On the geometric approach to the formulation of the standard model

Abstract

Abstract. A geometric interpretation of the spontaneous symmetry breaking effect, which plays a key role in the Standard Model, is developed. The advocated approach is related to the effective use of the momentum 4-spaces of the constant curvature, de Sitter and anti de Sitter, in the apparatus of quantum field theory.

The algebraic and geometric approaches to PJ-symmetric non-Hermitian relativistic quantum mechanics with maximal mass

“…Additionally, using the designation m/m max = sinμ, we can see that (32) and (33) for the case of upper signs become the expressions m 1 = 2m max sinμ/2 and m 2 = 2m max sin 2 μ/2, while for the case of lower signs they turn into m 3 = ν 1 2m max cosμ/2 and m 4 = 2m max cos 2 μ/2, which is in a complete agreement with (11). As has been already noted, with identification of the parameter m max and the parameter of maximal mass M used in the geomet ric approach (see, e.g., [5,6]) a full correspondence between the parameters that are used in Hamiltonians and in equations of motion of the models under study can be obtained. Additionally, with M ∞, we can see that the anti de Sitter geom etry does not differ from the Minkowski geometry in the pseudo Euclidean p space.…”

“…Kadys hevskii et al on the basis of the geometric approach [3][4][5][6][7][8][9][10][11][12][13][14].…”

“…While considering the fermion sector, it has been ascertained [5,6] that if a free Dirac operator in the ordinary formalism has the form (5) and can be regarded as a result of factorization of the Klein-Gordon operator…”

“…there are no operators that act on the x 5 coordinate and this parameter without loss of generality can be chosen equal to zero [5,6]. Thus, Hamiltonians corresponding to Eqs.…”

“…(2) as an additional postulate) received further development in [7][8][9][10][11][12][13][14][15]. Thus, the new theory con structed on the basis of purely geometric principle pre tends to a role of adequate SM generalization in the high energy region E ≥ M [5,6].…”