Honours Projects in Theoretical Physics

The renormalization of field theories is of fundamental importance to modern physics. Our understanding of three of the four fundamental forces of nature is contained in the Standard Model, which is a quantum field theory simultaneously describing the electromagnetic, strong, and weak interactions. Quantum field theories have no physical meaning until they are renormalized since without renormalization no calculations can be done. There have been great advances in our understanding of the nature of renormalization and old-fashioned concerns about naive infinities are seen to be irrelevant. The purpose of this project is to further develop our understanding of the relationship between nonperturbative and perturbative renormalization in the context of the Standard Model and its components.

C-2 U(1) PROBLEM

(Supervisor: Dr RJ Crewther)

Quantum chromodynamics (QCD) can be the theory of strong interactions only if it explains why chiral symmetry does not require the pion triplet to be accompanied by an isoscalar meson of similar mass. The only "out" appears to be a quantum correction known as the axial anomaly. Exactly how this can work is still very controversial. The project will concentrate one or two of the following themes:

* vacuum structure and relation to topological charge spectrum and boundary conditions;

* many-colour limit of QCD;

* Wess-Zumino consistency of effective Lagrangians for QCD;

* quantum mechanical analogies: what replaces Bloch waves?

* corrections to index theorems, e.g. on the lattice;

* a related problem: why no strong CP violation?

C-3 NON-LEPTONIC WEAK DECAYS

(Supervisor: Dr RJ Crewther and A/Prof AG Williams)

Theoretically, a decay such as K ® 2p should proceed with isospin transitions DI = ½ and DI = 3/2 of similar magnitudes. Experimentally, DI = ½ dominates. This long-standing problem still attracts a variety of explanations. The project will either examine one of these ideas, or consider what other processes exhibit similar properties.

C-4 NONPERTURBATIVE QCD

(Supervisor: Dr RJ Crewther and A/Prof AG Williams)

This includes methods such as the many-colour limit, semi-classical approaches (e.g. instantons), or lattice gauge theory, and also anomalous effects – Wess-Zumino Lagrangian, Skyrme Lagrangian, Schwinger-Dyson equations.

C-5 FRACTIONAL STATISTICS

(Supervisor: Dr RJ Crewther)

“Anyons” are a generalization of bosons and fermions, ie under interchange, there is a general phase factor instead of +1 or -1. Physical anyons live in two dimensions, eg in the layers of a crystal (perhaps). The project will consider one of the tentative proposals for a quantum mechanics, statistical mechanics or quantum field theory of anyons.

C-6 WHY IS THE PION LIGHT? CHIRAL SYMMETRY AND THE NONPERTURBATIVE QCD VACUUM.

(Supervisors:Dr A Kalloniatis)

Chiral symmetry concerns transformations on the left and right handed helicities of massless quark fields y. This symmetry is known to be spontaneously broken: the ground state of the strong interaction does not respect the symmetry. The Goldstone theorem then explains why the pion is so light compared to other mesonic particles. Associated with this phenomena is a non-zero expectation value of the operator in the nonperturbative QCD vacuum. In a beautiful paper, Banks and Casher showed that this ``chiral condensate'' can be related to the properties of the low-lying spectrum of quarks in the background gluon field.

This project reviews the mechanisms by which the chiral condensate can be formed within the context of the Banks-Casher relation and how these relate to the underlying non-trivial vacuum structure of gluons in QCD. A toy model will be proposed which seeks to capture this essential physics.

C-7 STRANGENESS IN THE NUCLEON

(Supervisors:Dr DB Leinweber, Prof AW Thomas and A/Prof AG Williams)

Nucleon properties were long thought to be well described by the dynamics of three valence quarks carrying the quantum numbers of the nucleon, bound together by nonperturbative gluon interactions.

However, recent studies of nucleon spin structure functions in polarized deep inelastic scattering experiments at CERN and SLAC, have turned up a surprisingly large and negative polarization from the strange quark in the nucleon. In addition, there are other long-standing discrepancies that may be reconciled if a significant strange-quark content in the nucleon is admitted. This project will explore the various experimental and theoretical signatures of the strange quark in the nucleon and focus on determining the strange-quark magnetic moment of the nucleon, a quantity which is of tremendous experimental interest.

