-
transformations that
preserve the
direction of time are
called orthochronous. The
subgroup of
orthochronous transformations is
often denoted O+(1, 3).
Those that...
- transformations. If Λ is a
proper orthochronous Lorentz transformation, then TΛ is
improper antichronous, PΛ is
improper orthochronous, and TPΛ = PTΛ is proper...
- specifically, the
proper ( det Λ = 1 {\textstyle \det \Lambda =1} ),
orthochronous ( Λ 0 0 ≥ 1 {\textstyle {\Lambda ^{0}}_{0}\geq 1} ) part of the Lorentz...
- / C 2 , {\displaystyle \mathrm {O} (n,1)/\mathrm {C} _{2},\ } the
orthochronous Lorentz group, for n ≥ 3. But
these are
apparently distinct geometries...
-
orthogonal group): An ≅ E(n) / O(n)
Negative curvature:
Hyperbolic space (
orthochronous Lorentz group,
point stabilizer orthogonal group,
corresponding to hyperboloid...
-
extended to
include either parity or time
reversal (i.e.
subgroups of the
orthochronous and time-reversal respectively), is
sufficient to give us all the standard...
-
class Invariance Conserved quantity Proper orthochronous Lorentz symmetry translation in time (homogeneity)
energy E
translation in
space (homogeneity)...
- orientations. This
notation is
related to the
notation O+(1, 3) for the
orthochronous Lorentz group,
where the +
refers to
preserving the
orientation on the...
- }} is the
identity component of the
proper Lorentz group (the
proper orthochronous Lorentz group). The
center of the spin groups, for n ≥ 3, (complex and...
- _{-}\Delta ^{*}} In particular, note that the
representation Δ of the
orthochronous spin
group is a
unitary representation. In general,
there are Clebsch–Gordan...
