Gauge-fixing dependence ofΦ-derivable approximations

Abstract

Abstract. We examine the problem of gauge dependence of the 2PI effective action and its Φ-derivable approximations in gauge theories. The dependence on the gauge-fixing condition is obtained. The result shows that Φ-derivable approximations, defined as truncations of the 2PI effective action at a certain order, have a controlled gauge dependence, i.e. the gauge dependent terms appear at higher order than the truncation order. Furthermore, using the stationary point obtained for the approximation to evaluate the complete 2PI effective action boosts the order at which the gauge dependent terms appear to twice the order of truncation. We also comment on the significance of this controlled gauge dependence.

Aspects of the functional renormalisation group

“…First of all this concerns the interrelation of functional methods like the general flows studied here, Dyson-Schwinger equations [149][150][151][152][153][154][155][156][157], stochastic quantisation [158][159][160], and the use of N PI effective actions [161][162][163][164][165][166][167][168][169][170][171][172][173][174][175][176][177]. All these methods have met impressive success in the last decade, in particular if it comes to physics where a perturbative treatment inherently fails.…”

“…The derivation of (7.38) highlights the fact that (7.31) also constitutes the Slavnov-Taylor identity for the 2PI effective action, e.g. [175,176]. To that end we restrict ourselves to a = a and quadratic regulators R ab .…”

“…Within regularisation of the 2PI effective action that regularises three point functions the source Q ab can be eliminated analogously to (7.38). This is an interesting option for N PI regularisations of gauge theories, in particular in view of consistent approximations [174][175][176][177].…”

Renormalization of Φ-derivable approximations in scalar field theories

“…Φ-derivable approximations are known to be "conserving" approximations [2], that is, they are consistent with global symmetries of the Lagrangian [11]. However since they lead to modifications of the propagators while leaving the vertices unaffected, they violate the Ward identities associated to local symmetries; consequences of such violations have been recently explored quantitatively [12], and shown to be suppressed with respect to naive estimates based on power counting.…”

Gauge dependence of the fermion quasiparticle poles in hot gauge theories

“…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.…”