All Questions
Tagged with mathematical-physics mathematics
173
questions
1
vote
2
answers
126
views
Why does a singularity imply the need for a distribution?
I am following Section 11 of Prof. Etingof's MIT OpenCourseWare notes on "Geometry And Quantum Field Theory" in which he says:
...for $d = 1$, the Green's function $G(x)$ is continuous at $...
- 3,350
1
vote
0
answers
75
views
Use of mathematical structure on physics [closed]
I want resources for studying in detail the connection between the mathematical structures of physical theories and said physical theories.
For example, i know what a Hilbert space or a principal ...
1
vote
0
answers
81
views
Applying Kato-Rellich to the hydrogen atom model to prove stability of first kind [closed]
Trying to Understand the lower bound on the Schrodinger Operator of the Hydrogen atom. Using the kato-rellich theorem. My education has been in physics and i am slowly adding to my mathematics toolset....
1
vote
0
answers
96
views
Newtonian generalisation of binomial theorem for commuting operators
Suppose $\hat{A}$ and $\hat{B}$ are commuting operators on some Hilbert space, $[\hat{A},\hat{B}]=0$, chosen suitably to ensure operators $1/\hat{A}$, $1/\hat{B}$ and $\hat{A}/\hat{B}$ are suitably ...
1
vote
2
answers
97
views
How can motion along a spiral curve conclude in a finite time, but have infinite turns around the origin?
The first question of the book "200 puzzling problems in physics" has 3 point objects forming a triangle(equal sides), and they start moving towards one another - A always moves towards B, B ...
- 430
-8
votes
1
answer
147
views
Which summation should be chosen for a divergent series arising from the expression of relative mass in order to always preserve the same mass? [closed]
In all physical theories, the appearance of infinity is generally regarded as a sign that the theory is either incorrect or being applied outside its applicable domain, necessitating the search for ...
- 1
2
votes
1
answer
140
views
Schur's Lemma in Zee's Group Theory book for reducible representations
Main question
Schur's lemma says:
$$D(g) A = A D(g) \Rightarrow A = \lambda I\tag{1}$$
if $D$ is irreducible. How can I use this to show that if $D$ is reducible and if $SDS^{-1}$ is a direct sum of ...
3
votes
2
answers
312
views
Different parts of spectrum appearing in the spectral theorem in terms of generalized eigenvectors
Question: How to exactly relate both expansions quoted below: Can one be "transformed" into the other? What is the interplay between the various parts of the spectrum appearing?
In Ref. 1 it ...
- 8,094
1
vote
0
answers
118
views
Prandtl boundary layer equations for two-dimensional steady laminar flow of incompressible fluid over a semi-infinite plate are given by [closed]
Prandtl boundary layer equations for two-dimensional steady laminar flow of incompressible fluid over a semi-infinite plate are given by
jpg
- 11
2
votes
0
answers
141
views
Is Santilli's hadronic mechanics sound and useful? [closed]
I'm a mathematician. Some math papers and books related to mutation algebras (a kind of nonassociative algebras which are Lie-admissible), and even an entry in the Encyclopedia of Mathematics (Lie-...
- 121
5
votes
1
answer
120
views
Correlation Functions as Morphisms
In https://arxiv.org/abs/1911.07895, the authors consider a generalization of correlation functions to make sense of the $O(n)$ symmetry for $n \in \mathbb{R}$. As explained in Sec. 7, each field $\...
- 71
2
votes
0
answers
58
views
Simplification of a mathematical expression: (involving green's function)
We have an expression for the current in $z$-direction:
$$
I_z=\lim_{\eta \to 0}\frac{\hbar}{4\pi}\epsilon_{xyz}\int d\mathcal{E} f\left(\mathcal{E} \right) \mathcal{E}^2 \text{Tr}\left[G_0^Rv_xG_0^...
- 831
0
votes
1
answer
99
views
Sensor Array Position Calibration in Anisotropic Media
Problem.
I have a sensor array consisting of $n \gg 4$ receivers at unknown locations $\langle x_n, y_n, z_n\rangle$ embedded in an anisotropic medium whose index of refraction varies as a known ...
- 799
5
votes
3
answers
1k
views
Do continuous wavefunction form a Hilbert space?
In quantum mechanics we are told that
the wavefunctions live in Hilbert space.
the wavefunctions are continuous.
It recently came to my notice that in Mathematics, there is a theorem which says ...
user341411
0
votes
0
answers
46
views
$q$-dilogartihm function power series
I was reading the $q$-dilogarithm function (Faddev-Kashaev)
https://arxiv.org/abs/hep-th/9310070
How can I derive $$\frac{1}{\Psi(x)}=\sum_{n=0}^{\infty} \theta^{n} x^{n} /(\theta)_{n}$$
by using the ...
- 21