Abstract
The gap in the mathematical derivation of Noether’s theorem, and also of the Ward-Takahashi identities, caused by performing variation before quantization is closed by introduction of variational calculus for operator fields. It is demonstrated that both Noether’s theorem and the Ward-Takahashi identities retain full validity in quantum field theory.
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References
E. L. Hill,Rev. Mod. Phys. 23, 253 (1957).
J. D. Bjorken and S. D. Drell,Relativistic Quantum Fields (McGraw-Hill, New York, 1965), in particular Chaps. 11.4 and 11.5.
M. Danos and J. Rafelski,Nuovo Cimento 49A, 326 (1979).
M. J. Lighthill,Introduction to Fourier Analysis and Generalized Functions (Cambridge University Press, Cambridge, 1958).
P. Roman,Introduction to Quantum Field Theory (Wiley, New York, 1969) Chap. 2.
S. L. Adler,Phys. Rev. 177, 2426 (1969).
J. S. Bell and R. Jackiw,Nuovo Cimento 60A, 47 (1969).
M. Danos and L. C. Biedenharn,Phys. Rev. D 36, 3069 (1987) See also T. D. Kieu,Phys. Rev. D 44, 2584 (1991); D. Efimov,Nelokal’nye Vzaimodeistvenenii v Kvantovoi Fiziki Polya (Nauka, Moscow, 1977), Chap. 9 (in Russian).
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Danos, M. Ward-takahashi identities and Noether’s theorem in quantum field theory. Found Phys 27, 995–1009 (1997). https://doi.org/10.1007/BF02551149
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DOI: https://doi.org/10.1007/BF02551149