Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expe ....Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expected that the new techniques generated will find further application in areas of mathematical physics and non-commutative geometry related to quantized calculus.
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Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
Advanced studies of QCD and the strong interaction. This project will significantly advance our knowledge of the subatomic structure of the universe. It will maintain excellence and strength in an area where Australia has built an outstanding international reputation over the past decade. It will place Australia at the cutting edge of fundamental and computational science research and it will maintain and grow strong international links. It will produce Australian graduates and research associa ....Advanced studies of QCD and the strong interaction. This project will significantly advance our knowledge of the subatomic structure of the universe. It will maintain excellence and strength in an area where Australia has built an outstanding international reputation over the past decade. It will place Australia at the cutting edge of fundamental and computational science research and it will maintain and grow strong international links. It will produce Australian graduates and research associates of high quality, who will benefit from participating in these state-of-the-art studies and from the advanced training in modelling, high-performance computer simulation and visualisation. This training will have major economic benefits for and provide strong links to Australian industry.Read moreRead less
The Essence of QCD Vacuum Structure. This first-principles study of quantum field theory will elucidate an outstanding mystery of modern particle physics. Understanding confinement is recognized as one of the top 10 Physics Questions to Ponder for a Millennium or Two. In support of the National Research Priorities, new scientific data visualization techniques will be transferred to industry, facilitating smart information use. Further economic benefits are realized through the training and devel ....The Essence of QCD Vacuum Structure. This first-principles study of quantum field theory will elucidate an outstanding mystery of modern particle physics. Understanding confinement is recognized as one of the top 10 Physics Questions to Ponder for a Millennium or Two. In support of the National Research Priorities, new scientific data visualization techniques will be transferred to industry, facilitating smart information use. Further economic benefits are realized through the training and development of expertise in high-performance parallel computing, promoting an innovation culture and economy. The opportunity for young Australian Honours and Postgraduate students to work at the forefront of nuclear and particle theory is an obvious social benefit.
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Advanced Studies of Non-Perturbative Quantum Electrodynamics (QED) and Relation to the Standard Model. The project is a high-precision study of nonperturbative quantum electrodynamics (QED). It will finally allow a detailed look into the inner workings of the "best theory we have". It will provide valuable guidance in understanding and constructing the "holy grail" of theoretical physics the so-called "theory of everything". It will place Australia at the cutting edge of fundamental theoretical ....Advanced Studies of Non-Perturbative Quantum Electrodynamics (QED) and Relation to the Standard Model. The project is a high-precision study of nonperturbative quantum electrodynamics (QED). It will finally allow a detailed look into the inner workings of the "best theory we have". It will provide valuable guidance in understanding and constructing the "holy grail" of theoretical physics the so-called "theory of everything". It will place Australia at the cutting edge of fundamental theoretical research. Australian graduate and undergraduate students will benefit from participating in this work and the state-of-the-art expertise that they will develop has a clear social and economic benefit for Australia.Read moreRead less
Studies of nonperturbative quantum electrodynamics. In order to test fundamental quantum field theories, which underlie all physical phenomena from galaxy formation to the behaviour of biological system, it is necessary to be able to solve these theories in all regions of interest. In particular, solving theories in the nonperturbative regime has proven a difficult and challenging problem. The most successful theory that we have in physics is perturbative quantum electrodynamics, even though in ....Studies of nonperturbative quantum electrodynamics. In order to test fundamental quantum field theories, which underlie all physical phenomena from galaxy formation to the behaviour of biological system, it is necessary to be able to solve these theories in all regions of interest. In particular, solving theories in the nonperturbative regime has proven a difficult and challenging problem. The most successful theory that we have in physics is perturbative quantum electrodynamics, even though in the nonperturbative regime it is widely believed to be a trivial or pathological theory. We will build on exciting recent successes in this field and use advanced supercomputers to understand the detailed nonperturbative behaviour of quantum electrodynamics.Read moreRead less
Option pricing via path integrals: a new perspective. The risk management of derivative securities is a very exciting challenge for financial market researchers. The knowledge base resulting from this proposal will benefit both large financial institutions and Australia's financial system by creating a more competitive and efficient economic environment, which will inevitably lead to more gross domestic product (GDP) gains.Furthermore a large amount of software and numerical analysis work to be ....Option pricing via path integrals: a new perspective. The risk management of derivative securities is a very exciting challenge for financial market researchers. The knowledge base resulting from this proposal will benefit both large financial institutions and Australia's financial system by creating a more competitive and efficient economic environment, which will inevitably lead to more gross domestic product (GDP) gains.Furthermore a large amount of software and numerical analysis work to be developed during the project can be turned into IP for Australia. This will contribute to catalysing development of internationally competitive financial risk management software industry.Read moreRead less
Cross sections for electron scattering from molecules and radicals of technological and environmental relevance. We will use two state of the art crossed beam spectrometers to measure absolute differential and integral cross sections for low energy electron scattering from molecules and their molecular fragments (radicals). The species to be considered are those of significant industrial (e.g. C2F4, C4F8 and CF2) and environmental (e.g. CO2 and H2O) interest, with the cross sections we will mea ....Cross sections for electron scattering from molecules and radicals of technological and environmental relevance. We will use two state of the art crossed beam spectrometers to measure absolute differential and integral cross sections for low energy electron scattering from molecules and their molecular fragments (radicals). The species to be considered are those of significant industrial (e.g. C2F4, C4F8 and CF2) and environmental (e.g. CO2 and H2O) interest, with the cross sections we will measure being crucial to our modelling both the processes involved in plasma enhanced chemical vapour desposition of semiconductor devices and the spectral emission characteristics of planetary atmospheres. The modelling will be conducted self-consistently with our enhanced statistical equilibrium simulation code, which is unique to Australia.Read moreRead less
Nonlinear spatial and spatiotemporal econometrics: theory with applications. Modern societies like Australia have major challenges in the forecasting, measuring and managing of risks associated with global economic and environmental/climate changes. These tasks require advanced econometric techniques in modelling and forecasting of complex nonlinear spatiotemporal variability in economic and social systems. This project will develop frontier econometric technologies that enable more accurate eco ....Nonlinear spatial and spatiotemporal econometrics: theory with applications. Modern societies like Australia have major challenges in the forecasting, measuring and managing of risks associated with global economic and environmental/climate changes. These tasks require advanced econometric techniques in modelling and forecasting of complex nonlinear spatiotemporal variability in economic and social systems. This project will develop frontier econometric technologies that enable more accurate economic and climate forecasts. The tools produced will provide Australia's scientists and policy-makers with a greater capacity to manage the risks associated with these challenges. A side-benefit of the research will be high-quality publications that enhance the nation's reputation in this cutting edge research.Read moreRead less
Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms tha ....Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms that will make possible practical analysis of operator-analytic models.Read moreRead less