arXiv subjects

W. Bietenholz

Publications and source records attributed to W. Bietenholz.

95 records · Page 6Linked to original sources

arXiv1994

Perfect Lattice Actions for the Gross-Neveu Model at large N

Fixed point actions for free and interacting staggered lattice fermions are constructed by iterating renormalization group transformations. At large N the fixed point action for the Gross-Neveu model is a perfect action in the sense of Hasenfratz and Niedermayer, i.e. cut-off effects are completely eliminated. In particular, the fermionic 1-particle energy spectrum of the lattice theory is identical with the one of the continuum even for arbitrarily small correlation lengths. The cut-off effects of the chiral condensate are eliminated using a perfect operator. (The paper is stored as a ps-file containing both the text and 5 figures.)

hep-lat↗

arXiv1994

Goldstone Bosons in a Finite Volume: The Partition Function to Three Loops

A system of Goldstone bosons - stemming from a symmetry breaking $O(N) \to O(N-1)$ - in a finite volume at finite temperature is considered. In the framework of dimensional regularization, the partition function is calculated to 3 loops for 3 and 4 dimensions, where Polyakov's measure for the functional integration is applied. Although the underlying theory is the non-linear $σ$ model, the 3 loop result turns out to be renormalizable in the sense that all the singularities can be absorbed by the couplings occuring so far. In finite volume, this property is highly non trivial and confirms the method for the measure. We also show that the result coincides with the one obtained using the Faddeev- Popov measure. This is also true for the maximal generalization of Polyakov's measure: none of the additional invariant terms that can be added contributes to the dimensionally regularized system. Our phenomenological Lagrangian describes e.g. 2 flavor chiral QCD as well as the classical Heisenberg model, but there are also points of contact with the Higgs model, superconductors etc. Moreover the finite size corrections to the susceptibility might improve the inerpretation of Monte Carlo results on the lattice.

hep-th↗

arXiv1994

Chiral Symmetry, Renormalization Group and Fixed Points for Lattice Fermions

We discuss fixed point actions for various types of free lattice fermions. The iterated block spin renormalization group transformation yields lines of local but chiral symmetry breaking fixed points. For staggered fermions at least the $U(1) \otimes U(1)$ symmetry can be preserved. This provides a basis for approximating perfect actions for asymptotically free theories far from the critical surface. For a class of lattice fermions that includes Wilson fermions we find in addition one non local but chirally invariant fixed point. Its vicinity is studied in the framework of the Gross Neveu model with weak four Fermi interaction.

hep-lat↗

arXiv1994

Solutions of the Spherically Symmetric Wave Equation in $p+q$ Dimensions

We discuss solutions of the spherically symmetric wave equation and Klein Gordon equation in an arbitrary number of spatial and temporal dimensions. Starting from a given solution, we present various procedures to generate futher solutions in the same or in different dimensions. The transition from odd to even or non integer dimensions can be performed by fractional derivation or integration. The dimensional shift, however, can also be interpreted simply as a modification of the dynamics. We also discuss the analytic continuation to arbitrary real powers of the D'Alembert operator. There, particular peculiarities in the pole structure show up when $p$ and $q$ are both even. Finally we give operators which transform a time into a space coordinate and v.v. and comment on their possible relation to black holes. In this context, we describe a few aspects of the extension of our discussion to a curved metrics.

hep-th↗

arXiv1993

Fixed Point Actions for Lattice Fermions

The fixed point actions for Wilson and staggered lattice fermions are determined by iterating renormalization group transformations. In both cases a line of fixed points is found. Some points have very local fixed point actions. They can be used to construct perfect lattice actions for asymptotically free fermionic theories like QCD or the Gross-Neveu model. The local fixed point actions for Wilson fermions break chiral symmetry, while in the staggered case the remnant $U(1)_e \otimes U(1)_o$ symmetry is preserved. In addition, for Wilson fermions a nonlocal fixed point is found that corresponds to free chiral fermions. The vicinity of this fixed point is studied in the Gross-Neveu model using perturbation theory.

hep-lat↗