# Tagged Questions

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2answers
781 views

### Matrix Representations of Quantum States and Hamiltonians

I am a high school student trying to teach himself quantum mechanics just for fun, and I am a bit confused. As a fun test of my programming/quantum mechanics skill, I decided to create a computer ...
2answers
185 views

### If the S-matrix has symmetry group G, must the fields be representations of G?

If the fields in QFT are representations of the Poincare group (or generally speaking the symmetry group of interest), then I think it's a straight forward consequence that the matrix elements and ...
2answers
135 views

### Element of area in 4-dimensional space-time

How would you proof that $$\mathrm {Tr} (\mathbf{S\cdot \bar S })=0$$ where $\mathbf S$ is an element of area delimited for the 4-vectors $\mathbf u$ and $\mathbf v$ given by S^{\alpha \beta}\equiv ...
4answers
384 views

### Is the momentum operator well-defined in the basis of standing waves?

Suppose I want to describe an arbitrary state of a quantum particle in a box of side $L$. The relevant eigenmodes are those of standing waves, namely  \left<x|n\right>=\sqrt{\frac{2}{L}}\cdot ...
1answer
128 views

### Creation and Annialation Operators and Kinetic Energy Matrix Elements

I'd like to write equations for $c_{ij}(t)$, With a hamiltonian of the form $$H=\sum_{kn}a^{\dagger}_k t_{kn}a_n + \frac{1}{2}\sum_{klmn}a^{\dagger}_k a^{\dagger}_l v_{klmn}a_m a_n$$ with $t_{kn}$ ...
2answers
139 views

### How to express continuous values as a matrix

Usually a quantity of a matrix is defined as the eigenvalues of the matrix. If so, how can anyone express continuous values, as in Schrodinger picture, into a matrix?
3answers
125 views

### Vector space of $\mathbb{C}^4$ and its basis, the Pauli matrices

How do I write an arbitrary $2\times 2$ matrix as a linear combination of the three Pauli Matrices and the $2\times 2$ unit matrix? Any example for the same might help ?
2answers
176 views

### Path integral on matrix model

I was looking at a 0-dimensional matrix model, where the variables are $N\cdot N$ Hermitean matrices. It had a gauge symmetry, e.g. $U(N)$. And in the path integral, the Faddeev-Popov trick was used. ...
0answers
75 views

### Decay Amplitudes Notation

This question is mostly about how to interpret notation used in Particle Physics. I am given that at lowest order the rate of $b\rightarrow s\gamma$ is proportional to \$\langle B_p|b^\dagger ...
1answer
35 views

### Diagonal matrix in k-space

I'm having some trouble with an integration I hope you guys can help me with. I have that: ${{\mathbf{v}}_{i}}\left( \mathbf{k} \right)=\frac{\hbar {{\mathbf{k}}_{i}}}{m}$ and ...
0answers
92 views

### Matrix element squared for up + antidown -> photon + W boson? [closed]

I am in trouble… I am a master student (first year) in theoretical particle physics and I have been working for several months on the calculation of the total cross-section at leading order for the ...
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