Two Topics in Non-Perturbative Lattice Field Theories: The U(1) Quantum Link Model and Perdect Actions for Scalar Theories

This thesis deals with two topics in lattice field theories. In the first part we discuss aspects of renormalization group flow and non-perturbative improvement of actions for scalar theories regularized on a lattice. We construct a perfect action, an action which is free of lattice artifacts, for a given theory. It is shown how a good approximation to the perfect action referred to as classically perfect can be constructed based on a well-defined blocking scheme for the 0(3) non-linear o-model. We study the O(N) non-linear r-model in the large-N limit and derive analytically its perfect action. This action is applied to the 0(3) model on a square lattice. The Wolff cluster algorithm is used to simulate numerically the system. We perform scaling tests and discuss the scaling properties of the large-N inspired perfect action as opposed to the standard and the classically perfect action. In the second part we present a new formulation for a quantum field theory with Abelian gauge symmetry. A Hamiltonian is constructed on a four-dimensional Euclidean space-time lattice which is invariant under local transformations. The model is formulated as a 5-dimensional path integral of discrete variables. We argue that dimensional reduction will allow us to study the behavior of the standard compact U(1) gauge theory in 4-d. Based on the idea of the loop-cluster algorithm for quantum spins, we present the construction of a flux-cluster algorithm for the U(1) quantum link model for the spin-1/2 quantization of the electric flux. It is shown how improved estimators for Wilson loop expectation values can be defined. This is important because the Wilson loops are traditionally used to identify confining and Coulomb phases in gauge theories. Our study indicates that the spin-1/2 U(1) quantum link model is strongly coupled for all bare coupling values we examined. Thesis Supervisor: Uwe-Jens Wiese Title: Assistant Professor of Physics Acknowledgments I wish to express my gratitude to Uwe-Jens Wiese for supervising my thesis research and giving me the opportunity to work on some of the most interesting ideas in lattice field theory. It has been an extremely enjoyable collaboration in the process of which I have been taught a great deal of physics. Uwe has the combined gift of a great teacher and a genuine field theorist who is able to convey to the uninitiated the deepest ideas in physics with the outmost clarity, enthusiasm and patience. His friendly, caring and understanding behavior has been very helpful through the sometimes frustrating stages of graduate studies. I wish to thank Profs. John Negele and Ed Bertschinger for reading my thesis and providing valuable comments and criticism. I wish to thank John Negele also for providing me with constant financial support during my five-year stay at the CTP. I thank also all the people that I had the opportunity to collaborate with during various stages of my work. Especially I thank Bernard Beard, Wolfgang Bietenholz, Rich Brower, Schailesh Chandrasekharan, Victor Chudnovsky, Juergen Cox, Kieran Holland and Ben Scarlet for all the discussions from which I have benefited a lot. I wish to thank also the following gentlemen: Pavlos Glicofridis, Leonidas Pantelidis, Jiannis Pachos, Nikos Prezas, Apostolos Rizos and Yiorgos Zonios for their invaluable friendship. Finally, I wish to thank my family, Theodora and Sotirios Tsapalis and Dimitra and Panayiotis Panagopoulos for their infinite love and support. A otcpwvc-rat o--rov(; -tovelo; ILOV 6608w pa rai, Ew-r 'pto To--araAl