Application of quantum field theory in particle physics, gravity, condensed matter physics and cosmology

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Gravitation: In 2013, with my student J. Belletête, we discovered it was possible to have configurations of energy and momentum, which behaved like particles of negative mass. These configurations were smooth deformations of certain singular solutions of Einstein’s equations with cosmological constant. Subsequently, with my student S. Mbarek, we demonstrated that they could be obtained with the energy-momentum of a perfect fluid. My present and future work on the subject is first to find a dynamical model, which can support static solutions with negative mass and the consequence of these configurations for cosmology. CP-Violation and solitons: We have studied an effective model of CP-violation that could be used to describe the decay of B mesons to 4 lighter scalar mesons. This corresponds to an effective 5 scalar field interaction that is CP violating. In the simplest such effective theory, we find a rich spectrum of solitons and instantons. The topological solutions would in principle give rise to non-perturbative corrections to CP-violating processes. It is an open important problem to understand the source of CP violation in the universe. Quantum spin systems: Large spin quantum systems can be analyzed using the spin coherent state path integral. We have computed tunnelling with this path integral. We have shown that high orders in perturbation theory can be efficiently computed using the path integral. The most important result that we have found corresponds to identifying the ground state of an N site, quantum spin chain, described by Haldane. Studying the related Blume-Capel-Haldane-Ising model, we find the interesting result that the solitons have a finite size, and could shed light on the Haldane conjecture which is still an open problem. Induced, false vacuum decay: We have studied induced false vacuum decay due to topological solitons. These solitons must contain a zero of the scalar field in their interiors, a point where the symmetry is unbroken. Thus a spontaneously broken, false vacuum would naturally be unstable if there existed a non-trivial vacuum structure in which these topological solitons can arise. We show that when the solitons are thin walled, they can be classically stable, but quantum mechanically meta-stable due to quantum tunnelling. Future work will involve taking into account gravitational corrections. Anyons and the virial expansion: We have developed a method to numerically simulate anyons on the lattice. Our method allows for a simple generalization to computing the canonical partition function for N anyons, and hence the virial coefficients. It is an open problem if the virial expansion is useful for a gas of anyons. Only the first few coefficients have been accessed theoretically, and it is not known if the equation of state admits a useful expansion in the virial coefficients. Anyons could be used for simulating quantum computation which would have significant impact.