- Olindo Corradini (Universidad Autonoma de Chiapas) - Quantum Mechanical Path Integrals: from Transition Amplitudes to Worldline Formalism. We present a pedagogical study of quantum mechanical path integrals, starting with nonrelativistic bosonic particle actions and the path integral representation of nonrelativistic transition amplitudes, and ending with relativistic spinning particles, emphasizing the role these models have in the first-quantized approach to quantum field theory, the so-called worldline formalism. To better achieve this purpose we also describe the worldline symmetries of the particle actions and their canonical quantization. Requisites: good knowledge of nonrelativistic quantum mechanics, basic knowledge of relativistic quantum mechanics and general relativity.
- Christian Schubert (IFM, Universidad Michoacana) - Applications of the Quantum Mechanical Path Integral in Quantum Field Theory. Content: The first four lectures will explain the "string-inspired" worldline formalism. Starting from worldline path integral representations of amplitudes and effective actions derived in the lectures by O. Corradini, an exact calculation of those path integrals is achieved which leads to parameter integrals that are equivalent to the ones obtained by standard Feynman diagrams, but organized in a superior way. Our main example are one-loop gluon and graviton amplitudes, but the construction of multiloop amplitudes is also shortly discussed. The fifth lecture is devoted to methods for a direct numerical computation of worldline path integrals. Requisites: Good knowledge of relativistic and nonrelativistic quantum mechanics, basic understanding of quantum electrodynamics and nonabelian gauge theory.
- Andrew Waldron (UC Davis) - Geometrical Methods in QFT. Starting from simple particle mechanics, we build step by step the geometric ingredients to describe physics in curved space times. In particular we focus on the central role of conformal structures. The aim here is to handle problems in Riemannian geometry in a way that maximally utilizes underlying conformal symmetries. We end with the notion of almost Riemannian geometry and describing its role in the AdS/CFT correspondence. Requisite: Basic knowledge of Hamiltonian and Lagrangian mechanics.
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