All Questions
34
questions
0
votes
0
answers
31
views
Lorentz transformation of Creation and Annihilation operators for a real scalar field theory - MIT OCW QFT I Problem set 3 [closed]
I have been working through the MIT OCW's QFT lecture notes and problem sets, but I have come to realize that I have a fundamental misunderstanding of what is meant by how objects transform under ...
2
votes
1
answer
350
views
Poincaré group representation generator commutators
I am currently trying to understand how to derive the commutation relations for the generators of the Poincaré group. What I am reading instructs to start with:
$$U( \Lambda, a) = e^{\frac{i}{2} \...
- 329
3
votes
2
answers
647
views
Lorentz transformation of annihilation operator
In Srednicki's Quantum Field Theory, chapter 4, the author claims that the Lorentz transformation for given a scalar field $\varphi(x)$,
\begin{align}
U(\Lambda)^{-1} \varphi(x) U(\Lambda) = \varphi(\...
- 1,540
0
votes
0
answers
39
views
Proving D matrix of the Lorenz group furnish a representation using a transformation rule
Given a transformation rule:
$$U^\dagger(\Lambda)\hat\Psi(x)U(\Lambda)=\sum_{\hat\sigma=1}^4D_{\sigma\tilde\sigma}(\Lambda)\hat\Psi_{\tilde\sigma}(\Lambda^{-1} x)$$
when $\Lambda$ is the homogenous ...
0
votes
1
answer
281
views
Unitary infinitesimal transformation
It is not clear to me how to show following is true.
$$U(1+\delta w)= I +\frac{i}{2}\delta w_{uv}M^{uv}$$
I have tried Taylor expanding this term using relation of unitary matrix to exponential ...
3
votes
1
answer
137
views
I do not understand this bra-ket notation equality for BCFW recursion
Background:
When learning about BCFW recursion I am shown the deformation equation:
$$\hat{p_1}=p_1 -zq \hspace{5mm}; \hspace{5mm} \hat{p_n} = p_n +zq$$
This deformation represents a $\langle1n]$ ...
- 753
1
vote
1
answer
92
views
What is the meaning of a "permutation -invariant " MHV amplitude?
When reading my notes, I read that the difference between 4 points colour-ordered MHV amplitude and gravitational MHV amplitude is that the gravitational MHV amplitude is permutation-invariant, unlike ...
user256673
1
vote
1
answer
79
views
Why does the spin of a particle system influence the MHV amplitude?
I know that the MHV amplitude for a 3-particle system is the following (based on the colour-ordered Feynman rules):
$$\mathcal{M} = \frac{\langle 12\rangle ^3}{\langle 23 \rangle \langle 31 \rangle}$$...
- 753
4
votes
1
answer
426
views
How is the helicity fixed by little group scaling?
When reading about Scattering Amplitudes Notes, the text said the following:
Under little group scaling of each particle $i = 1, 2, . . . , n$ , the on-shell amplitude transforms homogeneously with ...
- 753
1
vote
1
answer
109
views
Different expression of $\Delta(x, m^2)=(2\pi)^{-3}\int e^{ip \cdot x}\theta(p^0)\delta(p^2+m^2)d^4p$
Let $$\Delta(x, m^2)=(2\pi)^{-3}\int e^{ip \cdot x}\theta(p^0)\delta(p^2+m^2)d^4p.$$
Here $\theta$ is the step function at $0$.
I would like to show that this is the same as
$$\Delta(x, m^2)=(2\pi)^...
- 1,669
0
votes
0
answers
130
views
Matrix elements of stress-energy tensor $\langle q | T^{\mu\nu} |q\rangle$ in QFT?
In many QFTs we can define a stress tensor $T^{\mu\nu}$. What is the matrix element of $T^{\mu\nu}$ in momentum eigenstates? For instance, consider
$$\langle q | T^{\mu\nu} |q\rangle$$
in QCD, ...
- 1,982
1
vote
0
answers
396
views
Lorentz transformation of a polarized photon
Lorentz transformations for relativistic particles can be easily understood by starting from an arbitrary reference vector $p^{\mu}_{R}=(1,0,0,1)$ (where $R$ stands for rest frame), and applying the ...
- 1,172