where the  formula_52 on the summation sign indicates that the sum is not over formula_53 and is subject to the constraint that the total number of particles associated with the summation is formula_54 . Note that formula_55 still depends on formula_53 through the formula_57 constraint, since in one case formula_58 and formula_55 is evaluated with formula_60 while in the other case formula_61 and formula_55 is evaluated with formula_63  To simplify the notation and to clearly indicate that formula_55 still depends on formula_53 through formula_66 , define