# Definition of Feynmann integral ?

1. Apr 20, 2007

### tpm

Definition of Feynmann integral ??

Using the definition of integral as a limit of certain sums...couldn't we define an integral over paths $$x(t)$$ as the limit whenever 'epsilon' tends to 0 of the Sum:

$$\sum _{i} F[x(t)] (L[x(t)+i \delta (t-t')]-L[x(t)+(i-1)\delta (t-t')])$$

Where F is a functional and $$L[x(t)]=\int_{a}^{b}dtx(t)$$

Or something like that..in the sense that Riemann Path integrals are just the limit of a Riemann sum over an space of paths X(t)

Or in terms of 'hyperreal' function so $$x(t)+i \epsilon \delta (t-t')$$

for i=1,2,3,4,5,6,7,8,9,....... and 'epsilon' is a infinitesimal quantity.

Last edited: Apr 20, 2007