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Jennifer Lopez and Marc Anthony called it quits in July ... and at the time it seemed civilized, but now the two are at war due to JLo's new relationship with 24-year-old backup dancer Casper Smart, according to Us.

A source close to Lopez, 42, and Anthony, 43, tells the mag that the Latin crooner "hit the roof" after seeing photos of Smart playing in Hawaii over the Thanksgiving holiday with the couple's 3-year-old twins, Max and Emme.

"He wants to make Jennifer suffer because she's having fun with someone new, and he knows this will hurt her on the deepest level," the source adds.

Although the couple have already settle custody arrangements, Anthony may go "back on his word."

As for Lopez and Smart, we caught them shopping together at a jewelry store in Calabasas earlier this week. Sounds like it's getting serious!