Regular Series


Vol. 15 (1984), No. 5, pp. 317 – 451


Studies of Chiral Symmetry Breaking in Lattice Gauge Theory

abstract

We study chiral symmetry breaking in SU(2) and SU(3) lattice gauge theory using the quenched approximation. For the SU(2) theory we consider quarks in the \(l=1/2\), \(l=1\), \(l=3/2\) and \(l=2\) representations and find evidence for a hierarchy of relevant energy scales. In the SU(3) theory with fundamental quarks both the deconfinement and the chiral symmetry restoration transition occurs at the same temperature. In the absence of dynamical quark loops both transitions are first order.


QCD Sum Rules: An Introduction and Some Applications

abstract

I present an introduction to the basic ideas of QCD sum rules, and discuss various applications.


Non-Perturbative Studies in the CP\(^{n-1}\) Model

abstract

Two topics are discussed involving non-perturbative aspects of the quantum CP\(^{n-1}\) model in two dimensions. The first lecture deals with defining the topological charge and topological susceptibility through the lattice theory and the problems associated therewith. The second lecture discusses how to estimate the mass gap of the theory through a finite volume approach. The two lectures are tied together by considerations of universality.


Testing QCD with Current Algebra

abstract

Spontaneously broken chiral symmetry fixes the low energy structure of QCD to a large extent. I show how to determine the Green’s functions to first nonleading order in a simultaneous expansion in powers of the momenta and of the \(u\)- and \(d\)-quark masses. In particular, I discuss the corrections of order \(M^2_{\pi }\) to the low energy theorems for \(\pi \pi \) scattering.


Sum Rules and Exclusive Processes in QCD

abstract

A brief review is given of a new approach to exclusive form factors of the hadrons at moderately large momentum transfers. The basic idea is to fix the parameters of the soft wave functions of the hadrons by QCD sum rules and to incorporate the local quark–hadron duality to calculate the form factors. After comparing the results obtained with experimental data we conclude that the observed power-law behaviour of the hadronic form factors has nothing to do with short distances and scale invariance.


CP Violation: Status and Prospects

abstract

Our current knowledge of CP violation and of the limits of CPT violation is reviewed: The only positive evidence for CF violation comes from studying the neutral K meson system. Also the new initiatives to study CF violation are discussed, in particular the electric dipole moment of the neutron.


Supersymmetric Quantum Mechanics and the Atlyah–Singer Index Theorem

abstract

A new proof of the Atiyah–Singer index theorem is given using simple techniques developed in the context of supersymmetric field theories.


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