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References
J. G. Taylor:Phys. Rev. Lett.,18, 713 (1967); see also Taylor's lucid article inLectures in Theoretical High Energy Physics, edited byH. H. Aly (New York, 1968).
Actually,Taylor take massive Ψ and massless χ fields.
SeeR. E. Marshak, Riazuddin andC. P. Ryan:Theory of Weak Interactions in Particle Physics (New York, 1969), p. 17.
J. Schwinger:Phys. Rev.,173, 1536 (1968).
P. A. M. Dirac:Proc. Roy. Soc., A133, 60 (1931);Phys. Rev.,74, 817 (1948);G. Wentzel:Prog. Theor. Phys. Supplement,37–38, 163 (1966);J. Schwinger:Phys. Rev.,144, 1087 (1966).
J. Goldstone, A. Salam andS. Weinberg:Phys. Rev.,127, 965 (1962).
J. Goldstone:Nuovo Cimento,19, 154 (1961).
Y. Nambu:Phys. Rev. Lett.,4, 380 (1960). WhenP conservation is relaxed, there are extra terms; seeJ. Bernstein:Elementary Particles and their Currents (San Francisco, 1968).
J. S. Bell andR. Jackiw:Nuovo Cimento,60 A, 47 (1969);S. L. Adler:Phys. Rev.,177, 2426 (1969);C. R. Hagen:Phys. Rev.,188, 2416 (1969).
D. Gross andR. Jackiw:Phys. Rev. D,6, 477 (1972);H. Georgi andS. Glashow:Phys. Rev. D,6, 429 (1972);C. Bouchiat, J. Iliopoulos andPh. Meyer:Phys. Lett.,38 B, 519 (1972).
SeeD. Gross andR. Jackiw: ref. 10 ;
S. Weinberg:Phys. Rev. Lett.,19, 1264 (1964);27, 1688 (1971);A. Salam: inElementary Particle Theory, edited byN. Svartholm (Stockholm, 1968).
SeeD. Gross andR. Jackiw: ref. (10). Section IV C.
SeeS. Weinberg: ref. (12),, paper 2.
R. Acharya andZ. Horvath:Lett. Nuovo Cimento,4, 464 (1973); at the electromagnetic level, the Z-meson can be made axial with a vector photon by an appropriate choice ofP γ for theW (3)μ andB μ fields:\(\left( {\sqrt 3 + \frac{1}{{\sqrt 3 }}} \right)B_\mu ^\gamma - 2W_\mu ^{(3)} - \left( {\sqrt 3 - \frac{1}{{\sqrt 3 }}} \right)B_\mu ,\;\quad \left( {\sqrt 3 + \frac{1}{{\sqrt 3 }}} \right)W_\mu ^{(3)P_\gamma } = 2B_\gamma + \left( {\sqrt 3 - \frac{1}{{\sqrt 3 }}} \right)W_\mu ^{(3)} \) It is, of course, understood thatJ μ and\(\hat J\) represent thetotal electromagnetic and monopole currents respectively when hadrons are included so as to be rid of the anomaly.
S. Coleman: unpublished;N. Cabibbo andE. Ferrari:Nuovo Cimento,23, 1147 (1962);C. R. Hagen:Phys. Rev.,140, B 804 (1965).
E. Amaldi: inOld and New Problems in Elementary Particles (New York and London, 1968).
J. Schwinger:Phys. Rev.,144, 1087 (1966).
G. Guralnik, C. R. Hagen andT. W. B. Kibble: inAdvances in Particle Physics, Vol.2, edited byR. L. Cool andR. E. Marshak (New York, 1968), p. 567.
SeeR. Jackiw andK. Johnson: MIT preprint (May, 1973).
Relativistic invariance of the symmetric theory has been proved bySchwinger ref. (5)) and byB. Zumino:1966 International School of Physics «Ettore Majorana», p. 711. Incidentally, if one were to relax the restrictiong 2=3g 2, the monopole theory admits a static limit and the static monopole potential is\(V = \lambda _0 \exp [ - M_Z r]/r\). The force on the monopole in a homogeneous (uniform)H field may be obtained from the general expression\(F = \lambda _0 \int {d^3 r} \left\{ {M_Z^2 H(r)\frac{{\exp [ - M_Z r]}}{{4\pi r}} + H(0)\delta ^{(3)} (r)} \right\} = \frac{{\lambda _0 }}{{4\pi }}\int {d^3 rM_Z^2 \{ H(r) - H(0)\} } \frac{{\exp [ - M_Z r]}}{r}\) and hence can be seen to vanish. The associated electric field of a moving monopole may be neglected outsideR ≈m -1Z . Also, the classical expression for the angular momentumJ 3=eg/4π for the symmetric theory now becomesJ 3=(eg/2π)(m Z a)−2[1−exp[−M Z a](1+M Z a)]. The dependance ofJ 3 on the distance between the monopole and the charge makes the classical argument for quantization inapplicable.
T. D. Lee:Phys. Rev.,140, B 959 (1965); it is important to recognize that each interaction (electromagnetic and weak) is invariant under its ownC i ,P i andT i with\(C_\gamma P_\gamma T_\gamma = C_w P_w T_w \).But,\(C_\gamma \ne C_w , P_\gamma \ne P_w , T_\gamma \ne T_w \) in general.CP violation at the electromagnetic level was discussed byJ. Bernstein, G. Feinberg andT. D. Lee:Phys. Rev.,139, B 1650 (1965); see ref. (3). SeeR. E. Marshak, Riazuddin andC. P. Ryan:Theory of Weak Interactions in Particle Physics (New York, 1969), p. 684 for further references.
A. Salam:Phys. Lett.,22, 683 (1966);J. G. Taylor: unpublished.
Lee has stressed the need for incorporatingT violation in gauge theories;T. D. Lee:A theory of spontaneous T violation, Columbia University preprint, Co-2271-9 (1973).
The choiceg 2=3g' 2 is relevant in this context. OtherweseZ μ has both vector and axial vector couplings, even at the electromagnetic level.
L. Wolfenstein: in1968 “Ettore Majorana” School Proceedings, p. 219.
G. Barton andE. D. White:Phys. Rev.,184, 1660);D. J. Broadhurst:Nucl. Phys.,20 B, 603 (1970).
J. Bjorken andC. H. Llewellyn-Smith:Phys. Rev. D,7, 887 (1973), Appendix A.
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Acharya, R., Horváth, Z. Taylor's nonclassical theory of magnetic monopoles as a spontaneously brokenU L1 ⊗U R1 Model. Lett. Nuovo Cimento 8, 513–519 (1973). https://doi.org/10.1007/BF02728169
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DOI: https://doi.org/10.1007/BF02728169