C-8 QUARK MASSES

(Supervisors:Dr DB Leinweber and A/Prof AG Williams)

In the “Standard Model”, the quark masses are not constrained by fundamental principles. Instead they are left as phenomenological parameters, to be determined through matching QCD calculations to experimental measurements. At present, there are three calculational approaches carrying significant weight in state-of-the-art determinations of the three lightest quark masses; namely, chiral perturbation theory, QCD sum rules, and lattice QCD. Established values for these masses have recently come into question as lattice QCD calculations suggest quark masses of half the standard values. This project will examine the constraints placed on quark masses from each of these calculational approaches.

C-9 QCD SUM RULES>

(Supervisor: Dr DB Leinweber)

The QCD Sum Rule method is a nonperturbative analytic formalism firmly entrenched in QCD with minimal modeling. As such, it continues to be a highly active field. The influence of the field is reflected in over 1500 references to the seminal paper of Shifman, Vainshtein and Zakharov. The approach has been applied to a variety of hadronic observables in both vacuum and finite density nuclear matter. This project will review the key concepts of the approach, critically examine the assumptions made in extracting hadron properties, and explore new ways to improve the predictive ability of the approach.

C-10 HIGH ENERGY TESTS OF THE STANDARD MODEL

(Supervisors:Professor AW Thomas)

The standard model of particle physics has been phenomenally successful. It is therefore natural that any sign of a deviation from this model is greeted with great excitement by the high energy physics community. Just such a deviation - possibly as large as an order of magnitude - has now been observed at the very highest energies available at HERA. Perhaps this signals the onset of “new” physics or maybe it only indicates that we have insufficient understanding of the known “old” physics. The aim of this project is to explore the possible explanations of this unexpected result.

C-11 THE SHORT-DISTANCE NUCLEAR FORCE

(Supervisor: Professor AW Thomas)

Conventionally the strong nuclear force is described in terms of the exchange of virtual mesons between point-like nucleons. On the other hand we now know that both the nucleons and the mesons are made of quarks confined inside relatively large volumes. One of the great challenges of modern strong interaction physics is to understand how these two quite different pictures can produce results which are so often similar. It would be particularly significant to find one or two cases where the predictions of such models are qualitatively different. The aim of this project would be to understand the two approaches and then look at a specific case where their predictions may disagree.

C-12 CHIRAL SYMMETRY

(Supervisor: Professor AW Thomas and A/Prof AG Williams)

One of the fundamental symmetry properties of massless QCD is chiral symmetry. The key aim in this project would be to understand the ideas of chiral symmetry, beginning with the linear a-model of Gell-Mann and Levy, and spontaneous symmetry breaking. More advanced topics could include the chiral bag models (cloudy bag, Skyrmion, etc) chiral perturbation theory and so on.

C-13 CONFINEMENT IN QCD

(Supervisors:Professor AW Thomas and A/Prof AG Williams)

In QCD with heavy, static quarks (Q) “confinement” corresponds to a linear rise in the energy of a pair as they are moved apart. This is usually viewed as being associated with a linear rise in the volume of the colour electric flux tube (or string) joining the two quarks. In the presence of light quarks such a string will eventually break, yielding two colourless mesons and . The mechanism whereby the pair is created and the flux-tube broken is of crucial importance in the strong interactions. We propose to examine this problem from a number of points of view, including the lattice, a coupled-channels potential model and perhaps the phenomenology of proton-anti-proton annihilation.

C-14 QUARKS AND PARTONS

(Supervisor: Professor AW Thomas)

The most direct evidence for the reality of quarks as partons comes from deep inelastic scattering experiments at SLAC, CERN and Fermilab involving beams of electrons, muons and neutrinos.

This project would involve first learning about Feynman’s parton model, which was invented to describe the data. Then the focus would be upon the very recent work which has enabled links to be built between the parton description and the quark models used in spectroscopy.

