Questions tagged [mathematics]
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 The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics curriculum, such as, e.g., number theory, category theory, algebraic geometry, general topology, algebraic topology, etc.
1,387 questions
-8
votes
3
answers
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How can irrational numbers exist in the physical world? [closed]
How can a 1x1 square exist if the length from opposite corners is an irrational number?
Say you have a square with length 1, which makes the hypotenuse of the two right triangles comprising the ...
- 11
0
votes
0
answers
42
views
Non-simply connectedness of the Moebius group [migrated]
Assuming that a map of the form: $a\in SL(2,\mathbb{C}) \rightarrow m[a]$ with $m[a](z)=\frac{a_1z + a_2}{a_3z+a_4}$ is a group homomorphism, it is easy to show that this mapping is not bijective, ...
- 2,010
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votes
0
answers
24
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Origins of the Airy function [migrated]
The Airy functions $\text{Ai}(x)$ and $\text{Bi}(x)$, first studied by astronomer George Biddell Airy, are linearly independent solutions to the differential equation $$\frac{d^2 y}{dx^2} - xy = 0$$
I ...
4
votes
0
answers
68
views
Looking for a textbook which provides a good introduction to operator-valued distributions
I'm working on a quantum computing problem and have realized I need to develop a solid understanding of operator-valued distributions. So far the only textbooks I've seen in relation to the topic are ...
0
votes
0
answers
112
views
Vector transformations that preserve norms but changes inner products between different vectors
Unitary transformations conserve the inner product structure of a set of vectors, they only change the direction of the vectors, i.e. rotate them all in the same way. A unitary transformation $U$ can ...
- 418
1
vote
1
answer
128
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Partial Differential Equations (PDEs) in 2+1 Spacetime with Gradient of the Time Derivative
I have a set of 2 variables $f_1,f_2$, on the Domain of 1+1 spacetime $\{t,x\}$ and a set of PDEs with multiple terms of mixed 2nd-order partial-differentials.
$$\partial_t{f_1} = F_1(f_1,f_2, \...
- 81
2
votes
0
answers
93
views
How can I find the value of lambda from these two equations?
The Hilbert space is $\mathcal{H} = \mathcal{H}_q \otimes \mathbb{C}^2$.
A general spinor $\Phi \in \mathcal{H}$ is
$$
\Phi =
\begin{pmatrix}
\alpha \\
\beta
\end{pmatrix}
=
\begin{pmatrix}
\...
1
vote
1
answer
146
views
General relativity metric signature intuitive meaning
Premise I don't know the math about GR I know only what intuitively it means.
Often when talking about GR we take in consideration a metric signature (-,+,+,+) or (+,-,-,-) these metrics are said to ...
- 29
1
vote
1
answer
158
views
Does Heisenberg eq. of Motion stay invariant under commuting the Hamiltonian [closed]
If I have a general Heisenberg eq. of motion for an arbitary operator $\hat{A}$ and Hamiltonian $\hat{H} = a a a^\dagger a^\dagger$ that consists of fermionic/bosonic operators $a/a^\dagger$. It ...
- 310
0
votes
1
answer
172
views
Why does the non-rigorous maths produce verifiable results?
This may be due to confusion from my current undergrad level of understanding, but there are some derivations that I am shown that if a mathematician were to see them they would object about lack of ...
- 11
8
votes
1
answer
710
views
On the absolute convergence of Euclidean path integral
I am interested in knowing under which conditions Euclidean path integral absolutely converges.
I define an exponentially decaying function as
$$ f(x) = e^{-kg(x)},k>0$$
Where $kg(x)\geq C|x|^p+D$ ...
- 277
1
vote
0
answers
93
views
Details of the structure factor calculation
I’m interested in point processes, especially close to hyperuniformity.
The points are distributed within rectangle $-L/2 < x,y < L/2$ where $L$ is large enough ($L \sim 10^2$)
Number of points $...
