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Prog. Theor. Phys. Vol. 48 No. 2 (1972) pp. 574-595
The Association of the Sakata-Taketani (Feshbach-Villars) Field with the Kemmer Field, under Symmetry Breaking
Ephraim Fischbach,
Michael Martin Nieto* and
C. K. Scott**
Physics Department, Purdue University, Lafayette, Indiana 47907
*Research Institute for Fundamental Physics, Kyoto University, Kyoto
**Physics Department, McMaster University, Hamilton, Ontario
(Received October 28, 1971)
Abstract:
We discuss both the original and two new derivations of the covariant Sakata-Taketani “system of equations”, and of the identical relativistic, but non-covariant Sakata-Taketani (S-T) and Feshbach-Villars (F-V) equations. (These last two equations were originally derived from the Duffin-Kemmer-Petiau and Klein-Gordon (K-G) equations, respectively.) By considering the scaling properties of the Kemmer, K-G and S-T fields, we conclude that in the presence of SU(3) symmetry breaking the S-T field can no longer be associated with both the Kemmer and K-G fields, but only with the Kemmer field. This has important conceptual implications concerning the particle-particle nature of mesons.
URL :
http://ptp.ipap.jp/link?PTP/48/574/
DOI : 10.1143/PTP.48.574
References:
- H. Yukawa, Proc. Phys. Math. Soc. Jpn. 17 (1935), 48; ibid. 19 (1937), 712.
H. Yukawa and S. Sakita, Math. Soc. Jpn. 19 (1937), 1084.
H. Yukawa, S. Sakata and M. Taketani, Math. Soc. Jpn. 20 (1938), 319.
H. Yukawa, S. Sakata, M. Kobayasi and M. Taketani, Math. Soc. Jpn. 20 (1938), 720.
The above articles are reprinted in, Prog. Theor. Phys. Suppl. No. 1 (1955), 1[PTP]; ibid. No. 1 (1955), 11[PTP]; ibid. No. 1 (1955), 14[PTP]; ibid. No. 1 (1955), 24[PTP]; ibid. No. 1 (1955), 46[PTP].
- O. Klein, Z. Phys. 37 (1926), 895.
V. Fock, Z. Phys. 38 (1926), 242; ibid. 39 (1926), 226.
E. Schrödinger, Ann. der Phys. 81 (1962), 109.
J. Kudar, Ann. der Phys. 81 (1926), 632.
W. Gordon, Z. Phys. 40 (1926), 117.
Th. de Donder, Compt. rend. 182 (1926), 1380.
Th. de Donder and H. F. van den Dungen, Compt. rend. 183 (1926), 24.
-
R. J. Duffin, Phys. Rev. 54 (1938), 1114[APS].
- N. Kemmer, Proc. Roy. Soc. A 173 (1939), 91.
- G. Petiau, University of Paris thesis (1936). Published in Acad. Roy. de Belg., Classe Sci., Mem in 8° 16 (1936), No. 2.
- F. Booth and A. H. Wilson, Proc. Roy. Soc. A 175 (1940), 483.
A. H. Wilson, Proc. Camb. Phil. Soc. 36 (1940), 363.
- A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics, 2nd ed. (Interscience, New York, 1965), Ch. 9, p. 819.
-
A. Klein, Phys. Rev. 82 (1951), 639[APS].
-
E. Fischbach, F. Iachello, A. Lande, M. M. Nieto and C. K. Scott, Phys. Rev. Lett. 26 (1971), 1200[APS].
E. Fischbach, M. M. Nieto, H. Primakoff, C. K. Scott and J. Smith, Phys. Rev. Lett. 27 (1971), 1403[APS].
E. Fischbach, M. M. Nieto and C. K. Scott, Physics in Canada (Bull. Canadian Asso. Phys.) 27 (1971), 64.
- S. Sakata and M. Taketani, Scient. Pap. Inst. Phys. Chem. Res. (Tokyo) 38 (1940), 1. Reprinted in, Prog. Theor. Phys. Suppl. No. 1 (1955), 98[PTP].
M. Taketani and S. Sakata, Proc. Phys. Math. Soc. Jpn. 22 (1940), 757. Reprinted in, Prog. Theor. Phys. Suppl. No. 1 (1955), 84[PTP].
- W. Heitler, Proc. Roy. Irish Acad. 49 (1943), 1.
-
H. Feshbach and F. Villars, Rev. Mod. Phys. 30 (1958), 24[APS].
- E. Fischbach, M. M. Nieto and C. K. Scott, Phys. Rev. (to be published).
Among other things, the above paper corrects the misconceptions of B. Nagel and H. Snellman, Phys. Rev. Lett. 27 (1971), 761, [APS]on this point.
-
M. A. B. Bég, J. Bernstein, D. J. Gross, R. Jackiw and A. Sirlin, Phys. Rev. Lett. 25 (1970), 1231[APS].
-
Y. Takahashi, Phys. Rev. D 3 (1971), 622[APS].
-
P. Carruthers, Phys. Rev. D 3 (1971), 959[APS];
Phys. Rep. 1 (1971), 1[CrossRef].
- I. Fujiwara, Prog. Theor. Phys. 10 (1953), 589[PTP].
- H. Umezawa, Quantum Field Theory (North-Holland Pub. Co., Amsterdam, 1956), p. 86.
- B. Peirce, Linear Algebra (National Academy of Sciences, Washington, 1870), p. 27.
- B. L. van der Waerden, Moderne Algebra, Pt. 2 (Julius Springer Verlag, Berlin, 1931), p. 158.
H. Weyl, Theory of Groups and Quantum Mechanics, trans. from German by H. P. Robertson (Dover, Chicago, 1931), p. 312; Classical Groups (Princeton University Press, Princeton, 1946), p. 85.
- A. Kyrala, Theoretical Physics: Application of Vectors, Matrices Tensors and Quaternions (W. B. Saunders, Philadelphia, 1967), Chap. 9, p. 277.
- F. Iachello (unpublished).
-
L. L. Foldy and S. Wouthuysen, Phys. Rev. 78 (1950), 29[APS].
Citing Article(s) :
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Progress of Theoretical Physics Vol. 51 No. 5 (1974) pp. 1585-1597
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Structure of the Duffin-Kemmer-Petiau Matrix Element for Kl3 Decay
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Ephraim Fischbach, Michael Martin Nieto and C. K. Scott
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Progress of Theoretical Physics Vol. 94 No. 6 (1995) pp. 1109-1120
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Duffin-Kemmer-Petiau Equation on the Quaternion Field
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Stefano De Leo