\lectures of Sidney Coleman on Quantum Field Theory: Foreword by David Kaiser

This book treats the subject of gravitational waves (GWs) production in binary stars or black-holes and in the early universe, using tools of quantum field theory which are familiar to graduate students and researchers in particle physics. A special focus is given to the generation of templates of gravitational wave signals from Feynman diagram calculations of transition amplitudes, which interests active researchers in GWs. The book presents field theory concepts, like supersymmetry realized in spinning binaries and soft-graviton theorems, that can have practical applications in novel GW signals, like the memory effect. The book also aims at specialists in both GWs and particle physics addressing cosmological models of phase transition and inflation that can be tested in observations at terrestrial and space based interferometers, pulsar timing arrays, and the cosmic microwave anisotropy observations.

This is a monograph on geometrical and topological features which arise in quantum field theory. It is well known that when a chiral fermion interacts with a gauge field we have chiral anomaly which corresponds to the fact that divergence of the axial vector current does not vanish. It is observed that this is related to certain topological features associated with the fermion and leads to the realization of the topological origin of fermion number as well as the Berry phase. The role of gauge fields in the quantization procedure has its implications in these topological features of a fermion and helps us to consider a massive fermion as a soliton (skyrrnion). In this formalism chiral anomaly is found to be responsible for mass generation. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically.

After some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes.

The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory material that it can be read by mathematicians and theoretical physicists.