Following, e.g., [Wikipedia's definitions](http://en.wikipedia.org/wiki/Quantum_cohomology), the (small) quantum cohomology ring of $X$ is defined over a "Novikov ring" consisting of formal power series of the form $$ \sum\_{\beta \in H\_2(X;\mathbb{Z})} a\_\beta e^\beta,$$
where the $a\_\beta$ are in some fixed ring (which is probably usually $\mathbb{Q}$ or $\mathbb{C}$).

On the other hand, in the papers of Fukaya and company for instance, there seems to be a different "Novikov ring", consisting of power series of the form $$\sum\_{i=1}^\infty a\_i T^{\lambda\_i},$$
where $a\_i \in \mathbb{Q}$, $\lambda\_i \in \mathbb{R}$, and $\lim\_{i \to \infty} \lambda\_i = \infty$.

What's up with this? Why are there apparently two different Novikov rings? How do I reconcile this? I'm guessing that the $\lambda\_i$ in the second definition should correspond to something like $\int\_\beta \omega$ where $\beta$ is as in the first definition (and where $\omega$ is the symplectic form), but beyond this I'm not sure...