1

I see both of them used in mathematical articles as subjects, for example:

Examples from book Renormalization and effective field theory of Kevin Costello, who is an Irish mathematician.

If we do have a continuum quantum field theory (whatever that is!) we should, in particular, have a low-energy effective field theory for every energy.

We will assume that we have an action functional of the form ...

Thus, the Segal axioms for field theory propose that one assigns a Hilbert space of states to a closed Riemannian manifold of dimension d − 1.

Thus, this theorem allows one to quantize the theory associated to any classical action functional.

Examples from Habilitationsschrift Batalin-Vilkovisky formalism in topological field theory(pdf file) of P. Mnev, who is a Russian mathematician:

We should stress that neither quantum Chern-Simon theory, nor quantum Poisson sigma model are constructed by a perturbative path integral on manifolds with boundary...

We reserve symbol d for the de Rham differential on the source.

The followings are in page 6 of the pdf file above:

The idea of constructing topological quantum field theories via path integrals immediately runs into a number of problems:
(1) ... Instead one can try to define the "perturbative" path integral ...
(2) To apply the stationary phase formula, one needs the critical points of the action to be isolated...
(3) ... One has to prove then that the resulting partition functions are independent on the chosen geometric structure.
(4) ... One has to prove fIniteness (convergence) of the Feynman diagrams...
(5) ... one has to extend the path integral construction of TQFT partition functions

Question:

In the sentences above, what do words one and we refer to?

And when should one or we be used?

My ideas motivated by answers:

In abstract or conclusion part of a math article, "we" refers to the author(s). In statement and proof part, "we" creates an atmosphere as if the reader is participating with the author, and is used for the author(s) to really discuss / prove / make use of / assume / ... something (a theorem, an assumption, a condition, ...) in this article.

On the other hand, "one" is more like "anyone" or "whoever", and is used to just state some general cases without details or explanations.

2

"We" means "the authors" or sometimes "the author(s) and the reader", and it can be used describe what the authors did, or what the author and the readers will be able to learn:

In this paper we show that... / We will assume ... (we = the authors)

If we have a Hilbert space... (we = author and reader)

On the other hand, "One" is used for "other people" (including the reader or the author, perhaps)

allows one to quantize... (I could do this, but I didn't, or I didn't in this paper. You could do this too. Other people probably have done this, so look at the list of references)

Often there is an option. "We" more directly includes the author and reader and so is "warmer". "One" is more distant and more dispassionate.

1

I don't think there's any difference between the two. except that "we" sounds friendlier, as if the reader is participating with the author. "One" sounds stiffer and more awkward.
But the words don't actually refer to anything; they provide a dummy agent so that we don't (one doesn't) have to overuse "there is" and passive structures.

(Did it really say "...propose that one assigns..."? I would expect "assign'.)

3
  • Yes, it is "assigns" indeed. I think that's because the subject (one) is sigular. More examples are given in updates. – Andrews Jun 6 '20 at 5:05
  • It's more common to use the "plain form" of the verb, without the "s", as a subjunctive in subordinate clauses, at least in formal contexts, such as a technical paper. – Jack O'Flaherty Jun 6 '20 at 5:48
  • A reference to support your idea in collinsdictionary. – Andrews Jun 6 '20 at 14:17

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