The geometric structure of the space of fermionic physical observables

Chirality of Dirac Spinors Revisited

“…The standard inner product is inadequate because the bilinear ψ † 1 ψ 2 is not Lorentz covariant. From physical considerations (invariant length and current density), Crawford outlined the need of normalizing the bilinear forms defining the spinorial metrics [34][35][36]. He built metrics between Dirac spinors and their generalization in higher dimensional spaces [35][36][37].…”

“…From physical considerations (invariant length and current density), Crawford outlined the need of normalizing the bilinear forms defining the spinorial metrics [34][35][36]. He built metrics between Dirac spinors and their generalization in higher dimensional spaces [35][36][37]. We retain the metric M = γ 0 in Equation 5because it was shown that M generates bilinears satisfying to Lorentz invariance for length and current density [25,[34][35][36][38][39][40][41][42].…”

“…M is Hermitian and unitary (see Theorem 8). It was noticed that we can always choose a basis of gamma matrices so that M is diagonal [34,36] (this is the case in the Dirac basis: see Equation 2), but there is no particular reason to retain the Dirac basis to ensure Lorentz covariance of the bilinears built from M. The required properties of the metric is that it is Hermitian and that it render the gamma matrices self-adjoint [37].…”

Spinors e twistors no modelo paravetorial

“…Os spinors são entidades fundamentais na física para se descrever a matéria, já que os léptons e os quarks são férmions de spin 1/2. Do ponto de vista algébrico, os spinors são elementos de um ideal minimallateral de uma álgebra de Clifford [Cw89][ER89], definição essa devida a C. Chevalley [Ch54].…”