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POTENTIAL- FIELD RELATIONS AND THEIR EXISTENCE WAVE EQUATIONS,THEIR EIGENVALUES,DETERMINANTS AND QUANTISATION

Objective



Research objectives and content The objective of this project is the study of wave equations and the integrability conditions for Field - Potential relations. Particular issues we intend to address are: (1) The study of eigenvalues, determinants and the resulting spectra of Laplacians, in flat and curved spacetimes, with examples such as the Weyl and Lanczos tensors. We also aim to write various computer programs (SHEEP and Mathematica) to help with the computing of the eigenvalues as well as supplementing the theory. (2) The study of Potential - Field relations and the integrability conditions that accompany them together with possible restrictions of existence when we try to extend the systems to higher dimensions. Particular reference will be made to the existence of instantons and monopoles arising from the potentials and computer simulations of them. (3) The study of the already existing framework for Quantum Gravity using Ashtekar variables and the possible similarities between this and a fully quantised version of the Lanczos and Weyl tensors. Training content (objective, benefit and expected impact) The training content will include the learning of various approaches to quantising arbitrary Potential - Field relations, with particular reference to the Ashtekar formalism. Also a greater knowledge of eigenvalues and spectra of Laplacians with particular reference to the Atiyah-Singer index theorem will be achieved. Links with industry / industrial relevance (22)

Funding Scheme

RGI - Research grants (individual fellowships)

Coordinator

National University of Ireland - Maynooth
Address

47 Maynooth
Ireland