All Questions
21
questions
-3
votes
2
answers
107
views
Multi-particle Hamiltonian for the free Klein-Gordon field
The text I am reading (Peskin and Schroeder) gives the Hamiltonian for the free Klein-Gordon field as:
$$H=\int {d^3 p\over (2\pi)^3}\; E_p\; a^{\dagger}_{\vec p}a_{\vec p}$$
This does not seem to be ...
- 4,399
2
votes
0
answers
81
views
Why Fock representation holds only in a free quantum field theory?
With a quantum system with $N$ degrees of freedom, all the representations are unitarily equivalent to Fock representation. However, if the number of degrees of freedom goes to infinity, there are ...
- 159
0
votes
1
answer
139
views
Energy of multiple particles in quantum field theory
Consider the free scalar theory with the zeroed Hamiltonian (i.e. such that the vacuum energy is zero). What is the energy of a multi-particle state $\phi^n|\Omega\rangle$ or (perhaps the more ...
- 1,221
1
vote
0
answers
31
views
Quasi-periodic motion of $N$-particle systems [closed]
My question is about the time evolution of multi-particle systems in QFT. There are such systems evolving a-periodically. I struggle with the treatment of them, always obtaining periodic or quasi-...
- 11
2
votes
1
answer
179
views
Visual explanation for $|\psi(-\infty)\rangle^{\text{in}}= \lim_{t\rightarrow -\infty} e^{iH_0 t} e^{-iHt}|\psi\rangle $
I'm reading section 7.4, Scattering and the $S$-matrix of Quantum Field Theory: Lectures of Sidney Coleman. It says
For a scattering of particles in potential, we have a very simple formula for the S-...
- 11.9k
0
votes
2
answers
104
views
What is the role of Hermitian Hamiltonians in relativistic QFT?
In single-particle quantum mechanics, the probability of finding the particle in all space is conserved due to the hermiticity of the Hamiltonians (and remains equal to unity for all times, if ...
- 11.8k
1
vote
1
answer
184
views
Yukawa Theory Peskin and Schroeder
On page 116 of Peskin and Schroeder, the Yukawa theory Hamiltonian is given by
$$H=H_{Dirac}+H_{Klein Gordan}+\int\,d^3x g\overline{\psi}\psi\phi $$
and we are considering the fermionic scattering ...
- 73
7
votes
3
answers
1k
views
What is meant in condensed matter physics by a “gap” and why is it so important?
I come from a HEP background and moved to condensed matter physics. I keep seeing the word “gap” being thrown around a lot: this system has a gap, this is a gapless system, the spectrum is gapped, ...
- 1,544
1
vote
0
answers
73
views
Simple $S$-matrix example in Coleman's lectures on QFT
In Coleman's QFT lectures, I'm confused by equation 7.57. To give the background, Coleman is trying to calculate the scattering matrix (S matrix) for a situation in which the Hamiltonian is given by
$$...
- 11
0
votes
1
answer
207
views
Two-site fermion system
I've to study a two-site fermion system with hamiltonian
$$H=\sum_{\sigma=\uparrow,\downarrow}[\epsilon_1 c^+_{1\sigma}c_{1\sigma}+\epsilon_2 c^+_{2\sigma}c_{2\sigma}+w(c^+_{1\sigma}c_{2\sigma}+c^+_{2\...
- 13
0
votes
1
answer
490
views
Hamiltonian positive definite and vacuum state
For the self-interating $\phi^4$ Lagrangian density
$$\mathcal L=\frac{1}{2}\partial_\mu\phi \partial^\mu\phi-\frac{m^2}{2}\phi^2-\frac{\lambda}{4!}\phi^4,$$
the corresponding Hamiltonian is
$$H=\int ...
- 4,235
1
vote
2
answers
583
views
Vacuum fluctuations of quantum scalar field
Consider a free scalar quantum field
$$ H = \int d^3 x \left( \, \Pi(x)^2+(\nabla\phi(x))^2 \right). $$
Introducing the creation and annihilation operators we find the "vacuum catastrophe"
$$...
- 1,037
3
votes
1
answer
169
views
Why are time derivatives of states in QFT equal to zero?
In equation 6-38 on page 176 of the book "Student Friendly QFT" by Robert D. Klauber it is said that the partial derivative w.r.t. time of a multi-particle state is equal to zero since we ...
- 631
0
votes
2
answers
387
views
Energy eigenstate of full Hamiltonian in interacting theory
Does the energy eigenstate of a full Hamiltonian in interacting theory exist? Can we write $H|\psi\rangle = E_n|\psi\rangle$ where $H= H_0+ H_{int}$ ? I wanted to understand whether the derivation of ...
- 369
0
votes
0
answers
62
views
Hamiltonians and Hilbert spaces in QFT
Suppose we start from a theory with a given $\mathcal{L}$ and correspondigly a Hamiltonian $\mathcal{H}$. Now a state of this $\mathcal{H}$ is (say) $|p,q,r>$. Now suppose that we do a set of ...
- 159