Pietro Menotti

Symanzik's Improved Lagrangian for Lattice Gauge Theory

Abstract It is shown that Symanziks program, to all leading logarithms, can be accomplished, for pure Yang-Mills theory, by adding to the Wilson lagrangian the simplest term of dimension 6 i.e. the ractangle. Moreover no changes in the source terms are needed.

The propagator in the A0 = 0 gauge

Abstract We compute the Wilson loop in the A 0 = 0 gauge for abelian and non-abelian theories. We find to fourth order that only two choices for the longitudinal propagator are consistent with the results obtained in the Feynman and Coulomb gauges. In particular the principal value presciption does not work.

The energy-momentum tensor for lattice gauge theories

Abstract We show how to construct the energy-momentum tensor for lattice gauge theories by imposing the validity of the Ward identities related to the conservation of this tensor. Such a procedure is carried out both at the perturbative and non-perturbative level, and the one-loop calculation for QED is given. We then clarrify how the correct scale anomaly is recovered on the lattice.

Proof of Polyakov conjecture for general elliptic singularities

Abstract A proof is given of Polyakov conjecture about the accessory parameters of the SU(1,1) Riemann–Hilbert problem for general elliptic singularities on the Riemann sphere. Its relevance to (2+1)-dimensional gravity is stressed.

Faddeev-Popov determinant in 2-dimensional Regge gravity☆

By regularizing the conical singularities by means of a segment of a sphere or pseudosphere and then taking the regulator to zero, we compute exactly the Faddeev--Popov determinant related to the conformal gauge fixing for a piece-wise flat surface with the topology of the sphere. The result is analytic in the opening angles of the conical singularities in the interval (

The energy-momentum tensor on the lattice: the scalar case

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Riemann–Hilbert treatment of Liouville theory on the torus

,

FUNCTIONAL INTEGRATION ON TWO-DIMENSIONAL REGGE GEOMETRIES

4\pi

Liouville theory, accessory parameters and (2+1)-dimensional gravity☆

) and in the smooth limit goes over to the continuum expression. The Riemann-Roch relation on the dimensions of ker

Diffeomorphism invariant measure for finite dimensional geometries

(L^{\dag}L)