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- W1830733313 abstract "This work is about a formulation of abelian gauge theories out-of-equilibrium. In contrast to thermal equilibrium, systems out-of-equilibrium are not constant in time, and the interesting questions in such systems refer to time evolution problems. After a short introduction to quantum electrodynamics (QED), the two-particle irreducible (2PI) effective action is introduced as an essential technique for the study of quantum field theories out-of-equilibrium. The equations of motion (EOMs) for the propagators of the theory are then derived from it. It follows a discussion of the physical degrees of freedom (DOFs) of the theory, in particular with respect to the photons, since in covariant formulations of gauge theories unphysical DOFs are necessarily contained.After that the Eoms for the photon propagator are examined more closely. It turns out that they are structurally complicated, and a reformulation of the equations is presented which for the untruncated theory leads to an essential structural simplification of the EOMs. After providing the initial conditions which are necessary in order to solve the EOMs, the free photon EOMs are solved with the help of the reformulated equations. It turns out that the solutions diverge in time, i.e. they are secular. This is a manifestation of the fact that gauge theories contain unphysical DOFs. It is reasoned that these secularities exist only in the free case and are therefore artificial. It is however emphasized that they may not be a problem in principle, but certainly are in practice, in particular for the numerical solution of the EOMs. Further, the origin of the secularities, for which there exists an illustrative explanation, is discussed in more detail.Another characteristic feature of 2PI formulations of gauge theories is the fact that quantities calculated from approximations of the 2PI effective action, which are gauge invariant in the exact theory as well as in an approximated theory at each perturbative order, are not gauge invariant in general. A closely related phenomenon is the fact that the Ward identities, which are relations between correlation functions of different order, are not in general applicable to correlation functions which are calculated from the 2PI effective action. As an example the photon self-energy is presented, which is transverse in the exact theory as well as perturbatively at each order, but not if it is calculated starting from the 2PI effective action. It is shown that both these phenomena are caused by the complex resummation implemented by the 2PI effective action.Finally, a concrete approximation of the 2PI effective action is presented, and the self-energies are derived from it in a form which is suitable for the practical implementation on a computer. Some results are shown which have been obtained by the numerical solution of the 2PI EOMs." @default.
- W1830733313 created "2016-06-24" @default.
- W1830733313 creator A5065583678 @default.
- W1830733313 date "2013-04-08" @default.
- W1830733313 modified "2023-09-27" @default.
- W1830733313 title "Nonequilibrium Formulation of Abelian Gauge Theories" @default.
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