dorsal/arxiv
View SchemaA comment on the paper "Deformed Boost Transformations that saturate at the Planck Scale" by N.B.Bruno,G.Amelino-Camelia, and J.Kowalski-Glikman
| Authors | A. Granik |
|---|---|
| Categories | |
| ArXiv ID | physics/0108050 |
| URL | https://arxiv.org/abs/physics/0108050 |
Abstract
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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"abstract": "An alternative (simplified) derivation of the dispersion relation and the\nexpressions for the momentum-energy 4-vector $p_i,p_0$ given initially in [1]\nis provided. It has turned out that in a rather \"pedestrian\" manner one can\nobtain in one stroke not only the above relations but also the correct\ndispersion relation in $\\omega-k_i$ space, consistent with the value of a\nvelocity of a massless particle. This is achieved by considering the standard\nLorentz algebra for $\\omega-k_i$-space. A non-uniqueness of the choice of the\ntime-derivative in the presence of the finite length scale is discussed. It is\nshown that such non-uniqueness does not affect the dispersion relation in\n$\\omega-k_i$-space. albeit results in different dispersion relations in\n$p-p_0$-space depending on the choice of the definition of the time derivative.",
"arxiv_id": "physics/0108050",
"authors": [
"A. Granik"
],
"categories": [
"physics.gen-ph"
],
"title": "A comment on the paper \"Deformed Boost Transformations that saturate at the Planck Scale\" by N.B.Bruno,G.Amelino-Camelia, and J.Kowalski-Glikman",
"url": "https://arxiv.org/abs/physics/0108050"
},
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