Reddit mentions of The Quantum Theory of Fields, Volume 1: Foundations

> somebody knows a book about quantum field theory that is actually mathematically rigorous

I'm not sure that this really exists. You could maybe try Peter Woit's notes, but I wouldn't stick to a mathematician's take. I've never read Steven Weinberg, but I would trust him over pretty much anyone else. In any case, you may be underestimating the difficulty of physics even given a mathematics and physics background. Consider giving Sakurai or possibly Ballentine a thorough read before delving into quantum field theory. Asher Peres has a great book too. Chances are, you haven't really considered what, mathematically, the momentum and energy operators are actually doing. Respectively, they are generators of the groups of spatial translations/rotations (depending on if you are considering linear or angular momentum) or of time translation. This is pretty important to understand clearly, and I think it's worth appreciating the physical intuition before delving too deeply into the math involved.

One of my favourite books is Matrix Analysis, by Rajendra Bhatia. I think it's a crying shame that most (all?) undergraduate curricula do not cover the calculus of matrices (as opposed to the algebra of matrices). I think it's the logical conclusion of the sequence Single Variable Calculus --> Multivariable Calculus --> Vector Calculus. In particular, one should be aware that smooth functions of a diagonalizable matrix are equivalent up to a basis change to a smooth function of the eigenvalues of that matrix. This is a consequence of the Cayley-Hamilton theorem. But then you have to worry about the nastiness of errors in specifying either matrix elements or eigenvalues. There are lots of thorny but fascinating issues to consider here. This is, to me, the real foundation of quantum mechanics. All the junk about observables needs to be appreciated in context of the ability of measurement devices to respond to the eigenvalues of a Hamiltonian.

I think it's better to keep a focussed and small list of things to read. If you have some kind of electronic reading device, you'd be better advised to put PDFs of good books/notes/articles rather than carrying a bunch of paper. But if you're in Mozambique and therefore unlikely to have reliable power or internet (never been, so I could be wrong), I think you are better advised to pick one book and work through it diligently. I'd strongly recommend Hartshorne's Algebraic Geometry for this, but that's a pretty herculean effort. Algebraic Geometry is nice, though, because it requires every aspect of mathematical thought and is beautiful to boot.

A suggestion that is not so directly related to the ones you have given: Donald Knuth's The Art of Computer Programming. It could be the most important book of the twentieth century.

Theoretical particle physics: all three massive volumes of Weinberg's The Quantum Theory of Fields.

Every professor I know in the field has this on their bookshelf. People talk about "taking a year" to do a detailed reading of this book. It's so nitty gritty that I don't think any course in the world uses it, but you gotta know it.