Which means “to cut into two equal parts”?

The first sene: alice was performing a magic trick with a wand and a small spell book that her grandfather had given her. while she was practicing she saw matt who was one of the other contestants, while she was practicing matt bumped in to her and made her say the spell wrong. all of a sudden a swoosh of sparkling purple wind picked them up and put them back on the floor. when they looked at each other alice saw herself and that’s when she realized that they had switched bodies.