I am starting to studying condensed matter theory and I do not understand if Many-Body Quantum Mechanics and Quantum Field Theory are just synonyms or are two different methods.
It seems to me that the first is used when the starting point is a many-body wavefunction and then the occupation numbers formalism is adopted. In the second case, the starting point is a classical field which is quantized to describe some features of a material. However, in the end, it seems to me that the types of techniques are the same (Green's functions, Path integrals, Faymann diagrams and so on).
Are just two synonyms and QFT is just the cooler, newer name of the same topic or are they different methods?