2PI effective action and gauge dependence identities

Carrington, M. E.; Kunstatter, G.; Zaraket, H.

doi:10.1140/epjc/s2005-02277-x

Cited by 62 publications

(68 citation statements)

References 13 publications

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“…Given the manifestation of the phase transition in the correlation functions, it is an interesting question whether also the other thermodynamic information can be obtained from the correlation functions. Indeed, it is, in principle, possible to determine the thermodynamic potential by a 2PI/Luttinger-Ward-Cornwall-Jackiw-Tomboulis construction [239,280,[446][447][448][449][450][451][452]. The exact expression is given by [452] …”

Section: Ghost Schwinger Function In Four Dimensionsmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

2013

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Gauge theories of the Yang-Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity, which requires the introduction of non-local constraints. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the single most important first step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion.After gauge-fixing, it is possible to study gauge bosons in detail. The most direct access is provided by their correlation functions. The corresponding two-and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, particle-like properties at high energies, and the running coupling. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras.Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. In addition, this resolution provides an explicit and constructive solution to the Linde problem.Thus, the technical and conceptual framework presented here can be taken as a basis how to determine correlation functions in Yang-Mills theory, therefore opening up the avenue to investigate theories of direct practical relevance. The status of this effort will be briefly described, alongside with connections to other approaches to Yang-Mills theory beyond perturbation theory.

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Section: Ghost Schwinger Function In Four Dimensionsmentioning

confidence: 99%

Gauge bosons at zero and finite temperature

2013

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“…One is that it is straightforward to systematically extend the order of the approximation. Another is that the truncation respects the symmetries of the original theory, to the order of the approximation [21,22]. To solve the flow equations, one chooses μ large enough that when κ = μ the theory is classical and the 2-and 4-point functions are known functions of the bare parameters.…”

Section: -P4mentioning

confidence: 99%

“…Equation (22) gives a series of infinite hierarchies of coupled equations for the 2PI kernels in which kernels with fixed n and different m are coupled together. However, unlike the hierarchy produced from the 1PI effective action, when the 2PI effective action is truncated at some finite loop order, the hierarchy in (22) is also truncated.…”

Section: -P4mentioning

confidence: 99%

Techniques for calculations withnPI effective actions

M.E.

2015

EPJ Web of Conferences

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Abstract. We consider a symmetric scalar theory with quartic coupling in 2-and 3-dimensions and compare the self-consistent 4-point vertex obtained from the 4PI effective action with the Bethe-Salpeter 4-vertex from 2PI effective action. We show that when the coupling is large the contributions from the higher order effective action are large. We also show that one can solve the 2PI equations of motion in 4-dimensions, without introducing counter-terms, using a renormalization group method. This method provides a promising starting point to study the renormalization of higher order nPI theories.

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“…This situation is reminiscent of the recent proof that the truncated on-shell 2PI effective action has a controlled gauge dependence, with the explicit gauge-dependent terms always appearing at higher order [11][12][13].…”

Section: Gauge Dependence Of the Fermion Quasiparticle Polesmentioning

confidence: 99%

“…While the position of quasiparticle poles in the leading order HTL approximation are completely gauge independent [9,10], nevertheless gauge dependence will enter at subleading order and gauge-independent extensions beyond the leading order HTL results are not yet available. More recently, several authors [11][12][13] have shown that the truncated on-shell two-particle-irreducible (2PI) effective action has a controlled gauge dependence, with the explicit gauge-dependent terms always appearing at higher order. It would be interesting to study possible cancellation of the leading gauge dependence in the singularity structure of gauge boson and fermion propagators beyond the * Current Address: Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA; Electronic address: sywang@physics.udel.edu leading order HTL approximation.…”

Section: Introductionmentioning

confidence: 99%

Gauge dependence of the fermion quasiparticle poles in hot gauge theories

Wang¹

2004

Phys. Rev. D

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The gauge dependence of the complex fermion quasiparticle poles corresponding to soft collective excitations is studied in hot gauge theories at one-loop order and next-to-leading order in the hightemperature expansion, with a view towards going beyond the leading order hard thermal loops and resummations thereof. We find that for collective excitations of momenta k ∼ eT the dispersion relations are gauge independent, but the corresponding damping rates are gauge dependent. For k ≪ eT and in k → 0 limit, both the dispersion relations and the damping rates are found to be gauge dependent. The gauge dependence of the position of the complex quasiparticle poles signals the need for resummation. Possible cancellation of the leading gauge dependence at two-loop order in the case of QED is briefly discussed.

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2PI effective action and gauge dependence identities

Cited by 62 publications

References 13 publications

Gauge bosons at zero and finite temperature

Gauge bosons at zero and finite temperature

Techniques for calculations withnPI effective actions

Gauge dependence of the fermion quasiparticle poles in hot gauge theories

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