# Tag Info

### Partial derivatives vs Covariant derivatives in polar coordinates

Covariant derivatives take into account for both component and basis changes, thereby applicable for curved spaces - where partial derivatives only take component changes into account - is this ...

### Pre-requisites for V.I. Arnold's mathematical methods for classical mechanics

It is difficult to answer if the question is how to make intuitive the content if that book. The point is that, the goal of that book is just to make rigorous some important arguments and topics of ...

### Partial derivatives vs Covariant derivatives in polar coordinates

As OP correctly points out connections introduce a concept of differentiation of tensor fields or more in general of sections of vector bundles that takes into account how the bases of the fibers ...

### In general relativity, are light-like curves light-like geodesics?

Adding to the other answers, this is just to give an overall explanation. Case of 1+1 flat spacetime- We can first make the choice of co-ordinates and units such that geodesics are straight lines of ...
Accepted

### How does the wavefunction transform under an arbitrary change of variables?

TL;DR: As the overall phase of the wavefunction is not physical, OP's question has a non-unique answer that ultimately comes down to a choice of convention. Within a given class of situations we often ...
Accepted

### Classical systems with compact phase space

I could comment that a Hamiltonian system with compact symplectic phase space could appear after Lie-Poission reduction of a left (or right) invariant Hamiltonian defined on the cotangent bundle of a ...

### What does it mean for a quantum field theory to "live" on a manifold?

There are various layers to how a quantum field theory lives on a manifold. The simplest one is to note that a (classical) field is a mapping between a spacetime manifold and some target space like ...
The only general notion of total distance along a curve in general relativity is the proper time (or interval) \Delta \tau = \int \sqrt{-g_{\mu\nu} \frac{dx^\mu}{d\lambda} \frac{dx^\nu}{d\lambda}} d\...