Co-algebraic methods for String Field Theory and Quantum Field Theory

Abstract: In this work we extend the notion of co-algebra, co-algebraic Wess-Zumino-Witten formulation of Lagrangian Field Theory and the Homotopy transfer theorem to many strings and particle systems. We discuss in detail the construction of higher dimensional co-algebras and the computational methods derived from them with a special interest regarding String Field Theory and Quantum Field Theory. As a result of this work we will be able to effortlessly extend some of the newly developed tools to study the algebraic structure, compute effective actions and compute scattering amplitudes of more complicated QFTs.