# Questions tagged [mathematical-physics]

DO NOT USE THIS TAG for elementary physical questions. This tag is intended for questions on modern mathematical methods used in quantum theory, general relativity, string theory, integrable system etc at an advanced undergraduate or graduate level.

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### When will two isomorphic Lie algebras have the same representation?

What feature(s) of isomorphic Lie algebras distinguish between their respective representations? When will two isomorphic Lie algebras have the same or different representations? My particular case ...
8k views

### What are defining & fundamental representations?

In physics terminology, one hears of the fundamental & defining representations of lie algebras or groups - are these the same as irreducible representations?
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### Is $1+2+3+4+\cdots=-\frac{1}{12}$ the unique ''value'' of this series?

I'm reading about zeta-function regularization in physics and I have some mathematical doubt. I understand that, since a sum of infinite terms is not well defined in a field, a series that is ...
2k views

### Why do zeta regularization and path integrals agree on functional determinants?

When looking up the functional determinant on Wikipedia, a reader is treated to two possible definitions of the functional determinant, and their agreement is trivial in finite dimensions. The first ...
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### Quantum mechanical books for mathematicians

I'm a mathematician. I have good knowledge of superior analysis, distribution theory, Hilbert spaces, Sobolev spaces, and applications to PDE theory. I also have good knowledge of differential ...
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### What makes the Cauchy principal value the "correct" value for a integral?

I haven't been able to find a good answer to this searching around online. There is a related old question here, but it never received much attention. Suppose I have some physical property that I ...
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### Why does the "separation of variables" method for DEs work? [duplicate]

Heyho, I am using the separation-of-variables method for quite a while now, but what was always bothering me a bit, is why is it possible to do those operations. I'll give a concrete example (source ... 651 views

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### Connection between the spectra of a family of matrices and a modelization of particles' scattering?

In the excellent book "Numerical Computing with MATLAB" by Cleve B. Moler (SIAM 2004), [Moler is the "father" of Matlab], one finds, on pages 298-299, the following graphical representation (fig. 10....
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### What exactly are pseudovectors and pseudoscalars? And where could I read about them?

I can't find good information on the internet. In my mathematical physics class the definition of a vector was given as: That object with magnitude and direction which doesn't change under ...
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### Why is the conjugate momentum $p(x,x')=\partial_2 L(x,x')$ an element of the cotangent space?

Imagine we have a particle described by $x \in M$, where $M$ is some manifold, then it is very intuitive I think that a velocity is an element of the tangent space at $x$, so $x' \in T_{x}M.$ Thus, by ...
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### What is a good reference for rigorous Electromagnetism and Electrodynamics?

Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for ...