Renormalized Lie perturbation theory

Renormalized Lattice Perturbation Theory

Apparent large failures of perturbation theory in lattice gauge theory at g* 5 1.0 result from the use of the bare coupling constant of the lattice regulator in the perturbative expansion. They can be cured by the use of a coupling constant defined by some physical process. Thissituation is thesame as that encountered in dimensionally regularized perturbation theory, where the use of a coupling...

Renormalized perturbation Theory: a missing chapter

Why a talk on Renormalized Perturbation Theory (RPT) in 2008? The consensus established in the 70’s under the acronym BPHZ is part of elementary particle physicists’ theoretical equipment. Yet, the corresponding literature is hard to penetrate for a mind endowned with good logical connections typically that of a professional mathematician. This state of affairs may be assigned, in parts, to som...

A Convergent Renormalized Strong Coupling Perturbation Expansion

The Rayleigh-Schrr odinger perturbation series for the energy eigenvalue of an anharmonic oscillator deened by the Hamiltonian ^ H (m) () = ^ p 2 + ^ x 2 + ^ x 2m with m = 2; 3; 4;. .. diverges quite strongly for every 6 = 0 and has to summed to produce numerically useful results. However, a divergent weak coupling expansion of that kind cannot be summed eeectively if the coupling constant is l...

MS-TP1-95-06 The renormalized φ4 4-trajectory by perturbation theory in the running coupling

The Lie algebra perturbation Lemma

We shall establish the following.