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Implicit metric signature in Einstein notation
ID: implicit-metric-signature-in-einstein-notation
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Implicit metric signature in Einstein notation
by
Ciro Santilli
37
Updated
2025-07-16
Then
a
specific
metric
is involved, sometimes
we
want to automatically add it to products.
E.
g
., in
a
context
considering the common
Minkowski inner product matrix
where the
η
4x4
matrix
and
μ
is
a
vector in
R
4
x
μ
x
μ
=
x
μ
η
μν
x
ν
=
−
x
0
2
+
x
1
2
+
x
2
2
+
x
3
2
;
(1)
which
leads
to the change of
sign
of some terms.
Total
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