Banca de DEFESA: VINICIUS NONATO ALVES LULA ROCHA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE : VINICIUS NONATO ALVES LULA ROCHA
DATA : 19/12/2019
HORA: 14:30
LOCAL: SALA 412 - INSTITUTO DE FÍSICA DA UFBA
TÍTULO:

An Algebraic Formulation of Relative Quantum Mechanics and Quantum Field Theory

PALAVRAS-CHAVES:

Dirac equation. Symplectic Dirac equation. Dirac superequation. DKP equa-tion. Symplectic DKP equation. DKP superequation. Clifford algebra. Clifford superalgebra. Fibre bundles. Algebra bundles. Quantum field theory.

PÁGINAS: 188
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Física
RESUMO:

We present in this dissertation some new results for the development of the relativistic
quantum theory within the algebraic approach proposed by Schönberg and developed
latter by Bohm, Hiley, Fernandes and Vianna and other autors. Firstly, by exploring the
DKP equation in the Bohm, Hiley, Fernandes and Vianna’s approach we have shown its
equivalence with the Klein-Gordon-Fock equation and the Proca equation; we also have
shown this algebraic formalism extend naturally the Kruglov approach of the non-massive
DKP equation including the 0-spin case. In the sequence we extend Schönberg’s formalism
to obtain DKP algebra by introducing a method, via equivalence class, to extract the
ParaDKP algebra (PDKP algebra) of the symplectic Clifford algebra of phase space; in
consequence of this methodology we have found symplectic versions of Klein-Gordon-Fock
like, Dirac like and DKP like equations. We also have developed a superalgebra in which
bosons and fermions are handled in a unified way and we have shown how to extract from
this algebra the Clifford superalgebra and the DKP superalgebra. In this approach we
proposed Klein-Gordon-Fock like, Dirac like and DKP like superequations. Finally we
have shown how the quantum field theory could be included in this formalism by using
the distributions and algebra bundles mathematical structures.

MEMBROS DA BANCA:
Presidente - 102.263.461-53 - JOSE DAVID MANGUEIRA VIANA - UFBA
Interno - 2060414 - MARIO CEZAR FERREIRA GOMES BERTIN
Externo à Instituição - MARCO ANTONIO SILVA TRINDADE - UNEB
Externo à Instituição - JOSE ABDALLA HELAYEL NETO - CBPF
Externo à Instituição - ADEMIR EUGENIO DE SANTANA - UnB