Staggered Bosons: Symmetry and Gaplessness

This lecture by the instructor explores the concept of staggered bosons, focusing on lattice realizations of gapless field theories with symmetry protection. The discussion delves into commutation relations, Hamiltonian formulation, mode expansion, Neel ordering, zero modes, translation symmetry, and the transition from bosons to half bosons. The lecture also covers topics such as T-duality, spin chains, criticality, and the projection to invariant states. The presentation concludes with a discussion on Kahler-Dirac bosons, supersymmetry, and the generalization of the concept to graphs with non-trivial Poisson brackets.