Poincar Group
In
physics
and
mathematics
, the
Poincaré group
is the
group
of
isometries
of
Minkowski spacetime
. It is a 10-dimensional
noncompact
Lie group
. The
abelian group
of
translations
is a
normal subgroup
while the
Lorentz group
is a subgroup, the
stabilizer
of a point. That is, the full Poincaré group is the
semidirect product
of the translations and the
Lorentz transformations
. Another way of putting it is the Poincaré group is a
group extension
of the
Lorentz group
by a vector
representation
of it. Its positive energy unitary irreducible
representations
are indexed by
mass
(nonnegative number) and
spin
(
integer
or half integer), and are associated with particles in
quantum mechanics
. In accordance with the
Erlangen program
, the geometry of Minkowski space is defined by the Poincaré group: Minkowski space is considered as an
homogeneous space
for the group. In component form, the
Lie algebra
of the Poincaré group satisfies
P_\nu
= 0
P_\rho
= \eta_{\mu\rho} P_\nu - \eta_{\nu\rho} P_\mu
M_{\rho\sigma}
= \eta_{\mu\rho} M_{\nu\sigma} - \eta_{\mu\sigma} M_{\nu\rho} - \eta_{\nu\rho} M_{\mu\nu} + \eta_{\nu\sigma} M_{\mu\rho}
where
P
is the
generator
of translation and
M
is the
generator
of Lorentz transformations. See
sign convention
.
See also
Euclidean group
Henri Poincaré
hyper generalized orthogonal Lie algebra
Lorentz group
Wigner's classification
<< Previous
Word Browser
Next >>
paul horn
how to prepare an onion cell slide
object copy
the garden of cyrus
heusden, belgium
acrylic
post
angular resolution
news of the world
birla
droit de seigneur
opengem
dartington hall
1982 golden raspberry awards
cyfra plus
mallard
ernie els
lodging
opcode
premature ventricular contraction
class of '74
bellbird (soap opera)
sepp kerschbaumer
predator (movie)
commando (movie)
mount elbrus
minkowski space
lorentz group
space like
fock space
caucasus mountains
number 96 (tv series)
elbrus (computer)
carrie nation
intraplate earthquake
matabele
bryde's whale
pastoral council
terezn
ahrem
seismic hazard
erft
seismic risk
erftstadt
Copyright 2005-2009 OnPedia.com. All Rights Reserved