Light-front dynamics of the covariant harmonic oscillator

Journal Article · Mon Oct 15 04:00:00 EDT 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.42.2898· OSTI ID:6160525

Fuda, M G ^[1]

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1. Department of Physics and Astronomy, State University of New York at Buffalo, Buffalo, New York 14260 (USA)

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, {ital ct}+{ital z}=0. An inner product for the null-plane wave functions is developed, and it is shown that the light-front mass operator {ital M} and spin operator {ital scr}{bold J} are Hermitian with respect to this inner product. Interaction dependent, nonlocal relative position and momentum operators {bold Q} and {bold P}, are introduced, and the mass and spin operators are expressed in terms of them. It is found that the part of {ital M}{sup 2} that contains the dynamics is proportional to a nonrelativistic harmonic-oscillator Hamiltonian in {bold P} and {bold Q}, and that the spin operator {ital scr}{bold J}={bold Q}{times}{bold P}. The eigenstates of {bold Q} and {bold 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.

• OSTI ID: 6160525
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 42:8; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BANACH SPACE
COMPOSITE MODELS
EIGENSTATES
EIGENVALUES
ELECTROMAGNETIC RADIATION
ELEMENTARY PARTICLES
FORM FACTORS
FUNCTIONS
HADRONS
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HARMONIC OSCILLATOR MODELS
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LIE GROUPS
LIGHT CONE
LORENTZ TRANSFORMATIONS
MASS
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MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
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PARTICLE MODELS
PARTICLE PROPERTIES
POINCARE GROUPS
QUANTUM MECHANICS
QUANTUM OPERATORS
QUARK MODEL
RADIATIONS
SPACE
SPACE-TIME
SPIN
SYMMETRY GROUPS
TRANSFORMATIONS
VISIBLE RADIATION
WAVE FUNCTIONS