Quark theory with internal coordinates

Journal Article · Mon Nov 15 04:00:00 EST 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.14.2790· OSTI ID:7329787

Hoh, F C

The free-particle Dirac wave function psi (x) is generalized to psi (x) xi/sub a/(z). Here, z denotes a set of three complex coordinates, called internal coordinates, in an abstract complex three-dimensional space, called internal space, a runs from 1 to 3, and xi/sub a/(z) is assumed to contain a representation of the state of a quark triplet. The mass in the free-particle Dirac equation is replaced by a second-order operator -partial/sub b//sub a/ operating on xi/sub a/(z). The so-modified Dirac equation is assumed to include a description of a free-quark triplet. Subsequently, symmetry-preserving interactions between two quark triplets are introduced. Two SU/sub 3/-symmetry-breaking interactions, one transforming like the eighth component of an SU/sub 3/ octet vector and the other like the SU/sub 3/ charge operator, are also introduced. A similarly generalized Bethe-Salpeter equation in the ladder approximation is obtained. This equation is treated in greater detail in the accompanying paper in which the Gell-Mann--Okubo formula for pseudoscalar mesons is derived with the coefficients determined by given relations. Then, spherical coordinates and corresponding spherical harmonics in the internal space are introduced. Finally, the equation for a one-quark system is briefly treated. (AIP)

• Research Organization: 4618 Spruce Street, Philadelphia, Pennsylvania 19139
• OSTI ID: 7329787
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 14:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BASIC INTERACTIONS
BETHE-SALPETER EQUATION
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EQUATIONS
FIELD THEORIES
FUNCTIONS
INTERACTIONS
LADDER APPROXIMATION
LIE GROUPS
MATHEMATICAL MODELS
PARTICLE MODELS
QUANTUM FIELD THEORY
QUARK MODEL
STRONG INTERACTIONS
SU GROUPS
SU-3 GROUPS
SYMMETRY BREAKING
SYMMETRY GROUPS
WAVE EQUATIONS
WAVE FUNCTIONS