# Tagged Questions

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4answers
900 views

### General relativity in terms of differential forms

Is there a formulation of general relativity in terms of differential forms instead of tensors with indexs and subindexs? If yes, where can I find it and what are the advantages of each method? If ...
1answer
198 views

### What does $|x⟩|0⟩$ actually mean in bra-ket notation?

Consider the following quote from Wikipedia's page on Shor's algorithm: Initialize the registers to $Q^{-1/2} \sum_{x=0}^{Q-1} \left|x\right\rangle \left|0\right\rangle$ where $x$ runs ...
2answers
89 views

### Can I simply reverse the indices in a contraction?

Suppose I have something like $$\left( \nabla_\mu \nabla_\beta - \nabla_\beta \nabla_\mu \right) V^\mu = R_{\nu \beta} V^\nu$$ Can since all the terms involving $\mu$ on the left and $\nu$ on the ...
2answers
266 views

### Correct tetrad index notation

There seems to be some different conventions on the indexes of the tetrad. I am wondering which is the standard, which is correct, and which is an abuse of notation. In Sean Carroll's notes and in ...
1answer
186 views

### Vector fields and tensors in E&M

I'm confused by a very basic property of electric fields. The electric field is a vector field. Vectors are tensors. Wikipedia has the following statement in the article about the electromagnetic ...
1answer
92 views

### Tensor notation

I'm trying to understand the Maxwell Stress tensor notation. I'm given that each element in the tensor is given by ...
1answer
128 views

### What is the difference between $\nabla _{\sigma}$ and $\nabla^{\sigma}$?

What is the difference between: $\nabla _{\sigma}$ and $\nabla^{\sigma}$? I've been told that the first is the covariant derivative, however I'm just starting a course on spacetime geometry and ...
1answer
280 views

### Sign crazyness on the stress energy tensor?

I would like to know on what depends the sign of the stress energy tensor in the following formula : $T_{\mu\nu}=\pm(\rho c^2+P)u_{\mu}u_{\nu} \pm P g_{\mu\nu}$ In my case the metric is equal to ...
2answers
197 views

3answers
97 views

### Rotation in the x-t plane

I am currently studying special relativity using tensors. My lecture notes (which happen to be publicly accessible, see top of page 99) say that the standard configuration can be viewed as a rotation ...
1answer
95 views

### In continuum mechanics, why is the stress vector $T=\sigma\cdot n$ not a covector?

In continuum mechanics, the stress vector (see Cauchy stress tensor) $T=\sigma\cdot n$ is the surface density of a force. Forces are covectors, since they map a displacement vector to a scalar energy. ...
2answers
219 views

### Sign of the totally anti-symmetric Levi-Civita tensor $\varepsilon^{\mu_1 \ldots}$ when raising indices

I am confused with the sign we get when we want to raise or lower all indices of the totally anti-symmetric tensor of any rank. Take the metric to be mostly plus ($-+\ldots+$). Then is it ...
2answers
396 views

### The definition of transpose of Lorentz transformation (as a mixed tensor)

In the appendix of the textbook of Group Theory in Physics by Wu-Ki Tung, the transpose of a matrix is defined as the following, Eq.(I.3-1) $${{A^T}_i}^j~=~{A^j}_i.$$ This is extremely confusing for ...
3answers
150 views

### Linear independence of the Covariant Derivative

What's the easiest way to show that the covariant derivative $\nabla U^{\mu}$ is linearly independent to $U^{\mu}$, which is a vector? I mean I'm assuming they are since I'm proving the second ...
2answers
155 views

1answer
735 views

### Derivation of the volume element (which uses the metric tensor)?

I have often seen $\sqrt{-g}$ in integrals, especially actions, where $g=\mathrm{det}(g_{\mu \nu})$. Does anyone know of a derivation that shows that this is indeed the volume element which must be ...
1answer
254 views

### How quantum field transforms in case of some particular spin

Except when a particle is spin-0, field of all particles transforms when frame of reference is changed, and this defines what spin is. The question is, specifically how does the quantum field ...
1answer
283 views

### Symmetrical Spinors and Symmetrical Tensors

In Quantum Electrodynamics by Landau and Lifshiz there is the following: The correspondence between the spinor $\zeta^{\alpha \dot{\beta}}$ and the 4-vector is a particular case of a general ...
1answer
101 views

### On the Lorentz Group representation [closed]

I am going through the notes on QFT by Srednicki (which is certainly a worth reading on the subject, and can be found online, see http://web.physics.ucsb.edu/~mark/qft.html). When describing ...
1answer
141 views

0answers
531 views

### The connection between classical and quantum spins

I have two questions, which are connected with each other. The first question. In a classical relativistic (SRT) case for one particle can be defined (in a reason of "antisymmetric" nature of ...