2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99736The physics of spontaneous chiral symmetry breaking in the case of the simultaneous presence of a magnetic field and a fermionic quartic interaction is discussed for both local and nonlocal kernels in 2+1 and 3+1 dimensions. The approach is based on the use of Valatin-Bogoliubov canonical transformations, which allow, in the absence of fermionic quartic terms, to completely diagonalize the Hamiltonian and construct the vacuum state.17 pages, 4 figures, new content and results presented, version to appear in Nucl. Phys. AHigh Energy Physics - Theorytext