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fourmomentum

The four-momentum is a four-vector in special relativity that encodes a particle’s energy and three-momentum in a single, Lorentz-covariant object. In conventional notation with c explicit, it is Pμ = (E/c, px, py, pz); in natural units (c = 1) it is written as Pμ = (E, p). The four-momentum transforms under Lorentz transformations as any four-vector.

The time component is related to the energy, while the spatial components are the components of the

A key property of the four-momentum is its invariance. The Lorentz-invariant scalar PμPμ equals m2c2 (with the

In quantum theory and field theory, the four-momentum operator Pμ generates spacetime translations, and its square

Applications of four-momentum include relativistic collision kinematics, invariant-mass calculations, and the analysis of decays and scattering

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three-momentum.
For
a
particle
of
rest
mass
m,
the
energy
and
momentum
are
E
=
γmc2
and
p
=
γm
v,
where
γ
=
1/√(1
−
v2/c2).
The
rest
energy
is
Ere1st
=
mc2.
A
particle
with
nonzero
mass
satisfies
the
relativistic
energy–momentum
relation
E2
=
p2c2
+
m2c4.
For
massless
particles,
m
=
0
and
E
=
pc.
common
metric
signature
(+,
−,
−,
−)
so
that
(E/c)2
−
p2
=
m2c2).
The
total
four-momentum
of
a
system
is
the
vector
sum
of
its
constituents,
and
it
is
conserved
in
isolated
interactions.
is
a
Casimir
invariant
of
the
Poincaré
group.
Physically,
PμPμ
=
m2c2
labels
the
mass
of
a
particle,
while
for
m
=
0
one
has
PμPμ
=
0
and
E
=
pc.
processes
in
high-energy
physics.