Quick Search:
Prog. Theor. Phys. Vol. 41 No. 5 (1969) pp. 1309-1327
A Canonical Field Theory of Chiral Symmetry
Shoji Ozaki
9-43, Ochiai, Chiryu, Chiryucho, Hekkaigun, Aichiken
(Received October 2, 1968)
Abstract:
A canonical field theory of chiral SU(2) ×SU(2) current is constructed by using only pseudoscalar mesons. Although equal-time commutators between time and space components of current are derived from canonical commutators of fields and are different from Sugawara's corresponding ones, equations of motion, continuity equation of current and stress tensor are expressed in terms of current densities alone and have the same form as Sugawara's corresponding ones apart from a numerical factor 1/2. Chiral symmetry breaking term deducing the PCAC hypothesis satisfies the conservation law of stress tensor and does not alter equations of motion. The self-consistency, relativistic covariance, stress tensor conservation, etc., are checked.
URL :
http://ptp.ipap.jp/link?PTP/41/1309/
DOI : 10.1143/PTP.41.1309
References:
-
S. Weinberg, Phys. Rev. Lett. 18 (1967), 507[APS];
Phys. Rev. 166 (1968), 1568[APS].
J. Schwinger, Phys. Lett. B 24 (1967), 473[CrossRef];
Phys. Rev. 167 (1968), 1432[APS].
J. A. Cronin, Phys. Rev. 161 (1967), 1483[APS].
J. Wess and B. Zumino, Phys. Rev. 163 (1967), 1727[APS].
L. S. Brown, Phys. Rev. 163 (1967), 1802[APS].
P. Chang and F. Gürsey, Phys. Rev. 164 (1967), 1752[APS].
T. Shiozaki, Prog. Theor. Phys. 39 (1968), 189[PTP]; ibid. 39 (1968), 195[PTP].
Y. Ohnuki and Y. Yamaguchi, “Chiral Dynamics”, Institute for Nuclear Study, Tokyo University Preprint, INS Report 119 (1967).
S. Gasiorowicz and D. A. Geffen, “Effective Lagrangian”, Argonne National Lab. preprint, ANL/HEP 6809 (1968).
-
R. F. Dashen and D. H. Sharp, Phys. Rev. 165 (1968), 1857[APS].
D. H. Sharp, Phys. Rev. 165 (1968), 1867[APS].
C. G. Callan, R. F. Dashen and D. H. Sharp, Phys. Rev. 165 (1968), 1883[APS].
M. B. Halpern, Phys. Rev. 164 (1967), 1878[APS].
-
H. Sugawara, Phys. Rev. 170 (1968), 1659[APS].
-
K. Bardakci, Y. Frishman and M. B. Halpern, Phys. Rev. 170 (1968), 1353[APS].
-
C. N. Yang and R. L. Mills, Phys. Rev. 96 (1954), 191[APS].
T. D. Lee, S. Weinberg and B. Zumino, Phys. Rev. Lett. 18 (1967), 1029[APS].
-
S. Weinberg, Phys. Rev. 166 (1968), 1568[APS].
Weinberg's Dµ φ has two errors of sign. Text's sign is correct.
-
J. Schwinger, Phys. Rev. 130 (1963), 406[APS].
- M. Gell-Mann and M. Lévy, Nuovo Cim. 16 (1960), 705.
Citing Article(s) :
-
Progress of Theoretical Physics Vol. 43 No. 3 (1970) pp. 842-843
:
-
Current as Dynamical Variables
-
Shoji Ozaki
