Equations of motion for scalar and spinor fields in a four-dimensional non-euclidean momentum space

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

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

“…It is interesting to compare this result with [9], where the geometric approach to studying equations of motion was investigated for scalar and spinor fields in the curved momentum de Sitter space characterized by the negative curvature M:…”

“…In particular, transformations were obtained in [9] that connect the mentioned equations in the de Sitter space and the corresponding equations in the Dirac theory. However, there is no difficulty to find that, unlike Eq.…”

“…(4)) expressions (5) and (8) coincide, i.e., (8) converts to an ordinary Dirac operator. It is very important that the new Klein-Gordon operator 2M(p 5 -Mcosμ) can be separated into matrix multipliers using the other method completely independently of (7): (9) where, as before ε 1 = ±1, ε 2 = ±1.…”

“…(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].…”