- 173
0
votes
0
answers
94
views
Eigenvectors of Bosonic Bogoliubov transform
I have a Bosonic Hamiltonian of the form
\begin{align}
H = - \sum_{k} \Big[
& A (\, a_k^\dagger a_k
+ \, b_k^\dagger b_k )
+ \frac{B}{2} \left( a_k a_{-k} + a_k^\dagger a_{-k}^\dagger
+ b_k b_{-...
- 1
5
votes
1
answer
155
views
Is the Lindbladian evolution invertible?
In the context of the Lindblad equation and finte dimensional systems:
$$\partial_t \rho(t) = \mathcal{L}(t)\rho(t)$$
we can introduce a evolution superoperator $\mathcal{E}(t,t_0)$ that fulfills the ...
- 73
0
votes
1
answer
193
views
Doubt regarding method to find centre of mass of a cone
I was trying a certain method to find the centre of mass of the cone i.e. to prove that for a solid cone, the centre of mass is 1/4th the height from the base . This method involves cutting the cone ...
0
votes
2
answers
154
views
How are Scalar and Vector Product Different?
I have a doubt in my mind from a long time it is,
That How do we get to know that where to use the Scalar Product, and where to use Vector Product.
I have asked 3 of my collage teachers this question ...
2
votes
0
answers
115
views
Stokes' theorem in non-Riemannian geometry [duplicate]
Does Stokes's theorem in curved space, usually written in the context of GR:
$$\int_V \nabla_\mu A^\mu \sqrt{|g|}d^nx = \int_{\partial V}A^\mu n_\mu \sqrt{|\gamma|}d^{n-1}x$$
(Where $\nabla$ is the ...
- 661
1
vote
2
answers
151
views
Dimension of Lorentz Group (as a Lie Group/Manifold)
The restricted Lorentz subgroup, $SO^{+}(1,3)$ is a subgroup of Lorentz Group, which has a real dimension 6. What then is the manifold dimension of $SO(1,3)$, the full Lorentz Group?
0
votes
0
answers
39
views
Interchange of derivatives [duplicate]
Consider a function $f(x, t)$ where $x = x(t)$.
(i) In this case, can you interchange the partial derivatives of $f$ with $t$ and $x$. That is, can you write
$$
\dfrac{\partial^2 f}{\partial x \...
- 21
-4
votes
4
answers
212
views
Physical implications of the inexact value of circumference of a circle
Since $\pi$ is an irrational non-terminating non-repeating fraction therefore if it is multiplied by any real number that cannot be represented as a product of $\pi$, the result will be a non-...
2
votes
1
answer
138
views
Do I need to study mathematical logic to understand advanced physics? [closed]
I'm currently studying Calculus II and Ordinary Differential Equations, mainly to build the mathematical foundation needed for understanding advanced physics. However, I've never studied mathematical ...
- 21
0
votes
1
answer
126
views
Mass Moment of Inertia- Rectangular Plate [closed]
Is there some simplification that I'm missing to evaluate the mass moment of inertia of the plate( uniform density $\rho$) about the $z$ axis in the figure below:
As it stands now, I believe I have ...
- 131
0
votes
2
answers
190
views
Question about Change of variables
I often see in physics textbooks that variables are simply substituted in differential equation — for example, replacing $x$ with $−x$. I'm wondering whether this is mathematically valid. Generally, ...
- 17
5
votes
1
answer
223
views
How to give rigorous meaning to $\int :\phi^4:(x) dx$?
I asked a very similar question on MathOverflow a few months ago which was very helpful, but one detail about the construction remains unclear to me.
Consider a scalar field theory in 1+1 spacetime ...
- 4,852
0
votes
2
answers
156
views
The consistency of the calculation of connection on a manifold
Original question
As far as I know, there are two ways to calculate connection on a manifold, $\Gamma^{\mu}_{\nu\rho}$.The first one is the result of metric compatibility, $\nabla_{\rho}g_{\mu\nu}=0$, ...
- 333