TY - JOUR

T1 - Generalized relativistic kinematics

AU - Manida, S. N.

PY - 2011

Y1 - 2011

N2 - We propose a method for deforming an extended Galilei algebra that leads to a nonstandard realization of the Poincar´e group with the Fock–Lorentz linear fractional transformations. The invariant parameter in these transformations has the dimension of length. Combining this deformation with the standard one (with an invariant velocity c) leads to the algebra of the symmetry group of the anti-de Sitter space in Beltrami coordinates. In this case, the action for free point particles contains the dimensional constants R and c. The limit transitions lead to the ordinary (R → ∞) or alternative (c → ∞) but nevertheless relativistic kinematics.

AB - We propose a method for deforming an extended Galilei algebra that leads to a nonstandard realization of the Poincar´e group with the Fock–Lorentz linear fractional transformations. The invariant parameter in these transformations has the dimension of length. Combining this deformation with the standard one (with an invariant velocity c) leads to the algebra of the symmetry group of the anti-de Sitter space in Beltrami coordinates. In this case, the action for free point particles contains the dimensional constants R and c. The limit transitions lead to the ordinary (R → ∞) or alternative (c → ∞) but nevertheless relativistic kinematics.

KW - principle of relativity

KW - relativistic kinematics

KW - Galilei algebra

KW - Poincar´e group

KW - anti-de Sitter space

U2 - 10.1007/s11232-011-0141-8

DO - 10.1007/s11232-011-0141-8

M3 - Article

VL - 169

SP - 1643

EP - 1655

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 2

ER -