Text this: Is the fermionic exchange phase also acquired locally?

   _____     ___     __   _      ___     __   _   
  / ___//   / _ \\  | || | ||   / _ \\  | || | || 
  \___ \\  | / \ || | '--' ||  / //\ \\ | '--' || 
  /    //  | \_/ || | .--. || |  ___  ||| .--. || 
 /____//    \___//  |_|| |_|| |_||  |_|||_|| |_|| 
`-----`     `---`   `-`  `-`  `-`   `-` `-`  `-`