Lüders and Pauli proved the \(\mathcal{CPT}\) theorem based on Lagrangian quantum field theory almost half a century ago. Jost gave a more general proof based on “axiomatic” field theory nearly as long ago. The axiomatic point of view has two advantages over the Lagrangian one. First, the axiomatic point of view makes clear why \(\mathcal{CPT}\) is fundamental—because it is intimately related to Lorentz invariance. Secondly, the axiomatic proof gives a simple way to calculate the\(\mathcal{CPT}\) transform of any relativistic field without calculating \(\mathcal{C}\), \(\mathcal{P}\) and \(\mathcal{T}\)separately and then multiplying them. The purpose of this pedagogical paper is to “deaxiomatize” the \(\mathcal{CPT}\) theorem by explaining it in a few simple steps. We use theorems of distribution theory and of several complex variables without proof to make the exposition elementary.
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References
Güders L. (1954). Det. Kong. Danske Videnskabernes Selskab, Mat.-fys. Medd. 28(5),
Pauli W., ed., in Niels Bohr and the Development of Physics (McGraw-Hill, New York, 1955), pp. 30–51.
Jost R. (1957). Helv. Phys. Acta. 30: 409
J. Schwinger, Proc. Natl. Acad. Sci. 44, 223 (1958) and cited references.
A. S. Wightman, Phys. Rev. 101, 860 (1956); A. S. Wightman and L. Garding, Ark. Fys. 23, Nr. 13 (1964).
R. Jost, in Theoretical Physics in the Twentieth Century (Interscience, New York, 1960).
Jost R. (1965). The General Theory of Quantized Fields. American Mathematical Society, Providence
Streater R.F., and Wightman A.S. (1964). PCT, Spin & Statistics, and All That. Benjamin, New York
Bogoliubov N.N., Logunov A.A., and Todorov I.T. (1975). Introduction to Axiomatic Quantum Field Theory. Benjamin, Reading
Haag R. (1996). Local Quantum Physics. Springer, Berlin
Itzykson C., and Zuber J.-B. (1980). Quantum Field Theory. McGraw-Hill, New York
Peskin M.E., and Schroeder D.V. (1995). An Introduction to Quantum Field Theory. Addison Wesley, Reading
Weinberg S. (1995). The Quantum Theory of Fields, Vol. I, Foundations. Cambridge University Press, Cambridge
van der Waerden B.L. (1974). Group Theory and Quantum Mechanics. Springer, Berlin
Hall D.W., and Wightman A.S. Det. Kong. Danske Videnskabernes Selskab, Mat.-fys. Medd. 31, No. 5 (1957).
Wigner E.P., Göttinger Nachrichten, Math-Phys. 546 (1932); Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra (Academic, New York, 1959), Chapter 26. Translated from Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren (Vieweg, Braunschweig, 1931) by J. J. Griffin.
Greenberg O.W., Phys. Rev. D 73, 087731 (2006).
Greenberg O.W. (1998). Phys. Lett. B 416:144
Weinberg S., op. cit., pp. 244–246.
Greenberg O.W., Phys. Rev. Lett. 89, 231602 (2002).
Greenberg O.W. (2003). Phys. Lett. B 567: 179
Barenboim G., and Lykken J. (2003). Phys. Lett. B 554: 73
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Greenberg, O.W. Why is \(\mathcal{CPT}\) Fundamental?. Found Phys 36, 1535–1553 (2006). https://doi.org/10.1007/s10701-006-9070-z
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DOI: https://doi.org/10.1007/s10701-006-9070-z