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Quantum Field Theory : Introductions to Quantum Gravity, Supersymmetry and String Theory (Vol 2)
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This book takes a pedagogical approachto explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics.The first part of the book introduces quantum gravity, withoutrequiring previous knowledge of general relativity (GR). The necessarygeometrical aspects are derived afresh leading to explicit general Lagrangiansfor gravity, including that of general relativity. The quantum aspect ofgravitation, as described by the graviton, is introduced and perturbativequantum GR is discussed. The Schwinger-DeWitt formalism is developed to computethe one-loop contribution to the theory and renormalizability aspects of theperturbative theory are also discussed. This follows by introducing only thevery basics of a non-perturbative, background-independent, formulation ofquantum gravity, referred to as “loop quantum gravity”, which gives rise to aquantization of space.
In the second part the author introduces supersymmetry andits consequences. The generation of superfields is represented in detail. Supersymmetric generalizations of Maxwell’sTheory as well as of Yang-Mills field theory, and of the standard model areworked out. Spontaneous symmetry breaking, improvement of the divergenceproblem in supersymmetric field theory, and its role in the hierarchy problemare covered. The unification of the fundamental constants in a supersymmetricversion of the standard model are then studied. Geometrical aspects necessaryto study supergravity are developed culminating in the derivation of its fullaction.
The third partintroduces string theory and the analysis of the spectra of the mass (squared)operator associated with the oscillating strings. The properties of theunderlying fields, associated with massless particles, encountered in stringtheory are studied in some detail. Elements of compactification, duality andD-branes are given, as well of the generation of vertices and interactions ofstrings. In the final sections, the author shows how to recover GR and theYang-Mills field Theory from string theory.