p\,)=\frac{1}{f(E,\vec p\,)}
\hspace{2cm}\mbox{and}\hspace{2cm} \tilde{c}(E,\vec
p\,)=\frac{\omega}{|\vec k|}=c\,\frac{f(E,\vec p\,)}{g(E,\vec p\,)}.$$ For high energies $\tilde\hbar$ increases, increasing the quantum-mechanical uncertainties. We shall restrict ourselves to the case $\tilde c=c$, i.e. $f=g$.

In analogy to (\[beta\]) we assume a lowest-order relation ($p=|\vec p|$ and $k=|\vec k|$) $$p=\tilde{\hbar}k\approx\hbar
k\left[1+\kappa\left(\frac{p}{m_P}\right)^n\right],$$ leading to the wavelength $$\lambda=\frac{1}{k}\approx\frac{\tilde\hbar}{2p}.$$ (Note that $k$ is the wave vector of the exchange particle, $p$ is the momentum of one incoming particle.) As before, from (\[imp\]) one obtains the correction of the scattering angle, $$\cos\frac{\vartheta}{2}\approx\left[1-\kappa\left(\frac{p}{m_P}\right)^n\right]\cos\frac{\vartheta_0}{2}.$$ With the same choice of transformation functions between the different sets of variables in first approximation, GUP has yielded just the opposite sign of the DSR correction in (\[thet\]).

Conclusion
==========

One main result of the considerations of this paper is the condition that DSR corrections to SR must be quadratic in $p/m_P$ in lowest order to fulfill the correspondence principle in the given example. It is not shown that this condition is sufficient in every situation and the calculations do not show how DSR differs from GR, when higher particle energies are involved. A relation of the present result with the interpretation of DSR in [@top] as the topological part of GR would depend on the properties of 