Dirac's delta and units

1. Jan 11, 2005

Gonzolo

Consider :

$$E = \int P(\tau) d\tau = \int A\delta(\tau) d\tau$$

E is in Joules and $$P(\tau)$$ is in Watts, what are the units of A? What about $$\delta$$?

I have a hunch, but need to have all doubts removed.

2. Jan 11, 2005

mathman

The delta function has the dimension of the reciprocal of the variable of integration. Thus delta(tau)d(tau) is non-dimensional. Therefore A has the same dimension as E, i.e. Joules.

3. Jan 11, 2005

Gokul43201

Staff Emeritus
And you can see why the dirac delta has units of the reciprocal of the integration variable from

$$\int _{-\infty} ^{\infty} \delta (p-p_0) dp = 1$$,
where p is any parameter.

4. Jan 11, 2005

Thanks guys!