Tangent space of loop space.

Question

Let $\Omega$ be the path space of a riemannian manifold $M$. I have to define the tangent space of $\Omega$ in a path $\omega$, that I denote with $T_p \Omega$. I think that this space is the vector space of all vector fields $W$ defined along $\omega$ such that $W(0)=W(1)=0$. How can I define precisely $T_{\omega}\Omega$?