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In some modern field theory texts such as Siegel's Fields it is claimed that canonical quantisation of fields is obsolete as it is not used it modern research papers. Thus, it should be removed from curricula and replaced with more modern methods.

Siegel says that the path integral should be the primary technique taught. However, canonical quantization makes it obvious that the quanta of the fields are particles. I have never seen this done using path integrals. Indeed I have only seen path integrals used for calculating things such as S-matrix elements, which it is certainly much more efficient at.

Essentially my question boils down to this; Can one show the particle content of fields using the path integral? If not, can canonical quantization really be considered obselete when first learning field theory?

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  • $\begingroup$ $\uparrow$ Which page? $\endgroup$
    – Qmechanic ♦
    Dec 18, 2015 at 18:34
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    $\begingroup$ It's mentioned on the webpage for the book insti.physics.sunysb.edu/~siegel/errata.html as well as pages 6, 31, 77 of ver.4 of the book. $\endgroup$
    – Okazaki
    Dec 18, 2015 at 19:57
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    $\begingroup$ As both formulations of QFT are equivalent, this question is kind of opinion based. Anyway, IMHO, canonical is not obsolete at all, and a deep understanding of it is essential even though one uses path integrals in one's research (not to speak of the pedagogical value of operator quantisation, which IMHO should always be taught in full detail before path integrals) $\endgroup$
    – AccidentalFourierTransform
    Dec 18, 2015 at 20:19

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It is not at all obsolete. Weinberg, in his book on Quantum Field theory (Vol I, Chapter 7), makes a case for it, and treats it before the path integral. Formally, the methods are equivalent, but the devil is in the details.

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