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It seems strange to me that in such a simple case as the following the equation of motion depends on the choice of metric! In flat space we have say:

[tex]

\partial^{\mu}\partial_{\mu}\phi=\frac{dV}{d\phi}

[/tex]

Suppose \phi depends on space alone and we work in 1+1 dimension. then

[tex]

\eta_{\mu \nu}=\left (-1,1 \right ) \rightarrow \frac{d^2\phi}{dx^2}=\frac{dV}{d\phi}

[/tex]

and

[tex]

\eta_{\mu \nu}=\left ( +1,-1 \right ) \rightarrow -\frac{d^2\phi}{dx^2}=\frac{dV}{d\phi}

[/tex]

What is wrong here? Obviously the field configuration can not depend on the metric choice! Generally particle physicists and cosmologists use opposite signatures. Can anybody please point out?

[tex]

\partial^{\mu}\partial_{\mu}\phi=\frac{dV}{d\phi}

[/tex]

Suppose \phi depends on space alone and we work in 1+1 dimension. then

[tex]

\eta_{\mu \nu}=\left (-1,1 \right ) \rightarrow \frac{d^2\phi}{dx^2}=\frac{dV}{d\phi}

[/tex]

and

[tex]

\eta_{\mu \nu}=\left ( +1,-1 \right ) \rightarrow -\frac{d^2\phi}{dx^2}=\frac{dV}{d\phi}

[/tex]

What is wrong here? Obviously the field configuration can not depend on the metric choice! Generally particle physicists and cosmologists use opposite signatures. Can anybody please point out?

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