Linked Questions

22
votes
16answers
4k views

Can a mathematical proof replace experimentation?

I know that this is very similar to How important is mathematical proof in physics? as well as Is physics rigorous in the mathematical sense? and The Role of Rigor. However, none of the answers to ...
49
votes
7answers
9k views

Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
0
votes
0answers
91 views

Reference request for mathematical physics from an axiomatically rigorous perspective [duplicate]

Being a grad student in math, and a rather pedantic one indeed, I was unable to accept many of the things taught to me in undergrad physics courses. I am now trying to learn the applications of ...
1
vote
0answers
66 views

Using intuition to understand physics concepts, how and when to let that need for intuition go? [closed]

Those of us who grew up solving Newtonian mechanics, electrostatics, and calculus of 1-3 variables problems developed good intuition for understanding simple concepts. This helped me condition a ...
5
votes
1answer
264 views

Set theories used in mathematical physical theories

For most theorems, this is unimportant - a typical problem will have the same solutions in NFU, ZFC or some other theory, since said theories got popular precisely because they give pretty much the ...
16
votes
9answers
4k views

Is physics rigorous in the mathematical sense?

I am a student studying Mathematics with no prior knowledge of Physics whatsoever except for very simple equations. I would like to ask, due to my experience with Mathematics: Is there a set of ...
79
votes
11answers
25k views

Quantum Field Theory from a mathematical point of view

I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view. Are there any good books or other reference ...
32
votes
3answers
2k views

What is the issue with interactions in QFT?

I've started studying QFT this year and in trying to find a more rigorous approach to the subject I ended up find out lots of people saying that "there is no way known yet to make QFT rigorous when ...
5
votes
1answer
320 views

The Role of Rigor II

The purpose of this question is to supplement an earlier question The Role of Rigor and to ask about the role of mathematical rigor in physics. In order to formulate a question that can be answered, ...
5
votes
2answers
948 views

Is there a way to justify perturbation theory in QFT?

I can accept that some problems do require a perturbation theory approach to be solved. The development of perturbation theory is perfectly rigorous. So at first, even though many people say that no ...
0
votes
0answers
159 views

Is mathematical rigour irrelevant in most physics fields? [duplicate]

Are mathematical notions like closed sets, limits of sequences, measures, and function spaces basically irrelevant in the day to day work of a physicist? Naturally, such concepts are the foundations ...
1
vote
1answer
624 views

Delta functional in path integrals

In a few articles dealing with path integral quantization I came across some calculations where apparently identities of the form \begin{equation} \int (\mathcal{D}\Phi)\, \delta(-\partial_0\Phi+j)\,\,...
12
votes
2answers
582 views

Are derivations of physical laws less important than the laws themselves? [closed]

The proportionality between the kinetic energy of gas molecules and temperature is a well-known result. This is usually shown by considering a cubical box containing an ideal gas, and postulating that ...
28
votes
2answers
8k views

Wick rotation in field theory - rigorous justification?

What is the rigorous justification of Wick rotation in QFT? I'm aware that it is very useful when calculating loop integrals and one can very easily justify it there. However, I haven't seen a ...
20
votes
5answers
3k views

What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?

I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly. Hilbert's sixth problem consisted roughly about finding axioms for physics (...

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