Linked Questions

12
votes
2answers
581 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 ...
7
votes
2answers
5k views

How important is mathematical proof in physics?

How important are proofs in physics? If something is mathematically proven to follow from something we know is true, does it still require experimental verification? Are there examples of things that ...
5
votes
2answers
943 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 ...
16
votes
1answer
1k views

What does it mean for a QFT to not be well-defined?

It is usually said that QED, for instance, is not a well-defined QFT. It has to be embedded or completed in order to make it consistent. Most of these arguments amount to using the renormalization ...
5
votes
1answer
319 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
1answer
261 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 ...
3
votes
1answer
291 views

Rigorous mathematical formalism of particle physics

Can anyone provide me with a rigorous mathematical definition of the fundamental particles (all fundamental bosons and fermions), reflecting the analogy of action of groups with interaction of ...
1
vote
1answer
160 views

Trajectories piecewise smooth?

In my studies of calculus and real analysis I have found the proofs of several theorems, commonly used in physics, such as those concerning the conservativity of fields, for example like If $\...
1
vote
1answer
612 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)\,\,...
3
votes
0answers
124 views

Is rigorous functional analysis useful for theoretical physics? [duplicate]

I'm an undergraduate physics without much quantum mechanics at all under my belt. I'm studying functional analysis, and I want to know whether or not this will be useful for me in theoretical physics ...
1
vote
0answers
63 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 ...
0
votes
0answers
49 views

Selfstudying math with rigour is useful for a physics undergrad who want be a theoretical physicist (String theory, quantum gravity)? [closed]

When I say "math" I'm referring specifically to Topology, Differential Geometry and Group Theory. I've seen some colleagues studying such mathematical topics only superficially, i.e in group theory, ...
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 ...
0
votes
0answers
791 views

QFT as a rigorous mathematical theory [duplicate]

I understood that quantum field theory is essentially based on a problematic mathematical basis. Can someone please explain what is the fundamental problem to formulate QFT as a rigorous mathematical ...
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 ...

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