Abstract
We apply the BMHV scheme for non-anticommuting γ5 to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories.
Abstract
I derive a formula for the coupling-constant derivative of the coefficients of the operator product expansion (Wilson OPE coefficients) in an arbitrary curved space, as the natural extension of the quantum action principle. Expanding the coefficients themselves in powers of the coupling constants, this formula allows to compute them recursively to arbitrary order. As input, only the OPE coefficients in the free theory are needed, which are easily obtained using Wick’s theorem. I illustrate the method by computing the OPE of two scalars ϕ in hyperbolic space (Euclidean Anti-de Sitter space) up to terms vanishing faster than the square of their separation to first order in the quartic interaction gϕ4, as well as the OPE coefficient "Image missing" at second order in g.
We investigate the basic assumptions leading to Schwinger’s quantum action principle in quantum mechanics. We present this principle in a new way that clarifies some previous developments, for example, the derivation of the fundamental commutators among the canonical variables and the Heisenberg equation for operators. We define operators associated with the classical transformations of the Galilei group, i.e., translations, boosts, and rotations and show their commutators obey the Lie algebra of the Galilei group.PACS Nos.: 83.65.Ca, 11.10.Ef
We study the appearance of anomalies of the Master Ward Identity, which is a universal renormalization condition in perturbative QFT. The main insight of the present paper is that any violation of the Master Ward Identity can be expressed as a local interacting field; this is a version of the well-known Quantum Action Principle of Lowenstein and Lam. Proceeding in a proper field formalism by induction on the order in ħ, this knowledge about the structure of possible anomalies as well as techniques of algebraic renormalization are used to remove possible anomalies by finite renormalizations. As an example, the method is applied to prove the Ward identities of the O(N) scalar field model.
Two-loop application of the Breitenlohner-Maison/’t Hooft-Veltman scheme with non-anticommuting γ5: full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory