Geometric formulation of the Covariant Phase Space methods with boundaries

Understand

We analyze in full-detail the geometric structure of the covariant phase space (CPS) of any local field theory defined over a space-time with boundary.

• To this end, we introduce a new frame: the "relative bicomplex framework".
• It is the result of merging an extended version of the "relative framework" (initially developed in the context of algebraic topology by R.~Bott and L.W.~Tu in the 1980s to deal with boundaries) and the variational bicomplex framework (the differential geometric arena for the variational calculus).
• The relative bicomplex framework is the natural one to deal with field theories with boundary contributions, including corner contributions.