# Can be x_1 * x_2 >= x_3 * x_4 represented as a second order conic (SOCP) constraint?

I'll like to know if the constraint x_1 * x_2 >= x_3 * x_4 can be represented as an SOCP constraint.

Note that setting matrix A = [ x_1 x_3 \\ x_4 x_2] the constraint is equivalent to det(A) >= 0, so it is an SDP constraint.