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## Main Question or Discussion Point

Which is the mass dimension of a scalar filed in 2 dimensions?

In 4 dim I know that a scalar field has mass dimension 1, by imposing that the action has dim 0:

[itex]S=\int d^4 x \partial_{\mu} A \partial^{\mu} A [/itex]

where

[itex]\left[S\right]=0[/itex]

[itex]\left[d^4 x \right] =-4[/itex]

[itex]\left[ \partial_{\mu} \right]=1[/itex]

[itex]\Rightarrow \left[A\right]=1[/itex]

Doing the same in 2 dim I found

[itex]\left[A\right]=0[/itex]

Is it right?

I need it for a model in supersymmetry.

In 4 dim I know that a scalar field has mass dimension 1, by imposing that the action has dim 0:

[itex]S=\int d^4 x \partial_{\mu} A \partial^{\mu} A [/itex]

where

[itex]\left[S\right]=0[/itex]

[itex]\left[d^4 x \right] =-4[/itex]

[itex]\left[ \partial_{\mu} \right]=1[/itex]

[itex]\Rightarrow \left[A\right]=1[/itex]

Doing the same in 2 dim I found

[itex]\left[A\right]=0[/itex]

Is it right?

I need it for a model in supersymmetry.