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### Mathematically-oriented Treatment of General Relativity

Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would Prove all theorems used. Use modern "mathematical notation" as ...
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### Is it foolish to distinguish between covariant and contravariant vectors?

A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a ...
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### Is there a symbol for “unitless”?

I'm making a table where columns are labelled with the property and the units it's measured in: Length (m) |||| Force (N) |||| Safety Factor (unitless) ||| etc... I'd like not to write "unitless" ...
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### What do term symbols with a half-integer “$L$” like $^3[3/2]_{1/2}$ mean?

Atomic term symbols are used to notate the angular momentum content of the electronic states of an atom, and are normally written down as $$^{2S+1}L_J$$ where the state has total spin $S$, spin ...
This Wikipedia page explains that for each of the four main gamma matrices $\gamma^{\mu}$, you can find the covariant matrices $\gamma_{\mu}$ with the equation $\gamma_{\mu} = \eta_{\mu\nu}\gamma^{\mu}... 1answer 93 views ### Staggered Indices ($\Lambda^\mu{}_\nu$vs.$\Lambda_\mu{}^\nu$) on Lorentz Transformations I have some open-ended questions on the use of staggered indices in writing Lorentz transformations and their inverses and transposes. What are the respective meanings of$\Lambda^\mu{}_\nu$as ... 5answers 454 views ### Why is the candela a base unit of the SI? The candela is defined as The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency$540\cdot10^{12}$hertz and that has a radiant ... 1answer 563 views ### Why is$L^2\$ norm of the gradient called kinetic energy?
I'm reading Lieb-Loss's book 'Analysis', chapter 7. The authors refer to the following integral: $$\tag{1} \lVert \nabla f\rVert_2^2=\int_{\Omega}\lvert \nabla f(x)\rvert^2\, d^nx$$ as the kinetic ...