# Questions tagged [notation]

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### Ket notation in alternate forms

I have been told that I can describe a system by its wave number states: $$|k_1\rangle|k_2\rangle,$$ and that the following is true: $$|k_1\rangle|k_2\rangle=|k_1+k_2\rangle|k_1-k_2\rangle,$$ I am ...
27 views

### Ricci Tensor component, index lowering doubt [closed]

$v^j$$v^k$$[R(e_i,e_j)]e_k$.$e_i$ gives $v^j$$v^k$$R^l$$_k$$_i$$_j e_l.e_i Then v^j$$v^k$$R^l$$_k$$_i$$_j$ $g$$_l$$_i$ Finally, $v^j$$v^k$$R$$_i$$_k$$_i$$_j$ Which upon summation on i gives $v^j$...
45 views

### Proving the Existence of Locally Inertial Coordinates

This question is regarding the proof of the existence of locally inertial coordinates, outlined in Sean Carroll's Spacetime and Geometry book (Chapter 2, page 74). In particular, I believe that extra ...
31 views

### Operators in QM acting on kets [duplicate]

I know that operators in quantum mechanics act on states (kets, assumed to be normalized), and return another state. So, an operator such as $\hat{p}$ when acted on a ket $|\psi\rangle$ will give me ...
60 views

### Chern-Simons, General relativity, and notations

Consider the Einstein-Maxwell-dilaton theory with an additional Chern-Simons term as in this paper \begin{equation} S = \int d^4 \sqrt{-g} \left[ \frac{1}{2} R - \frac{1}{2} (\partial\varphi)^2 - \...
114 views

### Calculus of variations: meaning of infinitesimal variation $\delta$ and action minimum

So I am studying classical mechanics through the MIT 8.223 notes, and encountered the derivation of the Euler Lagrange equation. There is a part I don't quite understand, which resides in the actual ...
57 views

### Squared vector field terms $\mathbf{E}^2$ and $\mathbf{H}^2$?

Consider the simple case of electromagnetic irradiation of a homogeneous isotropic dielectric, neglecting the dispersion of the refractive index. Assuming a transparent medium, the spatial density of ...
69 views

### Is notational compactness in tensors (compared to linear algebra) relevant? [migrated]

In this post you can read: A matrix is a special case of a second rank tensor with 1 index up and 1 index down. It takes vectors to vectors, (by contracting the upper index of the vector with the ...
74 views

### “$10^{\mathrm{th}}$” Index skipped in M-theory

Why is it that in M-theory, the 11-dimensional vectors are labelled with indices $0 \dots 9,11$. For example, the spatial momentum components are $p_{1}, \dots, p_{9}, p_{11}$. Why is the $10^{th}$ ...
55 views

67 views

### Contravariant rank-2 tensor transformation in index notation

I'm slightly confused about the placement of upper and lower indices for the transformation of a rank-2 contravariant tensor. A contravariant rank-2 tensor transforms as $$M' = \Lambda M \Lambda^{T}$$....