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by
Ciro Santilli
(
@cirosantilli,
36
)
Minkowski inner product
...
Physics
Particle physics
Relativity
Special relativity
Spacetime
Minkowski space
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Updated
2025-04-24
+
Created
1970-01-01
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Form
This
form
is not really an
inner product
in the common modern
definition
, because it is not
positive definite
, only
a
symmetric bilinear form
.
Table of contents
Minkowski inner product matrix
Minkowski inner product
Minkowski inner product matrix
(
η
μν
)
0
0
0
Minkowski inner product
The
matrix representation of the symmetric bilinear form
that is the
Minkowski inner product
.
Since that is
a
symmetric bilinear form
, the associated
matrix
is
a
symmetric matrix
.
By default,
we
will use the
time
negative representation unless stated otherwise:
η
μν
=
−
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
(1)
but another equivalent one is to use
a
time
positive representation:
η
μν
=
1
0
0
0
0
−
1
0
0
0
0
−
1
0
0
0
0
−
1
(2)
The
matrix
is typically denoted by the
Greek letter eta
.
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