C-15 A QUARK MODEL OF NUCLEAR MATTER AT HIGH DENSITY

(Supervisor: Professor AW Thomas)

At high density it is widely believed that the individual identity of neutrons and protons (nucleons) should dissolve into a soup of quarks and gluons. Studying this quark-gluon plasma is one of the aims of accelerators such as RHIC in which beams of relativistic heavy ions will collide. This new state of matter may also form at the centre of dense objects such as neutron-stars (pulsars). In order to understand the transition from nucleons to quarks and gluons, it is helpful to have a model of nuclear structure built in terms of nucleons which have sub-structure. We have recently made an exciting break-through in this pursuit and there are, as a consequence, a variety of exciting projects which can be undertaken in this field.

C-16 CP VIOLATION IN B-DECAYS

(Supervisor: Professor AW Thomas)

The excess of matter over anti-matter in the observable universe tells us that CP must be violated. Until recently it has only been possible to study CP violation in the neutral kaon system. However, there is now a major effort world wide to make so called B-factories, particle accelerators which will produce a very large flux of mesons containing b or quarks. The aim of this project would be to explore the current understanding of CP violation within the Standard Model and to examine the various ideas for probing this fundamentally important problem.

C-17 LATTICE GAUGE THEORY

(Supervisors: Dr DB Leinweber, A/Prof AG Williams and Prof AW Thomas)

Lattice gauge theory provides the only comprehensive method to extract, with controlled systematic errors, first-principles predictions from QCD for a wide range of observable phenomena. This approach consists of discretising space-time (ie. a space time lattice) and constructing quark and gluon field configurations as governed by the QCD Lagrangian. As the lattice spacing is reduced to zero, the continuum space-time limit of the theory is recovered. Taking this limit involves state of the art computing techniques and uses large parallel supercomputers such as Orion, one of the fastest supercomputers in the Southern Hemisphere when it was installed at the University of Adelaide in 2000. This project will focus on current issues in the field of Lattice Gauge Theory as discussed with the supervisors. Of particular current interest is the extraplotation of lattice results to the chiral symmery regime and the minimization and control of lattice artefacts.

C-18 NONPERTURBATIVE QED

(Supervisors: A/Prof AG Williams)

The most accurate and successful theory ever formulated is QED, ie, the quantum field theory of quantum electrodynamics which describes the interaction of photons with charged matters. The precision of the agreement between the predictions of the theory (QED) and experiments is unmatched by any other theory. This agreement occurs in the weak-coupling regime of the theory, where the fine-structure constant is small, = 1/137. On the other hand QED is widely expected to be an approximation to some more fundamental grand unified theory (GUT) and to develop some pathological behaviour at extremely high energies where the coupling becomes strong. It is thus extremely interesting to attempt to study QED in the strong-coupling region, where is of order 1 or larger. The purpose of this work is to understand how the successes of the "best theory we have" (i.e., QED) can be understood in spite of the almost certain fact that QED on its own is a pathological theory. The answer is believed to lie tin the fact that any Grand Unified Theory (unifying all four of the known forces in nature) will provide a natural cut-off at the Planck scale and thus render QED well-behaved. The project will undertake a systematic exploration of this issue.

C-19 THEORETICAL STUDIES OF HEART ARYTHMIA AND EPILEPSY

(Supervisors: Dr DB Leinweber, Prof AW Thomas and A/Prof AG Williams)

In recent years there has been tremendous interest in the applications of theoretical physics to the analysis of heart arythmia and epileptic seizures. The aim of this project would be to research the literature in these areas and to apply ideas to the analysis of real data. For example, a time series analysis from chaos theory allows one to reconstruct the strange attractor and possibly predict the onset of a heart attack or epileptic seizure

C-20 THE ANOMALOUS MAGNETIC MOMENT OF THE MUON

(Supervisors:A/Prof AG Williams)

Measurements of the anomalous magnetic moment of the electron have tested quantum electrodynamics (QED) to unparalled precision. Measurements of the equivalent quantity for the muon are currently being pushed to a high enough precision so that they provide a quantitative test not only of QED, but of the theories of the strong and weak nuclear interactions as well. The aim of this project is to gain an understanding of some of the diverse theoretical inputs (e.g. perturturbative QED, chiral perturbation theory, dispersion analyses, weak interactions) which go into the calculation of this fundamental quantity.

