# Questions tagged [mathematical-physics]

DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com. Mathematical physics is the mathematically rigorous study of the foundations of physics, and the application of advanced mathematical methods to problems in physics. Examples include partial differential equations (PDEs), variational calculus, functional analysis, and potential theory.

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### 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 ...
55 views

### References of Deficiency indices theorem (von Neumann)

I am looking for proof or some interpretation around why the domain of the new extension $D(A_U)$ in the Theorem below is given by its specific formula. I have already searched in papers and here but ...
3k views

### Making a cut trough a center of mass, can the masses of the pieces be equal?

Let's say point $P$ is the center of mass of an irregularly shaped object. If I make a straight cut trough point $P$ and split the object in two, is it possible for the two pieces to have the same ...
78 views

### Book recommendation on Quantum Mechanics which is a bit mathematically aligned and gives good introduction to Hilbert Space for beginners [duplicate]

I am a 4th-year undergraduate student and I have fully read R. Shankar's book on Quantum Mechanics and Griffiths book Quantum Mechanics. I have also done a bit of the Application of QM on ...
50 views

### Recommended books for introduction to Quantum Mechanics for students who are mathematically aligned [duplicate]

I am a 4th-year undergraduate student and I have fully read R. Shankar's book on Quantum Mechanics and Griffiths book Quantum Mechanics. I have also done a bit of the Application of QM on ...
533 views

### Transition probability derivation: How to prove $\lim_{\alpha\rightarrow\infty} \frac{\sin^2\alpha x}{\alpha x^2} ~=~\pi\delta(x)$?

How to prove $$\lim_{\alpha\rightarrow\infty} \frac{\sin^2\alpha x}{\alpha x^2} ~=~\pi\delta(x)~?$$ I have encountered this limit while learning time dependent perturbation and transition ...
36 views

### Finding out the shape of the body from blackbody radiation spectrum

I have an idea similar to this, but I thought looking for an answer on this question might be a good start. Would it be possible to configure the geometry, i.e. shape of the body when we know the ...
101 views

### Why are Cauchy boundary conditions an over-specification of boundary conditions for solving Poissonās equation?

I was referred to Physics.SE by the following content published in Jacksonās Classical Electrodynamics: This rather surprising result [the fact that the potential within a charge-free volume is ...
188 views

### Feynman diagrams as topology

When we talk about Feynman diagrams we know they are tools to make calculations easier and more intuitive. Moreover, it's said that they are "topological" representations of the interactions. But, ...
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### Expand superspace function into component form

In 2D (1,1) superconformal field theory, the invariant "distance" between two points $Z_1=(z_1,\theta_1)$ and $Z_1=(z_1,\theta_1)$ in superspace is $$Z_{12}=z_1-z_2-\theta_1\theta_2.$$ My question ...
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### Mathematically rigorours formulation of the Bogoliubov transform for bosons

Let $\mathfrak{H}$ denote the Hilbert space describing the single-particle states and $|k\rangle$ denote an orthonormal basis of $\mathfrak{H}$. Let $c_k$ denote the corresponding annihilation ...
228 views

### Rigorous procedure of gluing together two spacetimes

There seems to exist a procedure of "gluing two spacetimes together". In particular I've seem this mentioned in the context of gravitational collapse. The examples I've seem were that of gluing ...
61 views

### Asympototic analysis for the following series sum

I am wondering is there one way to extract the asymptotic behavior of $x$ in the following expression near $x=0$? $$\sum_{n=1}^{\infty} n\log(1-\exp(-n x))$$ where $x$ is real.
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### Is there something similar to Noether's theorem for discrete symmetries?

Noether's theorem states that, for every continuous symmetry of an action, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any ...
74 views

### Relationship between boundary states and primary states of a Kazama-Suzuki model

In [1] and [2] the authors claim that the boundary states (not just the Ishibashi states) of a Kazama-Suzuki model are labelled in the same way as the primary states of the model, so that the boundary ...
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### Orthochronous indefinite orthogonal group $O^+(m, n)$ forms a group

My question is based on Qmechanic's answer here which proves that $O^+(m, 1)$ forms a group -- that if two Lorentz transformations have positive time-time co-ordinate, so does their product. The key ...
43 views

### Conformal weight of a coset model, and a specific case

Given a coset model $(G\times SO(2d))/H$, what is the expression for its conformal weight (in terms of its central charge or, alternatively, in terms of the highest weights of irreducible ...