I live in Louisiana and my wife left me a couple months ago. We have no children together. When cann I start dating again without it causing me legal problems during the divorce?

Depends, would your soon to be ex want to cause you trouble.

You are not really "free" to date until you are actually divorced.
Have you filed for divorce yet ?

If you haven't started divorce procedures, here's what you should know:

No fault divorce in LA, the spouses have lived separate and apart continuously for at least one hundred eighty days prior to the filing for the divorce.

Fault:
(1) Adultery.
(2) imprisonment.
(3) Abandonment for a period of one year.
(4) Physical or sexual abuse.
(5) The spouses have been living separate and apart continuously for a period of two years.
(6) Living separate and apart continuously for a period of one year from the date the judgment of separation from bed and board was signed.
(Louisiana Code of Civil Procedure - Article: 103)

Don't jump into dating too fast, if she returns or finds out that you're dating a new gal, things may turn up side down.