Last Updated：2022/12/24
A massive spin 1 particle has three degrees of polarization for the obvious reason that in its rest frame its spin vector can point in three different directions. The three polarization vectors 𝜀𝜇⁽ᵃ⁾ are simply the three unit vectors pointing along the x, y, and z axes, respectively (a = 1, 2, 3): 𝜀𝜇⁽¹⁾=(0,1,0,0), 𝜀𝜇⁽²⁾=(0,0,1,0), 𝜀𝜇⁽³⁾=(0,0,0,1). In the rest frame k𝜇=(m,0,0,0) and so k𝜇𝜀_𝜇⁽ᵃ⁾=0 Since this is a Lorentz invariant equation, it holds for a moving spin 1 particle as well.
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A
massive
spin
1
particle
has
three
degrees
of
polarization
for
the
obvious
reason
that
in
its
rest
frame
its
spin
vector
can
point
in
three
different
directions.
The
three
polarization
vectors
𝜀_𝜇⁽ᵃ⁾
are
simply
the
three
unit
vectors
pointing
along
the
x,
y,
and
z
axes,
respectively
(a
=
1,
2,
3):
𝜀_𝜇⁽¹⁾=(0,1,0,0),
𝜀_𝜇⁽²⁾=(0,0,1,0),
𝜀_𝜇⁽³⁾=(0,0,0,1).
In
the
rest
frame
k^𝜇=(m,0,0,0)
and
so
