All Questions
46
questions
0
votes
1
answer
208
views
Time reversal operator and Dirac gamma matrices
How would you prove that $T^{-1}\gamma_\mu T=\gamma_\mu$? Being $T$ the time reversal operator defined as $T=\gamma_1\gamma_3 K$ with $K$ the complex conjugate operator and $\gamma$ the Dirac gamma ...
- 941
1
vote
1
answer
69
views
Feynman propagator from Hadamard propagator
The Feynman propagator is defined as
$$i G_F = \theta(t-t')G^+ + \theta(t'-t)G^-. \tag{1}$$
Using
$$G^{(1)} = G^+ + G^-,$$
$$G_R = -\theta(t-t')G, $$
$$G_A = \theta(t'-t)G, $$
$$\bar{G} = \frac{1}{2}(...
1
vote
0
answers
40
views
Plane wave expansion and time independence of Hamiltonian
I am confused by a statement made in "Lectures on Quantum Field Theory", 2nd edition by Ashok Das. The author is describing the interaction picture (IP) of QFT. In equation (6.52) he shows ...
- 513
4
votes
2
answers
612
views
Heisenberg's picture on complex field operators
I've been reading David Tong's lecture notes on QFT, and specifically on Lecture 2, he writes (section 2.6, eq. 2.8.3)
$$e^{i\hat{H}t}\,\hat{a}_{\vec{p}}\,e^{-i\hat{H}t}\,=\,e^{-iE_{\vec{p}}t}\,\hat{a}...
0
votes
1
answer
255
views
How are the creation and annihilation operators constructed for a single mode?
I'm reading Weinberg's QFT, and he defines the creation and annihilation operators as
\begin{align}
(a_k)_{n_1',n_2',\dots,n_1,n_2,\dots}&=\sqrt{n_k}\delta_{n_k',n_k-1}\prod_{j\ne k}\delta_{n_j',...
- 383
1
vote
1
answer
294
views
Verify that a field operator creates a particle
In example 4.1 of Lancaster and Blundell's "Quantum field theory for the gifted amateur", we verify that a field operator creates a particle as follow:
Let $|\Psi\rangle=\hat{\psi}^{\dagger}(...
- 53
3
votes
1
answer
286
views
How to calculate the 4th order perturbation energy of harmonic oscillator with diagram correctly?
I'm learning Feynman diagram. It is said that:
$$\Delta E=\frac {i} {T_{tot}}\sum connected\ vacuum\ diagram$$
in which $T_{tot}$ is the total time for perturbation acting.
I want to test the theorem ...
- 132
1
vote
1
answer
374
views
Deriving the Single Body Hamiltonian in QFT
I'm having some trouble with a few steps of the reasoning.
My first issue is why kinetic energy is diagonal in momentum representation, and why that means the Hamiltonian as a whole will be diagonal ...
- 383
-5
votes
2
answers
323
views
Does antimatter really exist and is it a given in the scientific community? [closed]
Antimatter erases ordinary matter when it meets, that is, it cannot be found on planet Earth. Can Karl Anderson’s experiment be disproved about his alleged discovery of the existence of antimatter? Is ...
- 95
0
votes
2
answers
176
views
Building Lagrangians for Classical Field Theory
I've been studying quantum mechanics and classical field theory for quite a while now. However, I still struggle with the idea of building scalars from vectors and tensors for the Lagrangian density.
...
- 1
0
votes
1
answer
529
views
Energy expectation values in quantum mechanics with the provided spatial wave function [closed]
Consider an electron is in a one-dimensional potential well of thickness $𝐿$, with infinitely high barriers on either side, and with the potential energy zero at the bottom of the well. The equation ...
- 121
2
votes
0
answers
81
views
Mode expansion using generalised Fourier transform
I'm looking at a generalised Lagrangian $L = \frac{1}{2} \left[\dot{\phi}² + \phi \mathcal{D} \phi\right]$, where $\mathcal{D}u_n = -\omega_n²u_n$, where $\left\{ u_n | n \in \mathbb{Z} \right\}$ span ...
4
votes
1
answer
263
views
QFT: strange interaction term?
I have QED plus a massive vector field $A'_{\mu}$. The Lagrangian is:
$$L = L_{QED} -\frac{1}{4} F'^{\mu \nu}F'_{\mu \nu} + \frac{a}{2} F^{\mu \nu}F'_{\mu \nu} -\frac{1}{2}M^2 A'_{\mu}A'^{\mu}+ \...
- 299
1
vote
1
answer
159
views
Perturbation expansion with path integrals
This is from Hugh Osborn's 'Advanced Quantum Field Theory' notes, Lent 2013, page 15.
I want to evaluate the expression
$$ Z = \exp\Big(\frac{1}{2} \frac{\partial}{\partial \underline{x}} . A^{-1} \...
- 1,075
1
vote
1
answer
239
views
Microcausality when quantizing the real scalar field with anticommutators
We know by the spin-statistics theorem that the real scalar field has to be canonically quantized by commutators. But if we try to use anticommutators, we would expand the field
$$\phi(x)=\int\frac{d^...
- 2,287