Show that the total (not density) 3-momentum ki for free scalars is conserved. Use our knowledge that the conjugate momentum for xi is ki, the total (not density) 3-momentum (expressed in covariant components), and it is conserved if L is symmetric (invariant) under the coordinate translation transformation xi→x′i=xi+αi, where αi is a constant 3D vector. Then, show the same result via commutation of the three-momentum operator of Chap. 3 (see Wholeness Chart 5-4, pg. 158) with the Hamiltonian. (Solution is posted on book website. See URL on pg. xvi, opposite pg. 1.)