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Quantum Electrodynamics at High Temperature: (II) Three Spatial Dimensions
Author(s) -
AlvarezEstrada R. F.
Publication year - 1988
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190360303
Subject(s) - physics , renormalization , imaginary time , quantum electrodynamics , photon , electron , path integral formulation , quantum field theory , debye , quantum mechanics , quantum , quantum statistical mechanics , supersymmetric quantum mechanics
The photon sector of QED in d = 3 spatial dimensions is analyzed at high temperature thereby generalizing nontrivially a previous study for d = 1. The imaginary time formalism and an improved renormalized perturbation theory which incorporates second order Debye screening are used. General results are presented for the leading high temperature contributions to all renormalized connected photon Green's functions for fixed external momenta (much smaller than the temperature) to all orders in the improved perturbation theory. Those leading contributiona are ultraviolet finite, infrared convergent and gauge invahnt, and display an interesting form of dimensional reduction at high temperature. A new path integral representation is given for the high temperature partition function with an external photon source, which is shown to generate all leading high temperature Green's functions mentioned above, and, so, it displays neatly the kind of dimemionel reduction which makes QED to become simpler at high temperature. This limiting partition function corresponds to an imaginary time dependent electron positron field interacting with an electromagnetic field at zero imaginary time, and it depends on the renormalized electron maas and electric charge, the second order contribution to the usual renormalization constant Z 3 and a new mass term, which is associated to the photon field with vanishing Lorentz index. The new mass term corresponds to a finite number of diagrams in the high temperature improved perturbation theory and carriers ultraviolet divergences which are compensated for by other contributions (so that the leading high temperature Green's functions referred to above are ultraviolet finite). The dominant high temperature contributions to the renormalized thermodynamic potential to all perturbative orders: i) are given in terms of the above leading high‐temperature contributions to the photon Green's functions (except for a few diagrams of low order in the improved perturbation theory), ii) are both ultraviolet and infrared finite.