Abstract:
Finite transformations of the one-parumetric relativistic quasiexchange group are found by
integrating the nonlinear differential equations that define the infinitesimal transformations of
this group. The elements of the quasiexchange group are transformations of the relative
momenta $\mathbf{q}$ and $\mathbf{p}$ of three identical relativistic particles that leave invariant the equation
$E=\sqrt{\mathbf{p}^2+m^2}+\sqrt{\mathbf{p}^2+4\mathbf{q}^2+4m^2}$ of the energy surface and the element of the three particle
phase volume. The group elements are expressed as a function of the parameter $\varphi$ in terms
of elliptic Jaeobi functions. In the nonrelativistic ease the latter go over into ordinary
trigonometric functions and the finite transformation reduce to a linear representation of
the corresponding subgroup of $SO_6$.
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