Quantum field theory, solitons and other quantum dynamical systems

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NUMERCIAL SIMULATIONS IN LATTICE (GAUGE) THEORY AND ANYONS: We wish to study of gauge field theory extending the analysis of U(1) gauge theory on a tetrahedral lattice in 3 Euclidean dimensions. Now we wish to extend our results to a Z3 lattice gauge theory a truncation of a non-abelian SU(3) gauge theory to its centre. The tetrahedral lattice affords the novelty that it allows for gauge flux tubes of magnetic flux one third. We hope to see confinement in this theory. Also we wish to continue our study of anyons in this model. It is an interesting question to compute higher virial coefficients and other thermodynamic quantities of an anyon gas. CONFORMAL GRAVITY: We wish to continue our study of conformal gravity, which is an alternative theory of gravity that can explain missing matter without the need for dark matter. We have proven the existence of solitons which correspond to spontaneous conformal symmetry breaking. We have also shown that gravitational waves in the theory do not carry any energy to second order, and the corresponding first order waves are pure gauge artefacts. This fact lends credence to the idea that the theory can be consistently quantized. VACUUM INSTABILITY AND SOLITONS IN STRING INSPIRED COSMOLOGY: Bold new proposals of string theory in cosmology correspond to obtaining the inflationary cosmological scenario as a consequence of string theory. There exists an ongoing collaboration between researchers at the IIT Bombay and UdeM exploring the robustness of some of the existing string theory proposals regarding stability with a view to phenomenological applications in high-energy physics as well as to unusual states of matter occurring in condensed matter physics. Instability of string cosmology models would have far reaching consequences on the viability of string theory in cosmology.