Abstract
Introduction:purpose: Noether’s theorem connects symmetry of the Lagrangian to conserved quantities. Quantum effects cancel the conserved quantities.
Methods: Triangle diagram, Path integral, Pauli-Villars regularisation.
Results: Quantum effects that spoil conserved quantities of local gauge symmetries endager renormalisability.
Conclusion: A careful treatment of anomalies is needed in order to obtain correct results. The π0 → γγ decay is perhaps the most notable “impossible” effect allowed by anomalies.
Keywords
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References
Adler, S.L. 1969. Axial-Vector Vertex in Spinor Electrodynamics. Physical Re- view, 177(5), pp.2426-2438. Available at: https://doi.org/10.1103/PhysRev.177.2426
Bell, J.S. & Jackiw, R. 1969. A PCAC puzzle:π0→γγ in the σ model. Il Nuovo Cimento A (1965-1970), 60(1), pp.47-61. Available at: https://doi.org/10.1007%2FBF02823296
Bollini, C.C. & Giambiagi, J.J. 1972. Dimensional renorinalization : The number of dimensions as a regularizing parameter. Il Nuovo Cimento B (1971-1996), 12(1), pp.20-26. Available at: https://doi.org/10.1007/BF02895558
Fabiano, N. 2022a. Path integral in quantum field theories. Vojnotehnički glas nik/Military Technical Courier, 70(4), pp.993-1016. Available at: https://doi.org/10.5937/vojtehg70-35882
Fabiano, N. 2022b. Regularization in quantum field theories. Vojnotehnički glasnik/Military Technical Courier, 70(3), pp.720-733. Available at: https://doi.org/10.5937/vojtehg70-34284
Fabiano, N. 2022c. Beta functions in the quantum field theory. Vojnotehnički glasnik/Military Technical Courier, 70(1), pp.157-168. Available at: https://doi.org/10.5937/vojtehg70-32131
Fujikawa K. 1979. Path Integral Measure For Gauge Invariant Fermion Theories. Physical Review Letters, 42(18), pp.1195-1197. Available at: https://doi.org/10.1103/PhysRevLett.42.1195
’t ’Hooft, G. & Veltman, M. 1972. Regularization and renormalization of gauge fields. Nuclear Physics B, 44(1), pp.189–213. Available at: https://doi.org/10.1016/0550-3213(72)90279-9
Noether, E. 1918. Invariante Variationsprobleme. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, 1918, pp.235-257 [online]. Available at: https://eudml.org/doc/59024 [Accessed: 25 April 2022].
Pauli, W. & Villars F. 1949. On the Invariant Regularization in Relativistic Quantum Theory. Reviews of Modern Physics, 21(3), pp.434-444. Available at: https://doi.org/10.1103/RevModPhys.21.434
Schwinger, J. 1959. Field Theory Commutators. Physical Review Letters, 3(6), p.296. Available at: https://doi.org/10.1103/PhysRevLett.3.296
Yang, C.N. & Mills, R. 1954. Conservation of Isotopic Spin and Isotopic Gauge Invariance. Physical Review, 96(1), pp.191-195. Available at: https://doi.org/10.1103/PhysRev.96.191
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