Modern particle physics, as described by the Standard Model, is a —a theory with local symmetries that dictate the interactions of particles. Quantizing such theories is a notoriously difficult problem. The Kostant-Sternberg BRST algebra (a collaboration with Bertram Kostant) provides an elegant and rigorous mathematical framework for this task.
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The reason we cannot detect dark matter particles is that they are not linear representations of our spacetime symmetry group. They are projective representations that only become linear if we couple them to an additional, hidden ( U(1) ) gauge field. Modern particle physics, as described by the Standard
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Group representation theory allows scientists to predict and classify new "topological invariants," leading to the discovery of materials that conduct electricity perfectly on their edges while remaining insulating on the inside. B. Quantum Information Theory and Quantum Computing
: Senior undergraduate and graduate students in physics or mathematics. Core Topics
: It begins with basic definitions of groups and group actions on sets. It covers Lie groups