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In the introductory chapter of the QFT book by Mark Srednicki the author notes that

[p. 26] So now we have two different approaches to relativistic quantum theory [...] Which [one of those two] we use is a matter of convenience and taste. And quantum field theory, the formalism in which position and time are both labels on operators, is much more convenient and efficient for most problems.

The other approach is described as follows:

[p. 25] Let us discuss the second option [...] to promote time to an operator. [...] We can use the proper time $\tau$ of the particle [...] as the time parameter. The coordinate time $T$ [...] is then promoted to an operator. [...] Relativistic quantum mechanics can indeed be developed along these lines, but it is surprisingly complicated to do so.

Does this "second option" have an own specific name (for distinction from quantum field theory, in Srednicki's sense)?

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It's usually called worldline field theory (you interpret $X,Y,Z,T$ as quantum fields living on the one dimensional space which is the worldline of a particle) and you read about it in string theory books since it is the more natural route to string theory in the form of world*sheet* perturbation theory. (There is also an approach to string theory called string field theory which is more analogous to ordinary QFT.) Basically both approaches are equivalent with different technical merits. QFT is far more elegant and useful than worldline theory for most practical purposes though. –  Michael Brown Sep 14 '13 at 14:14
    
@Michael Brown: "It's usually called worldline field theory" -- Thanks (that's plausible; google.de/… yields 9 hits. (And it surely seems to fit well with Einstein's "point coincidence" premiss ...)) (Hmm ... just noticed that, in contrast, google.com/… returns 35 results ...) –  user12262 Sep 14 '13 at 16:03
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@user12262 if you remove the quotes it returns a lot more results. See this for instance. arxiv.org/abs/hep-ph/9412358 –  Prathyush Sep 14 '13 at 23:53

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