# Tagged Questions

The tag has no wiki summary.

46 views

### The Riemannian Curvature in Deformations

Is there a direct correlation between the Riemannian Curvature tensor and the deformation gradient tensor in continuum mechanics?
790 views

### Understanding the difference between co- and contra-variant vectors

I am looking at the 4-vector treatment of special relativity, but I have had no formal training in Tensor algebra and thus am having difficulty understanding some of the concepts which appear. One ...
36 views

### Covariant derivative commutator on spinors [on hold]

What is this object $[\nabla_{\mu},\nabla_{\nu}]\epsilon$ in terms of curvature tensor $R_{\mu\nu}$? Where $\nabla_{\mu}$ is the covariant derivative on a four sphere and $\epsilon$ is spinor. PS: I ...
25 views

86 views

### Problem understanding Lorentz invariance [duplicate]

So they usually started with "...This is obviously Lorentz invariant, because of the 4-vector character of the quantity,..., (and after a two page long derivation) another quantity is also obviously ...
63 views

### Representations of Lorentz algebra

It is well known that the Lorentz algebra can be written as two $SU(2)$ algebras. By defining $$N_i=\frac{1}{2}(J_i+iK_i), \qquad N^{\dagger}_i=\frac{1}{2}(J_i-iK_i)$$ we have ...
235 views

### Dimension of vector resulting from tensorial product

I'm quoting what I found in a book about quantum computation: Individual state spaces of $n$ particles combine quantum mechanically through the tensor product. If $X$ and $Y$ are vectors, then ...
37 views

### Decomposition of a tensor under transformations

To illustrate my question I'll take an example from theory of relativity: An arbitrary 4-tensor $A^{ik}$ changes under a general coordinate transformation: $$A'^{ik} = C^{i}_mC^{k}_n A^{mn}$$ ...
43 views

### The significance of the pressure term within the momentum-energy tensor [duplicate]

EDIT: this question is based around my notion regarding the possible role of potential energy in the momentum energy tensor T$_{\mu\nu}$, The answer below resolves the question and I have deleted ...
373 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 ...
71 views

### How to act an operator on a two-particle spin state?

I'm doing an assignment for my quantum class at the moment and I'm having trouble figuring out how to act a Spin operator on a two-particle state - specifically in finding the eigenvalues - I've spent ...
75 views

### electrical conductivity and resistivity tensor

By definition of the conductivity tensor $\hat{\sigma}$ and the resistivity tensor $\hat{\rho}$, we have \begin{equation*} \begin{split} & j_{\alpha}=\sigma_{\alpha \beta}E_{\beta} \\ & ...
224 views

### Stress Force - Understanding Cauchy Stress Tensor

I've been trying to understand the derivation for the Cauchy Momentum Equation for so long now, and there is one part that every derivation glides over very quickly with practically no explanation ...
96 views

### Making sense out of covariance and contravariance

I just read about co- and contravariant vectors and I am not sure that I got it right: If we imagine that we have a n-dimensional manifold $M$ then a tangent space is spanned by the vectors ...
77 views

### Density Matrix Renormalization Group (DMRG) Simulation of a String-Net Model

In the following paper, Dr. Xiao Gang-Wen et. al. introduce the idea that string-net condensed states can be represented in terms of tensor product states: http://arxiv.org/pdf/0809.2821.pdf The ...
96 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 ...
150 views

### Why does the second Weyl scalar describe electromagnetic radiation?

I've been reading about the null tetrad, the Weyl tensor, and the Newman-Penrose identities, and so I found out about the Weyl scalars. While the zeroth, first, third, and fourth scalars describe ...
51 views

### What does a left-right arrow in a tensor formula mean?

I need help with some some notation I've not seen before. Is using the left-right arrow in this formula $$[P^μ,M^{ρσ}]=i\hbar(g^{\mu\sigma}P^\rho-(\rho\leftrightarrow\sigma))$$ equivalent to writing ...
I've resolved a relative displacement tensor into a strain tensor and a rotation tensor, where the strain tensor is:  \varepsilon_{i,j} =\begin{pmatrix} 0.2 & 0 & 0 \\ 0 & 0.8 ...