@article {Benz:2006:0001-9054:288,
author = "Benz, Walter and Schwaiger, Jens",
title = "A characterization of Lorentz boosts",
journal = "aequationes mathematicae",
volume = "72",
number = "3",
year = "2006",
abstract = "Suppose that X is a real inner product space of (finite or infinite) dimension at least 2. The following result will be proved in this note. A bijection λ ≠ id of the space-time <EquationSource Format="TEX"><![CDATA[$$Z = X oplus {user2{{mathbb{R}}}}$$]]></EquationSource> is an orthochronous Lorentz boost if, and only if, <OrderedList> <ListItem> <ItemNumber>(i)</ItemNumber> <ItemContent> There exists e ≠ 0 in X and <EquationSource Format="TEX"><![CDATA[$$tau :X to {user2{{mathbb{R}}}}backslash { 0}$$]]></EquationSource> with <Equation ID="Equa"> <MediaObject> </MediaObject><EquationSource Format="TEX"><![CDATA[$$ lambda {left( {x,{sqrt {1 + x^{2} } }} right)} = {left( {x + tau (x)e,{sqrt {1 + (x + tau (x)e^{2} )} }} right)} $$]]></EquationSource> </Equation> for all X∈X, and</ItemContent></ListItem> <ListItem> <ItemNumber>(ii)</ItemNumber> <ItemContent> l(v,w) = 0 implies l (λ(v), λ(w)) = 0 for all v,w ∈Z where l(Z1, Z2) designates the Lorentz-Minkowski distance of Z1, Z2 ∈Z.</ItemContent></ListItem></OrderedList> Moreover, we characterize (general) Lorentz boosts by distance invariance and the behavior on certain subspaces of Z.",
pages = "288-298",
url = "http://www.ingentaconnect.com/content/klu/10/2006/00000072/00000003/00002827",
doi = "doi:10.1007/s00010-006-2827-9",
keyword = "39B52, 51F25, 51P05, 83A05, Real inner product spaces, Lorentz transformations, Lorentz boosts, functional equations"
}