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Explore quantum mechanics and quantum field theory from algebraic and geometric perspectives in this comprehensive lecture by Albert Schwarz from the University of California at Davis. Delve into alternative viewpoints to conventional quantum mechanics, focusing on the algebraic approach using an algebra of observables and the geometric approach centered on a set of states. Discover how quantum mechanics can be viewed as classical mechanics with limited observable quantities, and learn about generalizations of quantum theory. Examine the emergence of probabilities in quantum theory through decoherence, and investigate the concept of particles as elementary excitations. Study scattering theory without relying on fields, locality, or Poincare invariance, including both conventional and inclusive scattering matrices. Explore the formalism of L-functionals as a concrete realization of the geometric approach, and its application to solving the infrared problem in quantum electrodynamics. Access accompanying slides for a visual aid to this 1 hour 44 minute lecture, part of a series based on a forthcoming minibook to be published by Springer.
