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3 Μαρ 2018 · $T^\mu{}_\nu$ and $T_\nu{}^\mu$ are both maps from a vector and a dual vector to $\mathbb R$, true. But they aren't necessarily the same map as each other. Mathematically, you can see this by considering the difference explicitly:
- Help to understand $\\mu\\nu$ notation and differential forms
My biggest question is what is the difference between...
- Help to understand $\\mu\\nu$ notation and differential forms
9 Νοε 2022 · My biggest question is what is the difference between superscripts and subscripts and is there any significance to when $\nu$ is used as opposed to $\mu$ or vice versa? How do I best understand things like $\partial^{\mu}\phi\partial_{\mu}\phi$ in the free part of the QFT Lagrangian?
29 Μαρ 2022 · In the case of the metric tensor we would write $g_{\mu\nu}$ where $\mu$ and $\nu$ are the row and column number in the matrix. It's traditional to use Greek letters as sub/superscripts when dealing with tensors, and this is why you so often see such sub/superscripts in equations related to GR.
Mathematical symbols use a roman, serif font ( ½, +, √, cos) — except when they are applied to calculations with units. Units are written with a roman, sans-serif font ( m, N, ℃) as are mathematical operations with numbers and units ( 7 kg × 10 m/s ÷ 3 s = 23.3 N ).
12 Σεπ 2022 · When the taut string is at rest at the equilibrium position, the tension in the string FT is constant. Consider a small element of the string with a mass equal to Δm = μΔx. The mass element is at rest and in equilibrium and the force of tension of either side of the mass element is equal and opposite.
If we know that $N(t)$ molecules have got by until $t$, then $N(t + dt)$, the number which get by until $t + dt$, is less than $N(t)$ by the number that have collisions in $dt$. The number that collide in $dt$ we have written above in terms of the mean time $\tau$ as $dN = N(t)\,dt/\tau$.
epsilon_0 mu_0 gets replaced by epsilon mu – which is equivalent to replacing c by c/n where n is the index of refraction. In most transparent materials mu is approximately mu_0 but epsilon is significantly larger than epsilon_0, and hence usually n = sqrt(1+chi_e).
