Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric Perspectives - Lecture 4

Explore advanced perspectives on quantum mechanics and quantum field theory in this lecture by Albert Schwarz from the Institut des Hautes Etudes Scientifiques (IHES). Delve into algebraic and geometric approaches that offer alternatives to conventional Hilbert space methods. Examine how quantum mechanics can be viewed as classical mechanics with limited observable quantities. Investigate the emergence of probabilities in quantum theory through decoherence caused by adiabatic interaction with random environments. Learn about particles as elementary excitations of ground states and quasiparticles as excitations of translation-invariant states. Study scattering concepts without relying on field theory, locality, or Poincare invariance. Discover the formalism of L-functionals as a concrete realization of the geometric approach, and its application to solving infrared problems in quantum electrodynamics. Access accompanying slides for visual support during this 1 hour and 27 minute presentation that challenges traditional quantum mechanics textbook methodologies.