Monte-Carlo Renormalisation Group for Lattice QCD

Author: Patel, Apoorva Dayaram

Year: 1984

Degree: Dissertation (Ph.D.)

Advisor: Fox, Geoffrey C.

Committee Members: Preskill, John P.; Feynman, Richard Phillips; Porter, Frank C.; Fox, Geoffrey C.

Option: Physics

DOI: 10.7907/m791-na19

Abstract

The properties of the SU(2) and SU(3) lattice gauge theories are investigated using the Real Space Monte-Carlo Renormalisation Group method. The "√3 block transformation" is found to be very efficient in this analysis. The non-perturbative β-function is calculated for the SU(2) lattice gauge theory over a large range of couplings and along both the Wilson axis and the Migdal-Kadanoff improved action line. A possible explanation of the observed nonperturbative features of the β-function is given. The same data sample is used to calculate the improved action needed for better numerical simulations, and the results are compared with those obtained using the Migdal-Kadanoff approximate renormalisation and Symanzik's perturbative improvement approach. A similar but less extensive analysis is done for the SU(3) lattice gauge theory as well.

The results indicate that even for the pure gauge theory, the present day Monte-Carlo calculations are far from establishing an agreement with the expected asymptotic scaling. However, an improved action approach, combined with the β-function determined using the Monte-Carlo Renormalisation Group technique, should make it possible to convincingly demonstrate the scaling behaviour in near future.

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