Dirac delta dimensionless?

1. Sep 7, 2011

fuzzyphysics

Probably a trivial question, but does Dirac delta function has (to have always) a physical dimension or is it used just as a auxiliary construct to express e.g. sudden force impulse, i.e. Force = Impulse \times \delta, where 'Impulse' carries the dimension?
Any comments would be highly appreciated.
FP

2. Sep 7, 2011

BruceW

When people use the word 'Dirac delta function', they usually mean the function which acts like this:
$$\int_{- \infty}^\infty f(t) \delta(t-T)dt=f(T)$$
Which is something different to what you're talking about. If I'm right, you're talking about Impulse=force times (small time interval), i.e.
$$I=F \ \delta t$$
In this case, the delta just signifies that the time interval is very small, and if we take it to be infinitesimally small, we get:
$$dI=Fdt$$
Which allows us to calculate the change in momentum when a non-constant force is applied.

So in this case, the delta carries the dimension of time. But I guess the use of delta doesn't always have to have dimension. (For example, it could be used to express a small change in some dimensionless ratio of parameters).