All Questions
Tagged with definition mathematics
38
questions
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How to state that a function has a certain andament in a limit? [migrated]
Assuming we have a function $f(r)$ that has the following limit
$$ \lim_{r\to0} f(r) = \frac{5}{3 r^2} \,.$$
What is the correct symbol to express that the denominator goes like $r^2$?
Is the ...
- 770
2
votes
2
answers
201
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Can the composition law of a group be defined only when considering a representation or realisation of the Group?
When we talk about, lets say, the Lorentz group, we define the action of the Lorentz transformation $\varLambda$ on
\begin{alignat}{1}
x^{\mu} & \in\mathbb{R}^{1,3},\\
x^{\mu} & \rightarrow x'^...
3
votes
2
answers
83
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In what sense is $\int (u \cdot \nabla) u \cdot u dx$ an energy flux?
Due to the nature of this question I have have cross-listed it on mathSE.
Let $u$ be either a solution to either the Euler equations or Navier-Stokes equations over a domain $\Omega$. In fluid ...
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0
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1
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107
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Mathematical meaning of a position eigenbra $\langle x_0 |$
Let $|x_0\rangle$ be an position eigenket. The physical picture I have for $|x_0\rangle$ is a particle located at $x_0$. Thus it should be represented by a delta function $\delta(x-x_0)$.
For $f\in L^...
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41
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How the partition be invariant if the correlator not invariant under global conformal transformation?
Under the global conformal transformation
$$\tau \rightarrow \frac{a\cdot \tau +b }{c\cdot \tau + d}, ad-bc=1, a,b,c,d\in\mathbb{Z} $$
the partition function is invariant
$$Z(\tau,\bar \tau)= Z( \frac{...
- 3,256
1
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How was holomorphic function (local) restricted to special conformal group (global) in 2d conformal transformation? [closed]
An example could be found on this pdf file and the discussion was the 2d conformal transformation. Usually, the conformal transformation was derived locally such that the local conformal ...
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1
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1
answer
175
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Jackson's Electrodynamics: Green's function prefactor
In Ch. 6 of Jackson's Classical Electrodynamics 3rd ed., the Helmholtz equation Green's function is written as satisfying the following inhomogeneous equation (Eqn. 6.36):
$$ (\nabla^2 + k^2)G(\mathbf{...
- 101
0
votes
1
answer
78
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Definition of vectors [closed]
I know that we call a quantity a vector if it has magnitude and direction and follows vector laws of addition(the triangle law and parallelogram law). But why only it should only follow addition laws ...
- 41
2
votes
4
answers
1k
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What exactly does it mean for a unit to be dimensionless?
For instance, why are moles and decibels considered dimensionless, but kg and meters aren't? Or, in other words, what exactly is a "dimension" in this context? Is just about the system of ...
- 2,327
25
votes
6
answers
5k
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What is the connection between a mathematician and physicist's definition of a tensor?
I study mathematics but I have a deep interest in physics as well. I have taken a course in smooth manifolds where a tensor is defined as an alternating multilinear function. Recently I have learned ...
- 3,350
0
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1
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43
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The difference between operator condition, differential condition and algebraic condition?
It is well known that the gauge potential $A_\mu=(\phi,-\vec{A})$ has gauge symmetry and one could impose Lorenz and Coulomb gauge simultaneously to it to eliminate redundant degrees of freedom. In ...
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2
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1
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61
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Notation: What's the group $G_1\backslash G_2$ compare to $G_2/G_3$?
Quote Clifford Johnson D-brane page 108
This group includes the T-dualities on all of the $d$
circles, linear redefinitions of the axes, and discrete shifts ofthe $B$-field. The full space of torus ...
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1
vote
1
answer
90
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Are physical dualities based on mathematical dualities? [closed]
I understand what a physical duality is and what a mathematical duality is. The function to obtain the dual of an theory/object is an invertible function in both physics and math. I wonder if it is as ...
- 113
0
votes
2
answers
717
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Fourier Transformation in 4D space
In mathematical physics course, I see Fourier transformation of function f(t) as
$$\bar{f}(\omega) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f(t)\ e^{-i\omega t} dt.$$
I wanted to know the ...
- 69
3
votes
1
answer
290
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Mathematical definition of annihilation and creation operators
I am self-studying quantum field theory and have gotten to creation and annihilation operators, respectively denoted $A^\dagger$ and $A$. Conceptually I understand what these objects are, at least on ...
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