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Register a new userFunctorial Quantum Field Theory in the Riemannian setting
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Santosh Kandel
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We construct examples of Functorial Quantum Field Theories in the Riemannian setting by quantizing free massive bosons.
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Boundary conditions in relativistic QFT can be classified by deep results in the theory of braided or modular tensor categories.
These third-year lecture notes are designed for a 1-semester course in topological quantum field theory (TQFT). Assumed background in mathematics and physics are only standard second-year subjects: multivariable calculus, introduction to quantum mechanics and basic electromagnetism. Keywords: quantum mechanics/field theory, path integral, Hodge decomposition, Chern-Simons and Yang-Mills gauge theories, conformal field theory
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A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the form of the field equations than the usual Lagrangian description. It is proved that Poisson brackets, Lagrange brackets, and canonical 2-forms exist that are invariant under canonical transformations of the fields. The technique to derive transformation rules for the fields from generating functions is demonstrated by means of various examples. In particular, it is shown that the infinitesimal canonical transformation furnishes the most general form of Noethers theorem. We furthermore specify the generating function of an infinitesimal space-time step that conforms to the field equations.
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