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1

When it comes to nonsymmetric tensors, the order of indices matter, even between covariant and contravariant indices. Let us take the difference between $T^a{}_b$ and $T_b{}^a$, multiplied by the metric $g_{ab}$ to raise and lower indices: $$g_{ac}(T^a{}_b-T_b{}^a)=g_{ac}T^a{}_b-g_{ac}T_b{}^a=T_{cb}-T_{bc},$$ which is zero only if $T_{bc}=T_{cb}$, i.e., if ...


2

The stress-energy tensor is not symmetric by its definition. It is symmetric only if we require the system to be rotationally invariant and to have no intrinsic spin (all representations of the internal Lorentz algebra must vanish). In particular one can show that: $$ M^{\mu}_{\alpha\beta} = (x_{\alpha}T^{\mu}_{\beta} - x_{\beta}T^{\mu}_{\alpha}) + \textrm{...


6

W.u stands for Weisskopf unit: [ref 1, ref 2]. Despite being called a 'unit', it does not have a universal value; the value of the Weisskopf unit depends on the mass number of the nucleus in question and which transition the nucleus is undergoing ($E\lambda$ or $M\lambda$). The references contain expressions for the value of a Weisskopf unit in terms of $A$ ...


5

In nuclear Physics estimates can be made using the shell model of the nucleus of the gamma ray transition rates in excited nucleii and such estimates are named after Victor Weisskopf. A measured rate is compared with the Weisskopf estimate and the ratio is said to be in Weisskopf units (W.u.).


2

I would choose as notation conventions: $\Delta X$ for a constant increment, ie if $X_{n}-X_{n-1}=\Delta X$ for all n and with underscript otherwise: $\Delta X_n=X_{n}-X_{n-1}$ I prefer the increment to have the index of the value it produces (adding increment $\Delta X_n$ gives value $X_{n}$) but that's a matter of taste. It's not clear to me what the A ...


2

I would name the period at $n$ as $P_n$, and to the change in period as $\Delta P_n$. In such a case you have the rate of change of the period, that is the change in period per unit of time is $\Delta P/t_A=\left(\frac{1}{f_{n+1}}-\frac{1}{f_n}\right)/t_A$. However, to define the angular acceleration, $\alpha$, you do not need the period, the definition is ...


2

You typically cannot write subscripts or superscripts (easily) as comments in code, so I'll assume you are rather interested in writing this into a specification or some kind of documentation that does support such notation. When notation becomes cumbersome, here's what I'll generally do: 1) for discrete increment always use $(n), or (k)$ or the like ...



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