2
votes
0answers
64 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 ...
60
votes
11answers
12k 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 ...
34
votes
9answers
5k 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, ...
30
votes
6answers
3k views

Formalizing Quantum Field Theory

I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or ...
11
votes
7answers
2k 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 ...
15
votes
5answers
1k 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 ...
9
votes
2answers
2k 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 ...
7
votes
2answers
2k 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 ...
16
votes
1answer
755 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 ...
11
votes
2answers
454 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 ...
1
vote
3answers
203 views

Why does the Copenhagen interpretation assert randomness if this cannot be tested?

Why does the Copenhagen interpretation of QM assert that random events occur if such a claim cannot ever be proven or disproven? A related question: How to tell if QM is really random? Edit On ...
3
votes
1answer
230 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 ...
0
votes
0answers
290 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 ...
1
vote
1answer
117 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
87 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)\, ...

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