Geometry and Quantum Theory Seminar: A Rigorous Construction of the Free Quantum Field

In this talk we will build on last week’s discrete intuition and rigorously construct our first continuum quantum field theory: the free field. Following Chapter three of Chatterjee’s notes, we will realize it as a Gaussian random field in Euclidean spacetime, prove that it has the Markov property in time, and then use the procedure outlined in previous lectures to get its Hilbert space and Hamiltonian.