Physics – General Physics
Scientific paper
2001-08-26
Physics
General Physics
9 pages, LaTex
Scientific paper
An alternative (simplified) derivation of the dispersion relation and the expressions for the momentum-energy 4-vector $p_i,p_0$ given initially in [1] is provided. It has turned out that in a rather "pedestrian" manner one can obtain in one stroke not only the above relations but also the correct dispersion relation in $\omega-k_i$ space, consistent with the value of a velocity of a massless particle. This is achieved by considering the standard Lorentz algebra for $\omega-k_i$-space. A non-uniqueness of the choice of the time-derivative in the presence of the finite length scale is discussed. It is shown that such non-uniqueness does not affect the dispersion relation in $\omega-k_i$-space. albeit results in different dispersion relations in $p-p_0$-space depending on the choice of the definition of the time derivative.
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