All Questions
24
questions
1
vote
0
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90
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In the path integral formulation of QFT, how do we get quantized particles out of a field?
Every QFT textbook starts by basically postulating that we have discrete states connected by creation and annihilation operators. In Quantum Mechanics, we started from a differential equation and ...
- 1,262
4
votes
0
answers
106
views
How to interpret QFT fields (in relation with QM)? [duplicate]
In QM we deal with the Schrödinger equation:1
$$i\frac{\partial}{\partial t}\psi = H \psi$$
the wave function $\psi(x)$ is the main object of interest: it can be interpreted as a scalar field, in the ...
- 4,577
1
vote
0
answers
75
views
What does a quantized field in QFT do? [duplicate]
I'm studying for an exam called Introduction to QFT. One of the main topics in this class is the quantized free fields.
I can now find the fields that solve the Klein-Gordon equation and the Dirac ...
- 19
-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
1
answer
74
views
On creation annihilation operators of the free Klein-Gordon field [closed]
I want to calculate multiparticle states like $|\vec p,\vec p\rangle$ from $|0\rangle$. It seems that I would need to compute from things like: $a^{\dagger}_{\vec p}a^{\dagger}_{\vec p}|0\rangle$?
It ...
- 4,399
-2
votes
1
answer
144
views
Does the QFT Klein-Gordon equation describe the state of the field or the field operator?
In the canonical quantization of QFT we talk about:
states representing a field.
field operators.
The quantum Klein-Gordon equation is expressed in terms of the field φ. Is φ (in the equation) the ...
- 454
2
votes
0
answers
78
views
QFT Formalism, Relation between different POVs
A Klein-Gordon field on a Minkowski background can be written in the following expansion
$$ \hat{\phi}(x) = \int \frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_p}} (\hat{a}_p e^{-ip x} + \hat{a}^\dagger_p e^{...
- 136
2
votes
1
answer
174
views
Path integral in a boundary QFT
I'm trying to compute the following path integral
\begin{equation}
Z = \int\mathcal{D}\phi\exp\left(-\int_{\mathbb{R}^d_+}\frac{d^dx}{2}\phi(-\partial_\mu^2 + m^2)\phi \right) \propto \frac{1}{\sqrt{\...
- 401
0
votes
1
answer
168
views
Can we solve the Klein-Gordon equation in the Schrodinger picture?
In QFT, the Klein-Gordon equation is solved with the field operator $\hat \psi(x)$/$\hat \psi^\dagger(x)$ in the Heisenberg picture, and (as I understand it) gives the evolution of a single on-mass-...
- 2,604
7
votes
3
answers
1k
views
Euler-Lagrangian equation of motion of quantum fields in QFT
A canonical way of doing quantum field theory is by starting with some Lagrangian, for example, that of free scalar field
$$L=\frac{1}{2}\partial_{\mu}\phi \partial^{\mu}\phi-\frac{1}{2}m\phi^2$$
Then ...
- 442
4
votes
0
answers
667
views
Normalization of One-Particle States for Klein-Gordon Field Quantization
Peskin & Schroeder in their QFT textbook discusses how we may normalize one-particle states $|\textbf{p}\rangle$ for Klein-Gordon field quantization in pages 22-23. The excerpts are given below.
...
- 3,023
1
vote
0
answers
265
views
Finite norm for solutions of K.G. equation
Before getting into my actual question, let me give an example of a similar problem and its solutions. In non-relativistic wave function quantum mechanics, one usually assigns the Hilbert space of the ...
- 1,056
2
votes
1
answer
195
views
How to compute normalization of one-particle states for Klein-Gordon field quantization
I am reading through Dr. Schwartz's book on quantum field theory; in section 2.3.1, he writes the following relation: $$\langle\mathbf{p}|\mathbf{k}\rangle=2\omega_p(2\pi)^3\delta^3(\mathbf{p}-\mathbf{...
- 3,967
2
votes
1
answer
252
views
How can $⟨0|ϕ(x)|p⟩=e^{ip⋅x}$ be mathematically shown?
I was reading Peskin and Schroeder's quantum field theory and going through the book mathematically. Then I got stuck at one equation.
Consider a single, non-interacting real scalar field. The book ...
- 35
0
votes
0
answers
184
views
Transition from phi basis to occupation number in quantum field theory
We can construct the unitary transformation for change of basis from $x$ to number operator $n$ in harmonic oscillator by using $a|0\rangle=0$ and then multiply $\langle x|$ to the both side and ...
- 45