In many theories of CMT, we assume the nature of quasi-particles (without giving proper justifications). For example, we assume nature of quasi-particles to be fermionic in case of a interacting fermion system we began with and impose anti-commutation relations accordingly. Like in BCS theory, while using the Bogoliubov-Valatin transformation to diagonalize the Hamiltonian, we assume that the new operators are also fermionic in nature. Please explain more on this step and how is it justified.
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