Light-front dynamics of the covariant harmonic oscillator

Following Leutwyler and Stern, the two-particle covariant harmonic-oscillator model of Feynman, Kislinger, and Ravndal is reformulated within the framework of light-front dynamics. The light-front dynamics of the oscillator is obtained by constraining the manifestly covariant formulation to the null plane, ct+z=0. An inner product for the null-plane wave functions is developed, and it is shown that the light-front mass operator M and spin operator scrJ are Hermitian with respect to this inner product. Interaction dependent, nonlocal relative position and momentum operators Q and P, are introduced, and the mass and spin operators are expressed in terms of them. It is found that the part of M2 that contains the dynamics is proportional to a nonrelativistic harmonic-oscillator Hamiltonian in P and Q, and that the spin operator scrJ=Q×P. The eigenstates of Q and P are determined, and are used to construct position and momentum representations for the null-plane oscillator. In these representations the light-front dynamics takes on the appearance of nonrelativistic quantum mechanics. In particular, the nonlocal inner product for the null-plane wave functions goes over to the local nonrelativistic form. The obvious relevance of these results to the quark model of the hadrons is briefly discussed.