# Questions tagged [coordinate-systems]

A set of numbers used to quantify location in space.

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### Is there an equivalent of Rindler coordinates for an object in centripetal motion?

Rindler coordinates are a parametrization of (a subset of) Minkowski space that are "natural" for an object experiencing constant acceleration - more specifically, an object experiencing constant ...
429 views

### On the embedding of the Schwarzschild metric in six dimensions

At every point of the 4-D space-time, it's metric, being a symmetric 2-tensor, has $\frac{D(D+1)}{2}=10$ independent components. From this we can subtract four degrees of freedom according to the four ...
272 views

### How the Poisson bracket transform when we change coordinates?

I'm studying the book Geometric Mechanics by Darryl D. Holm and there's one exercise in the book I'm not quite getting what has to be done. The same discussion the author makes in the book is made on ...
27 views

### Fixed coordinate frame as limit of rotating coordinate frame

I have a question about a fixed coordinate system as limit of rotating system. Consider for example a pendulum. The Lagrangian in the rotating frame is given by L(\mathbf{r}, \mathbf{\...
206 views

### Generating function of point transformation

I am asked to show that the generating function corresponding to a point transformation in Lagrangian mechanics can be taken as null. The point transformation consists of $$Q_i=Q_i(q,t),$$ and ...
221 views

### Does the spin1/2 rotation operator rotate spin in real space?

in quantum mechanics, the rotation operator for spin one half is $R_{\alpha}\left(\hat{\boldsymbol{n}}\right)=\mbox{exp}\left(-i\frac{\alpha}{2}\boldsymbol{\sigma}\cdot\hat{\boldsymbol{n}}\right)$. ...
162 views

### EM Field Quantization in Spherical polars

Is it possible to quantize the electromagnetic field in spherical polar coordinates instead of cartesian ones? Such that creation and annihilation operators correspond to harmonic oscillator modes ...
364 views

### Is classical electromagnetism conformally invariant? (and a bit of general covariance)

The contest is a flat $4d$ Minkowsky space. A conformal transformation is a diffeomorphism $\tilde x(x)$ such that the metric transforms as \begin{equation*} \tilde g_{\tilde \mu \tilde \nu} = w^2(x) ...
76 views

### General Relativity - Confusion between choosing basis (orthonormal & coordinate) and coordinate transformations

I am reading the book 'Gravity' by Hartle and presently I am at the section discussing orthonormal and coordinate bases. I am confused about a few points I had read previously and can't exactly ...
55 views

### Variations of tensors are tensors?

Recently I posted a question about variation of metric. I thought I understood it and talked with my friend about it. After that he said he's not convinced because he can't prove variation of metric ...
82 views

### How is time “homogeneous”?

My book$^1$ states: Let's consider a clock moving freely over a curve such as: $$\frac{dx^i}{dt}=\text{const} \tag{1.20}$$ We define the proper time $\tau$ as the ...
164 views

### Rindler Coordinates Derivation

In my GR lectures we've derived Rindler coordinates by first showing that the four velocity, which we defined as $$u^{\mu} = (\gamma c, 0, 0, \gamma u),$$ as a function of proper time can be written ...
109 views

### Using action-angle variables in non-periodic system

I'm a little confused by the discussion in the last section $\S 50$ of Landau and Lifshitz's (Classical) Mechanics (1960, first English ed.). Here, they consider finite motion of a system whose ...