- #1

eljose79

- 214

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Can the coupling constant be rescaled to get always a dimensionless one?

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- Thread starter eljose79
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- #1

eljose79

- 214

- 1

Can the coupling constant be rescaled to get always a dimensionless one?

- #2

vanesch

Staff Emeritus

Science Advisor

Gold Member

- 5,109

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Now, the action needs to be dimensionless (same unit as h = 1). The action is the 4-dim integral of the lagrangian density, so L has to have dimensions L^(-4) = M^4. Mass still has, well, M as dimension. A typical mass term for a scalar field is m^2 phi^2, so it follows that a scalar field has to have dimensions M. As such, you can puzzle together the dimensions of different fields from their "free field" terms. The dimensionality of the interaction term coefficients (the coupling constants) is very important because it determines the renormalizability of the theory.

cheers,

Patrick.

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