On the similarity transformations in second quantized fermion-boson interacting hamiltonian and the BCS theory
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.
| Main Authors: | , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Sociedade Brasileira de Física
2016
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| Online Access: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172016000300410 |
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