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Quoting the first two paragraphs of V. I. Arnol'd, On teaching mathematics, Uspekhi Mat. Nauk 53 (1998) 229-234, translated to English in Russian Math. Surveys 53 (1998) 229-236 (a transcription may a …

The (non-unique) bundle isomorphism between the bundle $J^r E$ of $r$-th order jets of sections of a vector bundle $\pi:E\rightarrow M$ and the direct sum $$\bigoplus^r_{k=0}\vee^kT^*M\otimes E\righta …

The standard reference for constructive QFT is the classic book by J. Glimm and A. Jaffe, Quantum Physics: a Functional Integral Point of View (2nd. ed., Springer-Verlag, 1988). It is certainly more t …

There is the construction of the C${}^*\!$-algebra of canonical anticommutation relations (CAR's), which is actually somewhat easier than the construction of free bosonic fields: given any complex pre …

I will leave to Yemon Choi discussing the answer from Gelfand-Raikov-Shilov's book (Commutative Normed Rings, I suppose?), and restrict myself to more recent discussions on the matter... There is an …

I am looking for a reasonably complete reference for Ennio De Giorgi's theory of sets of locally finite perimeter (also christened by him as Caccioppoli sets, after Renato Caccioppoli's pioneering wor …

This is easy and comes from the fact that $V$, being a Fréchet space, is barrelled, that is, the locally convex topology of $V$ coincides with its strong topology $\beta(V,V')$ (where $V'$ = topologic …

This can be done in certain special cases besides the usual Lie derivatives along a vector field. More precisely, let $X$ and $Y$ be tensor fields over a manifold $\mathscr{M}$. The Lie derivative $\m …

Yes, there is. The (Constant) Rank Theorem for Banach spaces is Theorem 2.5.15 of the book of R. Abraham, J.E. Marsden and T. Ratiu, Manifolds, Tensor Analysis and Applications (3rd. edition, Springer …

Tao's "smoothed sums" can be seen as a particular class of so-called matrix summation methods in the modern (post-Hardy) literature, see e.g. J. Boos, Classical and Modern Methods in Summability (Oxfo …

A related problem (if you look at it from the viewpoint of disintegration of states in C*-algebras) is the problem of disintegration of measures in a nonseparable setting. There is a recent paper whic …

In the formulation of QFT using formal functional integrals, as mentioned by Igor in his answer, the Schwinger-Dyson equation becomes an infinite-dimensional differential equation for the partition fu …

A good starting point for the topics you want to study, considering your stated background, is the book by Barrett O'Neill, Semi-Riemannian Geometry (Academic Press, 1983), especially Chapter 4. That …

There is also the little book by Robert Kaplan, The Nothing that is: a Natural History of Zero (Oxford University Press, 2000).

The fourth volume of I. M. Gel'fand's "Generalized Functions", subtitled "Applications of Harmonic Analysis" (written together with N. Ya. Vilenkin and published by Academic Press in 1964, now recentl …