The Constitution delegates the power to “declare war” to Congress, not the President.
A leading University of Virginia constitutional law professor did an in-depth study of the founding era understanding of the phrase “to declare war” for a 2007 Cornell Law Review article. He concluded that the founders – and the founding generation understood the phrase as meaning “to decide to enter a war,” and includes acts of war as well as formal declarations of war.
In other words, the act of establishing a no-fly zone, ordering a drone strike, or dropping bombs is fundamentally a declaration of war – and the president doesn’t have the constitutional authority to do it without authorization from Congress.
Here’s how George Washington put it:
“The Constitution vests the power of declaring war with Congress, therefore no offensive expedition of importance can be undertaken until after they have deliberated upon the subject, and authorized such a measure.”