A characterization of Lorentz boosts

Link:
Autor/in:
Erscheinungsjahr:
2006
Medientyp:
Text
Schlagworte:
  • Functional equations
  • Lorentz boosts
  • Lorentz transformations
  • Real inner product spaces
Beschreibung:
  • 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 Z = X ⊕ ℝ is an orthochronous Lorentz boost if, and only if, (i) There exists e ≠ 0 in X and τ :X → ℝ\ {0} with λ(x,√ 1 + x2) = (x +τ (x)e,√ 1 + (x + τ (x)e)2) for all x ∈ X, and (ii) l(v,w) = 0 implies l (λ(v), λ(w)) = 0 for all v,w ∈ Z where l(z 1, z 2) designates the Lorentz-Minkowski distance of z 1, z 2 ∈ Z. Moreover, we characterize (general) Lorentz boosts by distance invariance and the behavior on certain subspaces of Z. © Birkhäuser Verlag, Basel 2007.
Lizenz:
  • info:eu-repo/semantics/closedAccess
Quellsystem:
Forschungsinformationssystem der UHH
Interne Metadaten
Quelldatensatz
oai:www.edit.fis.uni-hamburg.de:publications/1a9b798d-9c2c-431c-ad50-bbe19b902d03