Split Chern–Simons Theory in the BV-BFV Formalism

The goal of this note is to give a brief overview of the BV-BFV formalism developed by the first two authors and Reshetikhin in (Cattaneo et al., Commun Math Phys 332(2), 535–603, 2014) [9], (Cattaneo et al., Perturbative Quantum Gauge Theories on Manifolds with Boundary, 2015) [10] in order to perform perturbative quantisation of Lagrangian field theories on manifolds with boundary, and present a special case of Chern–Simons theory as a new example.