All Questions
11 questions
2
votes
0
answers
43
views
How are Fermionic and vector valued quantum field theories rigorously defined?
A scalar (spin 0) quantum field is rigorously defined as an operator valued distribution. By Wick rotating to Euclidean space we can view a quantum field theory as a measure over distributions. How ...
- 3,992
2
votes
0
answers
63
views
Why care that 1-particle states $a^{\dagger}_{\mathbf{p}}|0\rangle$ have $\langle\mathbf{p}|\mathbf{q}\rangle$ which are lorentz invariant?
When defining momentum eigenstates, Peskin+Schroeder (in Chapter 2) define
$$
|\mathbf{p}\rangle = \sqrt{2E_\mathbf{p}} a^{\dagger}_{\mathbf{p}}|0\rangle.
$$
The prefactor of these states $\sqrt{2E_\...
- 3,764
2
votes
0
answers
148
views
What is the definition of bound state in quantum field theory?
I asked a question a while a go what is a bound state and the question was closed because there is a similar question.
Now since best description we have to describe nature in quantum field theory
How ...
- 485
1
vote
1
answer
203
views
Requirement of Jordan-Wigner string in creation operator on Fock state
Our lecture notes described the action of the particle creation operator on a fermionic Fock state:
$$c_l^\dagger |n_1 n_2...\rangle = (-1)^{\sum_{j=1}^{l-1}n_j}|n_1 n_2 ... n_l+1 ...\rangle.$$
I am ...
- 2,654
0
votes
1
answer
120
views
Is this definition of the Fourier Transform of a quantum field operator rigorous?
Let there be a a quantum field operator $\hat\phi(t,\vec{x})$ which, because it acts (pointwise) on a separable Hilbert space, I expect I can write as
$$\hat\phi(t,\vec{x}) = \sum_n\sum_m\phi^n_m(t,\...
- 34
6
votes
1
answer
663
views
Definition of the $S$-Matrix in Schwartz QFT-Book: Why is $\langle f, t_f | i, t_i \rangle$ in the Schroedinger picture, and not Heisenberg-picture?
On page 51, (equation 5.1), Mathew Schwartz introduces the $S$-matrix as
\begin{align}
\langle f| S | i \rangle_{Heisenberg} = \langle f, \infty | i, -\infty \rangle_{Schrödinger}
\end{align}
Were $|i,...
- 6,980
15
votes
1
answer
5k
views
Difference between Fock space and Hilbert Space
I am beginner in QFT. I would like to know why there is a need of constructing Fock space for a $N$-particle system? Why can't we represent this many body system just as the tensor product of Hilbert ...
- 1,408
0
votes
0
answers
160
views
Off-shell vs half off-shell vs fully off-shell $T$-matrix
I know what are on-shell particles, but I want to know what are off-shell, and half off-shell, and fully off-shell states? and how we decide to consider one of these states in evaluating $T$-Matrix?
- 11
1
vote
1
answer
742
views
Tracing over a Fock space?
Suppose you have a bosonic Fock space with a vacuum $|0\rangle$. A particular state is labeled by the parameter $N \in \mathbb{Z}$. You can construct states like
$$
| n_{N} \rangle = \frac{ \left( \...
- 3,764
3
votes
1
answer
2k
views
Hermitian Adjoint of Spinor
Say we have a four component spinor $\psi$:
$$
\psi=\begin{pmatrix}\psi_L\\\psi_R\end{pmatrix}
$$
Is the Hermitian adjoint of this:
$$
\psi^\dagger =\begin{pmatrix}\psi_L^\dagger \psi_R^\dagger\end{...
user77345
21
votes
1
answer
5k
views
Unitary quantum field theory
What do physicists mean when they refer to a quantum field theory being unitary? Does this mean that all the symmetry groups of the theory act via unitary representations? I would appreciate if one ...
- 415