C-21 LATTICE ACTION IMPROVEMENT

(Supervisors:Dr DB Leinweber and A/Prof AG Williams)

In formulating QCD on a space time lattice, the first step is to construct lattice discretised versions of QCD operators which reproduce the continuum operators as the lattice spacing tends to zero. For fermions such as quarks, this has proved to be challenging due to the famous fermion doubling problem. Many forms of improved lattice actions exist with varying strengths and weaknesses. The focus of this study is to explore the various approaches to lattice action improvement (including mean-field improvements and fat-links) and use established lattice QCD code to evaluate and select the preferred lattice action.

C-22 INSTANTONS ON THE LATTICE

(Supervisors:Dr DB Leinweber and A/Prof AG Williams)

Just as in General Relativity, the classical field equations of QCD admit a rich structure and there is tremendous excitement when analytic solutions to these classical equations are discovered. Perhaps the best known non-trivial solution is infinite space-time is the (anti-) instanton. Instantons are thought to play an important role in giving rise to hadron structure. However, there are no known non-trivial solutions in a finite volume with periodic boundary conditions (the four-torus, relevant to lattice QCD simulations. Yet instantons are observed on the lattice. This project will focus on the creation of instanton solutions on the lattice and explore the impact of boundary conditions on the solutions, including recent advances on twisted boundary conditions admitting new non-trivial solutions.

C-23 VISUALIZATIONS OF QUANTUM CHROMODYNAMICS (QCD)

(Supervisor: Dr DB Leinweber)

Quantum Chromodynamics is a nonperturbative quantum field theory, and it is the nonperturbative aspect of this theory that has held so many surprises in the way that the theory works. The lattice approach to QCD is the only known way to directly reveal the nonperturbative features of the theory. The focus of this project will be to visualize the massive amount of information produced in lattice calculations on supercomputers using leading-edge graphics software such as AVS Express - a volume rendering package capable of animating scalar fields in three dimensions. The aim of this study is to gain real insight into the manner in which quarks and gluons interact and account for the world observed around us.

C-24 EXCITED STATES OF THE NUCLEON

(Supervisors:Dr DB Leinweber, Prof AW Thomas and A/Prof AG Williams)

New experiments underway at Jefferson Lab in the USA are probing the properties of excited states of the proton and neutron with unprecedented accuracy. However, these excited states of the nucleon N^* are short lived and strongly decay presenting new challenges to theoretical calculations of N^* properties. This project will develop a new analytic method for incorporating these strong decay channels into our understanding of N^* structure.

C-25 TECHNICAL FINANCIAL MARKET ANALYSIS

(Supervisors: Drs DB Leinweber, AW Schreiber, Prof AW Thomas and A/Prof AG Williams)

It is well known that the application of mathematical analysis and modeling to financial market data provides market forecasting with increased merit. Following a review of financial products including options and futures contracts, the project will explore some of the more advanced analysis tools including statistical and eigenvalue analyses of correlation matrices, time series analysis and other techniques holding promise.

C-26 CONVERGENCE PROPERTIES OF EFFECTIVE FIELD THEORIES

(Supervisor: Prof AW Thomas)

Effective field theories (EFT) have a long and distinguished history. In studying the strong interaction chiral perturbation theory has proven particularly important in allowing one to make a systematic expansion of observables in powers of quark masses and momenta. Yet, as suggested by Dyson, Hurst and others almost fifty years ago the series expansions generated in EFT are almost always divergent or asymptotic. Recent studies at the CSSM have suggested that this problem may be overcome by clever resummation techniques, such as the Padé approximant. In this project we will explore the effectiveness of the Padé approximant and other related techniques in representing physical observables in regions where naive application of EFT may be expected to fail.