Partial diagonalization of Bethe--Salpeter type equations

Journal Article · Fri Aug 01 04:00:00 EDT 1975 · Ann. Phys. (N.Y.), v. 92, no. 2, pp. 262-314

DOI:https://doi.org/10.1016/0003-4916(75)90106-2· OSTI ID:4160659

Cronstroem, C

One considers an equation of the Bethe--Salpeter type, with arbitrary potential and kernel, respectively, for space-like momentum transfer. The invariance group of the equation is then the Lorentz-group in three dimensions, the O(1,2) group. The standard procedure for the diagonalization of such equations (valid for square integrable solutions only) is generalized to include the case of power bounded solutions, by means of a generalized O(1,2) expansion formalism. The result is a two-dimensional integral equation for the O(1,2) expansion coefficients. The right-most l-plane singularities of these determine the asymptotic behavior of the amplitudes as in ordinary Regge theory. The formalism can be applied to other dynamical equations possessing O(1,2) symmetry. (auth)

• Research Organization: Univ. of Helsinki
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-006625
• OSTI ID: 4160659
• Journal Information: Ann. Phys. (N.Y.), v. 92, no. 2, pp. 262-314, Journal Name: Ann. Phys. (N.Y.), v. 92, no. 2, pp. 262-314; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

*BETHE-SALPETER EQUATION
641300*
BOUNDARY CONDITIONS
DIMENSIONS
INTEGRAL EQUATIONS
KERNELS
LINEAR MOMENTUM TRANSFER
LORENTZ GROUPS
MATHEMATICAL SPACE
N76200* --Physics (Theoretical)--Quantum Field Theories
O GROUPS
REGGE POLES
SERIES EXPANSION
SINGULARITY
TWO-DIMENSIONAL CALCULATIONS