Prog. Theor. Phys. Vol. 43 No. 4 (1970) pp. 1071-1084
Schrödinger Picture for the Nambu-Takabayasi Equation and Transition Form Factors
Department of Physics, Nagoya University, Nagoya
(Received November 19, 1969)
It is shown that the Nambu-Takabayasi infinite-component wave equations in a particular class of Lorentz frames moving along the common z-axis are formally equivalent to the Schrödinger equation for the “hydrogen atom” in an internal space of three dimensions. The “relative distance” between two “constituents” receives a kind of dilatation under the action of the physical Lorentz transformations along the z-axis. The dilatation is shown to manifest itself as the transition form factors.
We evaluate the transition form factors between arbitray discrete (bound) states of the equation in closed form and then show that the result coincides with those obtained by a purely algebraic method.
DOI : 10.1143/PTP.43.1071
Y. Nambu, Phys. Rev. 160 (1967), 1171[APS].
See also, C. Fronsdal, Phys. Rev. 156 (1967), 1665[APS].
A. O. Barut and H. Kleinert, Phys. Rev. 156 (1967), 1541[APS].
- T. Takabayasi, Prog. Theor. Phys. Suppl. No. 41 (1968), 130, [PTP]and references therein.
See, for instance, D. Z. Freedman and J-M. Wang, Phys. Rev. 160 (1967), 1560[APS].
- D. Tz. Stoyanov and I. T. Todorov, J. Mat. Phys. 9 (1968), 2146.
- Bateman Manuscript Project, Tables of Integral Transforms (McGraw-Hill Book Comp. Inc.) Vol. 1 (1954), Eq. (35) on p. 175.
We have made a slight cange in the notation.
See, for instance, A. O. Barut and H. Kleinert, Phys. Rev. 156 (1967), 1546[APS].
- V. Bargmann, Ann. Math. 48 (1947), 568.
Citing Article(s) :
Progress of Theoretical Physics Vol. 45 No. 4 (1971) pp. 1354-1356
Electromagnetic Structure Functions of Hadrons in Infinite-Multiplet Theory
Masasi Fujigaki and Katsusada Morita