Questions tagged [mathematical-physics]
For questions regarding the mathematical aspects of physics.
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Which were the first PhD thesis in Mathematics and Physics?
Were there PhD thesis in the time of Galileo and Newton?
Did Newton and Galileo make a PhD thesis?
Due to the poor level of science (before calculus and so on), were PhD thesis made in math and ...
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Why is the angular momentum written as JJ in quantum mechanics?
Why is $\textbf{J}$ called angular momentum operator? Can anyone explain why the expectation value of J is angular momentum?
Here is how $J$ is defined: The rotation operator
$$
U(\alpha)=\exp(-i {\...
user6964
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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 ...
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History of PDE's in the 19th Century (part 2)
This is a follow up to this question: History of PDE's in the 19th Century
The question I have been given to answer is:
The history of partial differential equations in the 19th Century belongs ...
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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 ...
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Origin of operators in quantum mechanics
Historically, where did the concept of operators in quantum mechanics come from?
How did people first understand that momentum operator should be of the form of $i \hbar \frac{{\rm d}}{{\rm d}x}$?
...
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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?
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When Was Kaluza-Klein Theory Appreciated?
As far as I understand, the Kaluza-Klein theory, despite its unprecedentedly profound and beautiful character, had a modest following in its early days. I guess that two of the many reasons might be ...
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Time for big results to become widely recognized in the scientific community
What are some examples of big results in mathematics and or physics that took a long time to be considered groundbreaking? What was the length of time from the original publication to the recognition?
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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 ...
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Notational change with Integrals
A little over 50 years ago I took my first Calculus class and learned the conventional form of an integral as:
$$
\int f(x)\,\, \textrm{d}x
$$
That is, the integral sign (definite or indefinite) ...
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Who wrote down the equations governing gravity in a field language for the first time?
In his paper The search for unity: Notes for a history of quantum field theory [Daedalus 4, 106 (1977)], Steven Weinberg writes:
The first successful classical field theory was based on Newton's ...
Funzies
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Origin of diagrammatics illustrating the relation between cumulants and moments?
The exponential-log transformation of exponential generating functions (see OEIS A036040 and A127671) relate the classical cumulants to their associated moments.
Who were some of the first to ...
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Who was the first person to describe turbulence in mathematical terms?
Here I found that:
Sixty years later, Russian mathematician Andrey Kolmogorov furthered
our mathematical understanding of turbulence when he proposed that
energy in a turbulent fluid at length $R$ ...
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History of complex analysis
Does anyone know of a good book on the history of imaginary numbers and complex analysis and its role in physics?
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Has there been debate between relationship of philosophy of mathematics and physics?
Did there exist and does there still exist a debate over which school of mathematical thought (i.e. formalism, logicism, intuitionism, etc.) had the most affinity or application for physics? In ...
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when did polynomial coefficient matching start for solving equations?
Coefficient matching feels rather natural when solving equations and checking dimensions, however in footnote 2 to "Two alternative derivations of Bridgman's theorem" (Berberan-Santos M N, Pogliani L, ...
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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?
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Were matrix theory and functional analysis well-known to physicists before the invention of matrix mechanics?
Were matrix theory and analysis well-known to physicists circa 1920-1925? Did physicists make extended use of this theory in that period? The question is related to the discussion in How did ...
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Who introduced the Green function method into quantum mechanics?
Its power is amazing. For a Hamiltonian, you define the Green function as
$$G = \frac{1}{\lambda E-H} .$$
Who first come up with this definition? What was the motivation?
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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 ...
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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 ...
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Nowadays I see a distinct "line" dividing people working in Mathematics and the Physical Sciences. Why?
The direction in which leading research is heading in these subjects (Math, Physics) is very much different and don't seem to be in tandem. Is this something that developed in more recent times? This ...
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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 ...
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Is Vedic Science true? [closed]
I somewhere read that ancient Indian science was so advanced even in 2000 B.C. (or may be even before this) that Indian scientist and mathematicians calculated the value of distance between sun and ...
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Origin of the term "operator spectrum" and its relation to spectrum in physics
I believe i have been looking in the Internet once for the origin of the term "spectrum" in functional analysis and saw that the term was proposed by someone (by Hilbert?) with no relation to physics, ...
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History of the delta potential barrier in Quantum Mechanics [closed]
I'm interested in finding something out about the history of the problem of the delta potential barrier in QM. Who was the first to propose this problem, and perhaps any particular motivation for it. ...
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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 ...
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What did Lagrange do with his quantity (the Lagrangian in classical mechanics)?
When I was learning classical mechanics, I was quite baffled by the Hamilton's principle, since it involves a quantity named after Lagrange. So, it seems that the principle was not discovered by ...
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How has the definition of a tensor today changed compared to its original definition?
On page 71 of The Absolute Differential Calculus by Levi-Civita, a very clear definition of a tensor is given in terms of how the coefficients of a multi-linear form transform, such that the product ...
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What is Heaviside's version of Maxwell's equations?
I have read, in many places, statements like this:
Heaviside was able to greatly simplify Maxwell's 20 equations in 20
variables, replacing them by four equations in two variables. Today we
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On the development of Newtonian Mechanics
Having borrowed from the library an English translation of Newton's Principia (Motte's), I read the begining sections, Part 1 and the Systems of the world, and noticed that Newton did physics ...
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Who was the first pointing out the $U(1)$-gauge theories common structure?
It is well-known that in each $U(1)$-gauge theory one can define, in analogy with electromagnetism, a 1-form connection and an associated 2-form of curvature on an appropriate (principal) bundle, ...
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Who named the fugacity, who coined the variable name and did it already relate to complex analysis?
In Riemanns monumental paper, he expresses a prime counting function as an inverse Mellin transform of the log of the function he analytically continued into the complex plane
$$\Pi(x) = \frac{1}{2\...
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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, ...
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Why isn't Feynman's path integral taught more widely and earlier in today's academic physics curricula?
Anyone who has studied Feynman's path integral will know that it makes quantum mechanics more like classical mechanics. A student who has learned about the Lagrangian will easily understand the ...
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How come we attribute the general theory of relativity to Einstein?
How come do we attribute general theory of relativity to Einstein when David Hilbert published first?
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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♦
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