On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory

• Autor(a) principal: Dartora,C.A.
• Data de Publicação: 2016
• Outros Autores: Campos,Fillipi Klos Rodrigues de
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Revista Brasileira de Ensino de Física (Online)
• Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172016000300410
• topic: fermion-boson systems; similarity transformation; second quantization; superconductivity

A similarity transformation is an equivalence relation between square matrices which preserves determinant, trace and eigenvalues, playing a key role in quantum mechanics in simplifying complex hamiltonian systems and improving analytical results attainable from the use of perturbation theory. As a prototypical example, the conventional BCS theory of superconductivity is usually derived from a similarity transformation of the original electron-phonon hamiltonian, written in second quantized version. Here we discuss the general method for writing the similarity transformation operator in second quantized form, allowing one to recast a hamiltonian describing an interacting fermion-boson system into an effective theory in which only the desired degrees of freedom are kept after the transformation.