Effects of Non-locality in Gravity and Quantum Theory

This thesis is devoted to the systematic study of non-local theories that respect Lorentz invariance and are devoid of new, unphysical degrees of freedom. Such theories are attractive for phenomenological applications since they are mostly unconstrained by current experiments. Non-locality has played an increasingly important role in the physics of the last decades, appearing in effective actions in quantum field theory, and arising naturally in string theory and non-commutative geometry. It may even be a necessary ingredient for quantum theories of gravity. It is a feature of quantum entanglement, and may even solve the long-standing black hole information loss problem. “Non-locality” is a broad concept with many promising and fruitful applications in theoretical and mathematical physics. After a historical and pedagogical introduction into the concept of non-locality the author develops the notion of non-local Green functions to study various non-local weak-field problems in quantummechanics, quantum field theory, gravity, and quantum field theory in curved spacetime. This thesis fills a gap in the literature by providing a self-contained exploration of weak-field effects in non-local theories, thereby establishing a “non-local intuition” which may serve as a stepping stone for studies of the full, non-linear problem of non-locality.

Chapter1: Introduction.- Chapter2: Green functions in non-local theories.- Chapter3: Static and stationary solutions in weak-field gravity.- Chapter4: Ultrarelativistic objects.- Chapter5: Quantum-mechanical scattering.- Chapter6: Vacuum polarization and the fluctuation-dissipation theorem.- Chapter7: Black holes, generalized Polyakov action, and Hawking radiation.- Chapter8: Conclusions.

Jens obtained his Bachelor’s and Master’s at RWTH Aachen and the University of Cologne in Germany with a focus on black hole physics and obtained a second Master’s at Perimeter Institute/University of Waterloo in Canada in 2015. Upon completion he was awarded a doctoral recruitment scholarship by the University of Alberta and went on to do his PhD in the Alberta gravity group with Prof. Valeri Frolov (supervisor) and Prof. Don Page (committee), where he was later awarded a Canada Vanier Graduate Scholarship. Presently he is a postdoctoral research associate in high energy physics at William & Mary in the United States.