# 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).