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.
1,385 questions
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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
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0
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42
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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, ...
- 2,058
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Convention when saying "the plot of A vs B" [closed]
I am a high school student and as I've seen so far when referring to plots of two quantities A vs B, it is usually that the quantity A is on the $y$-axis and the quantity B is on the $x$-axis. Take ...
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Formal definition of $d$-dimensional integral for complex dimension $d\in\mathbb{C}$
This question concerns the definition of dimensional regularization in quantum field theory, specifically as presented in this Wilson paper (see free version here).
This operation must fulfill three ...
- 808
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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 ...
10
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2
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Irrational numbers from finitely many resistors
Given a rational number $p/q$ and a handful of unit resistors (resistors with resistance $1$ $\Omega$ each), we can naively put $q$ resistors in parallel to get an effective resistance of $1/q$, and ...
- 1,124
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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
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Prugovecki QM in Hilbert Space pg. 49 Why is $\mathsf{M}_E$ closed (in $\mathscr{H}_b^{(1)}$)?
More of a PDE, functional analysis question related to QM from Prugovecki's book, QM in Hilbert Space. pg. 49:
On line -2 pg. 49, it is stated, "Each one of the closed subspaces $\mathsf{M}_E$...&...
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1
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1
answer
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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.
$$\partial_t{f_1} = F_1(f_1,f_2, \...
- 81
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1
answer
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Validity of assuming the integral of a vanishing integrand over an infinitely large surface is equal to zero
In Griffiths' Electrodynamics, Chapter 8, Griffiths claims that if we compute the surface integral of a vector field that vanishes at infinity over an infinitely large surface, the result will be zero....
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How can I find the value of lambda from these two equations?
The Hilbert space is $\mathcal{H} = \mathcal{H}_q \otimes \mathbb{C}^2$.
A general spinor $\Phi \in \mathcal{H}$ is
$$
\Phi =
\begin{pmatrix}
\alpha \\
\beta
\end{pmatrix}
=
\begin{pmatrix}
\...
0
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3
answers
256
views
What does $\frac{\partial \mathscr{L}}{\partial A^\mu}$ mean?
Suppose we define a variation as
$$
\delta F \equiv F(x,a)-F(x,a=0)=\frac{\partial F}{\partial a}\bigg|_{a=0} a +\mathcal{O}(a^2),
$$
where $a$ is some continuous paramter and $x$ is a spacetime ...
- 345
1
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1
answer
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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 ...
- 39
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0
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Equation of motion, 4th order
I have the following term in my Lagrangian:
$$
L=V(r)((\Delta \phi )^2-5(\partial_i\partial_j \phi)^2).
$$
I am kind of confused about computing the equation of motion, I would say (is there a ...
- 515
1
vote
1
answer
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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 ...
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