Questions tagged [covariance]

Question 1

First of all, I am aware of existence of this question, as well as other relevant questions at MSE and PSE. However, all answers to those questions focus too much on why momentum can take a vector as ...

Question 2

When we consider no variations of the field configuration, we have: $$T^{\mu\nu}= \frac{\partial \mathcal{L}}{\partial(\partial_\mu \phi)}\partial^\nu\phi - g^{\mu\nu}\mathcal{L}.$$ How can one prove ...

Question 3

Let us start with some definitions. Given a (pseudo-)Riemannian manifold $(M,g)$ with a Levi-Civita connection $\nabla$, a smooth non-self-intersecting curve $\gamma : [0,1] \rightarrow M$ with $\...

Question 4

In many books on Physics, I read this: (i) Some quantities are represented in terms of numbers; they are called scalars. (ii) Some quantities are expressed in terms of numbers and directions; they are ...

Question 5

I am currently studying special relativity in depth for the first time, and have just encountered the concept of a Lorentz-invariant scalar field, $V(x,y,z,t)$. As I understand it, this is a scalar ...

Question 6

As I'm studying for my particle physics exam I have noticed that I do not know how to interpret the lorentz-invariant Fermi's Golden Rule. Or more precisely the transition rate $\Gamma_{fi}$. For ...

Question 7

I've committed myself to the analysis of electromagnetic fields seen by an electron in some accelerated frame of reference (circular acceleration through flat spacetime, in particular), but I am ...

Question 8

I have a confusion about how fields transform under active diffeomorphisms. Let me illustrate that confusion with the example of a particle sitting at point $p \in M$ on the manifold $M$. We can model ...

Question 9

The second covariant derivative of a scalar field $\phi$ in 4 dimensions, i.e. $\nabla_{\mu}\nabla_{\nu} \phi$, has 16 components. Due to the commutativity of covariant derivatives on a scalar field ...

Question 10

I'm taking at look at QED foundations, and started thinking about how it relates to Dirac's Equation. Dirac spinors are invariant under a global phase transformation $\psi(x)\mapsto e^{i\alpha}\psi(x)$...

Question 11

I am studying turbulence and I came across the concept of isotropic tensors, that is tensor that are invariant under rotations and translations. After googling for a while the thing I found is that, ...

Question 12

I am grappling with a consistency issue when analyzing the force on a charged particle from different inertial reference frames, strictly within the realm of classical (pre-relativistic) ...

Question 13

EDIT: The main question of this post is Why do we apply the Legendre transformation with a partial derivative $\partial_\mu$ by foliating spacetime rather than with the covariant derivative $\nabla_\...

Question 14

I am doing a calculation regarding transformation of a covariant derivative with respect to a scalar $\tau$: So, we will have: $$ A'^\lambda_{\quad ;\tau} = A'^\lambda_{\quad ,\tau} + \Gamma'^\...

Question 15

I'm currently trying to understand scalar field quantization on curved spacetimes and i'm stuck at the choice of commutation relations. The equal time commutator of the field and it's conjugate it's ...

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Questions tagged [covariance]

How come the fact that momentum is a covector does not contradict its coordinate change law?

How to prove that the $T^{\mu\nu}$ is a tensor? [closed]

Parallel vs. Fermi-Walker transport: do physicists restrict the meaning of parallel transport?

Scalars, Vectors, Tensors: are they all?

How does a Lorentz-invariant scalar field transform?

Interpretation of the lorentz-invarient transition rates (LI Fermi's Golden Rule)

Covariant derivative on a tetrad

A confusion over how fields transform under active diffeomorphism

When can the stress-energy tensor be written as $\nabla_{\mu}\nabla_{\nu} \phi$, and when can it not?

Quantum Electrodynamics from local gauge symmetry of Dirac Equation

Isotropic tensor function

Apparent Discrepancy in Lorentz Force on a Proton from Moving Reference Frames (Classical Electromagnetism)

What's the Legendre Transformation in Curved Spacetime?

Transformation of covariant derivative

Dirac delta on a Manifold

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