what formalities on divorce on grounds of irreconcilable differences?

Assuming you are Hindu you are governed by Hindu Marriage Act.

If you do not want to live with your wife then you can simply speak to her and file a mutual consent divorce under Section 13 B of Hindu Marriage Act thereby seeking divorce on mutual terms and condition. A joint petition signed by both parties is filed in court under said section. In the first motion statement of both parties are recorded and then signed on paper before the Hon'ble Court.

The 6 month period is given for reconciliation, (the hon'ble court gives a chance to the couple to change their mind) 6 months after the first motion or at the end of the reconcile period if both parties still don't agree to come together.

Then the parties may appear for the second motion for the final hearing.

Finally Divorce decree will be granted as the Hon'ble Court may deem fit. This process of divorce is faster and less time consuming.

However if your  does not agree to give you divorce, then you can file divorce petition under Section 13(1) of Hindu Marriage Act on any of the grounds  which suits your facts and circumstances