A new start for local composite operators

Abstract

We present a formalism for local composite operators. The corresponding effective potential is unique, multiplicatively renormalizable, it is the sum of 1PI diagrams and can be interpreted as an energy-density. First we apply this method to $\lambda {\Phi }^4$ theory where we check renormalizability up to three loops and secondly to the Coleman-Weinberg model where the gauge independence of the effective potential for the local composite operator $\varphi {\varphi }^{\ast }$ is explicitely checked up to two loops.

20 pages

Cited by in corpus (27)

• Toward ab initio density functional theory for nuclei
• The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge
• The anomalous dimension of the composite operator A^2 in the Landau gauge
• An analytic study of the off-diagonal mass generation for Yang-Mills theories in the maximal Abelian gauge
• The Landau gauge gluon and ghost propagator in the refined Gribov-Zwanziger framework in 3 dimensions
• Dynamical gluon mass generation from <A^2> in linear covariant gauges
• Renormalizability of the local composite operator A^2 in linear covariant gauges
• Renormalizability of the Refined Gribov-Zwanziger action in the linear covariant gauges
• The anomalous dimension of the gluon-ghost mass operator in Yang-Mills theory
• Large $N_f$ quantum field theory
• Gluon-ghost condensate of mass dimension 2 in the Curci-Ferrari gauge
• Effective Field Theory for Dilute Fermions with Pairing
• More on ghost condensation in Yang-Mills theory: BCS versus Overhauser effect and the breakdown of the Nakanishi-Ojima annex SL(2,R) symmetry
• Quantum properties of a non-Abelian gauge invariant action with a mass parameter
• Gribov ambiguities at the Landau -- maximal Abelian interpolating gauge
• The BRST-invariant vacuum state of the Gribov-Zwanziger theory
• Ghost condensates in Yang-Mills theories in the Landau gauge
• Infrared massive gluon propagator from a BRST-invariant Gribov horizon in a family of covariant gauges
• The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator $Tr\int d^{4}x{F}_{\mu \nu }(D^2{)}^{-1}{F}_{\mu \nu }$ in the Landau gauge
• A combined study of the gluon and ghost condensates <A^2> and <epsilon^{abc} cbar^b c^c> in Euclidean SU(2) Yang-Mills theory in the Landau gauge
• Dynamically massive linear covariant gauges: setup and first results
• A potential setup for perturbative confinement
• Composite operator and condensate in the $SU(N)$ Yang-Mills theory with $U(N-1)$ stability group
• Non-perturbative aspects of Yang-Mills theories
• Three loop effective potential for $⟨\frac{1}{2}{A_{\mu }^a}^2⟩$ in the Landau gauge in QCD
• The Abelian Higgs model under a gauge invariant looking glass: exploiting new Ward identities for gauge invariant operators and the Equivalence Theorem
• Gribov Propagator and Symmetry Breaking