynamics it isshown that, at finite temperature the final state in the bremsstrahlung process is just the eigenstate of the annihilation thermal-field operator which indicates that it is a coherent state. The coherent state is represented by a minimum uncertainty wave packet, the quantum correlation in these state is absent, so that it behaves as a quasi-classical state. It is such a property that leads to the results coincide completely with those obtained in semiclassical approximation.

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