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Questions tagged [mathematical-physics]

For questions regarding the mathematical aspects of physics.

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30 votes
2 answers
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When and how was the geometric understanding of gauge theories developed?

In theoretical physics, the modern perspective on gauge theory is that it is most elegantly described in the 'language' of differential geometry. I am interested in the history behind these ideas. ...
Danu's user avatar
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17 votes
5 answers
2k views

What was the motivation for Minkowski spacetime before special relativity?

If I understand correctly, the concept of a Minkowski space/metric was already known before Einstein's paper on special relativity. Was there any physical motivation for studying this type of metric ...
Prastt's user avatar
  • 271
14 votes
1 answer
1k views

Notation for Christoffel symbols

In Christoffel's 1869 paper in which he introduced the Christoffel symbols on the 3rd and 4th pages, they are written as $\left[\substack{ij \\ k}\right]$ and $\{\substack{ij \\ k}\}$. The notation $...
KCd's user avatar
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10 votes
1 answer
890 views

How were vector calculus nabla ∇ identities first derived?

(Math Stack Exchange suggested that the same question I posted there be migrated here; The one at Math Stack Exchange was thus deleted. The recommendation message of migration can be found here, ...
Secret's user avatar
  • 203
5 votes
1 answer
421 views

Who originally derived the general force law equation of force between current elements?

Wikipedia credits this to Maxwell. This derivation can be found in Maxwell's Treatise on Electricity and Magnetism vol. 2, part 4, ch. 2 (§§502-527). I went through the derivation and found two self ...
Joe's user avatar
  • 181
4 votes
1 answer
677 views

Who made the first derivation of the angle to maximise projectile range, which turned out to be wrong?

I remember hearing once that the first "proof" that the angle to maximise projectile range gave the correct answer, 45 degrees, but was later found that the proof was wrong. I can't remember ...
twentyyears's user avatar
4 votes
2 answers
697 views

What were the criticisms against the introduction of "vector analysis"?

Frequently, 19th century physicists—e.g., Helmholtz or Maxwell—did not use modern-day vector notation, which Gibbs contributed in large part to. For example, Helmholtz in his famous paper on the ...
Geremia's user avatar
  • 5,401
2 votes
1 answer
814 views

Origin of the Heaviside function?

I have tried to find the actual origin of the Heaviside unit step function and could not. I've searched and searched, read one complete biography of Oliver Heaviside, skimmed another, but nowhere can ...
147pm's user avatar
  • 123
32 votes
11 answers
8k views

Has physics ever given a physical significance to a mathematically abstract idea?

Consider a fundamental concept in maths that was created to 'solve' a problem that simply couldn't be solved by any other approach (or maybe for some other reason). Now let's assume that this concept ...
Adil Mohammed's user avatar
9 votes
1 answer
216 views

Did Sophie Germain find a flaw in Euler's equations for elastic vibrations?

I am a playwright working on a play about Sophie Germain. When Sophie was competing for the prix extraordinaire to find effective formulas to describe the vibrations of elastic surfaces, she believed ...
Brenda Kenworthy's user avatar
8 votes
1 answer
2k views

What was the real need of divergence and curl operators?

As I'm advancing my study in Electromagnetism I'm getting introduced to more mathematical operators which are exclusively used in Electromagnetism and Fluid Dynamics only. Let me try to explain myself ...
Knight wants Loong back's user avatar
5 votes
3 answers
782 views

Example of abstract math theory that was later found to be applicable to physical world?

In this video about the Banach-Tarski paradox the host stipulates that history is full of examples of abstract mathematical theories that were later found to be applicable to the physical world. Is he ...
daniel.sedlacek's user avatar
4 votes
2 answers
2k views

Who discovered the wave equation?

https://link.springer.com/chapter/10.1007/978-1-4684-5772-8_2 says: Using Newton's recently formulated laws of motion, Brook Taylor (1685–1721) discovered the wave equation by means of physical ...
user45664's user avatar
  • 173
4 votes
1 answer
515 views

Where in Gauss's works does he derive "Gauss's Law"?

Where in Gauss's works does he derive "Gauss's Law"? Or is "Gauss's Law" named after Gauss for a different reason?
Geremia's user avatar
  • 5,401
4 votes
2 answers
245 views

History of delta barrier in quantum mechanics

I'm interested in finding something out about the history of the problem of the delta potential barrier in quantum mechanics. Which was the first study to propose this problem, and perhaps any ...
Ed Wolf's user avatar
  • 71
4 votes
3 answers
806 views

Best books/papers on Newton and his mathematical physics

In your opinion, what are some of the best books/papers on Newton and his work that accurately cover the connections between his geometric proofs in the Principia and his development of the calculus ...
Tom Copeland's user avatar
3 votes
2 answers
951 views

History of PDE's in the 19th Century

I've been asked to write an essay on whether the work on PDE's in the 19th century belonged to applied or pure mathematics. Does anyone know of any useful sources I could use?
Bradley Hill's user avatar
3 votes
3 answers
755 views

Math development and under-appreciation of Maxwell's Equations

Freeman Dyson expresses the opinion in his 1972 essay titled "Missed Opportunities" that Maxwell's equations could have played a much bigger role, one that is comparable to classical ...
Lee David Chung Lin's user avatar
1 vote
0 answers
79 views

Complex potential in E227?

I have a reason to believe that Euler introduced the complex potential in his Continuation des recherches sur la theorie du mouvement does fluides, published in 1757. However, I am having hard time ...
timur's user avatar
  • 709