Abstract
We propose the model of a massive spinning particle traveling in four-dimensional Minkowski space. The equations of motion of the particle are obtained from the requirement that its classical paths lie on a cylinder with the time-like axis in Minkowski space. All the paths on one and the same cylinder are gauge equivalent. The equations of motion are found in implicit form for general time-like paths, and they are non-Lagrangian. The explicit equations of motion are derived for trajectories with small curvature and helices. The momentum and total angular momentum are expressed in terms of characteristics of the path in all the cases. The constructed model of the spinning particle has a geometrical character, with no additional variables in the space of spin states being introduced.
Highlights
The classical spinning particle is irreducible if its quantization corresponds to the irreducible representation of the Poincare group
The models of irreducible spinning particles are well-known [1, 2, 3, 4]. In most of these models the particle is considered as the point object in Minkowski space, while the spin positions take values in the internal space
The linear momentum p = pμdxμ and total angular momentum J = Jμνdxμ ∧ dxμ of the particle are determined by the world sheet position in the Minkowski space, p = mn, J = my ∧ n + sεμνρσnμaν dxρ ∧ dxσ, (6)
Summary
The classical spinning particle is irreducible if its quantization corresponds to the irreducible representation of the Poincare group. In the geometrical models the spin is described in terms of derivatives of the particle’s path, and no internal space is introduced. In the paper [10], the concept of the world sheet is proposed to describe massive particles with spin The idea of this concept is that the classical trajectories of irreducible particle lie on a certain cylindrical surface in Minkowski space. The geometrical model of massive spinning particle traveling lightlike and isotropic paths in three-dimensional Minkowski space was developed in the original work [10]. We construct the geometrical model of massive spinning particle traveling in four-dimensional Minkowski space.
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