All Questions
Tagged with quantum-field-theory operators
715
questions
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65
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Parity operator action on quantized Dirac field
I am stuck on equation 3.124 on p.65 in Peskin and Schroeder quantum field theory book.
There they are claiming that:
$$P\psi(x)P=\displaystyle\int\frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_{\bf p}}}\...
- 413
2
votes
0
answers
37
views
Double Discontinuity In CFT
In the paper Analyticity in Spin in Conformal Theories Simon defines the double discontinuity as the commutator squared in (2.15):
$$\text{dDisc}\mathcal{G}\left(\rho,\overline{\rho}\right)=\left\...
- 194
1
vote
3
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154
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What does the state $a_k a_l^\dagger|0\rangle$ represent?
Consider the action of the operator $a_k a_l^\dagger$ on the vacuum state $$|{\rm vac}\rangle\equiv |0,0,\ldots,0\rangle,$$ the action of $a_l^\dagger$ surely creates one particle in the $l$th state. ...
- 11.8k
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1
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106
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Does every field correspond to a particle?
I know that particles in QFT are just excitations of its corresponding field. But is it possible to have a field which cannot generate particles?
If yes, what terms must be added to the Lagrangian so ...
- 1,611
2
votes
1
answer
130
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Non-perturbative matrix element calculation
Following Peskin & Schroeder's Sec.7's notation, I would like to compute the matrix element
$$
\left<\lambda_\vec{p}| \phi(x)^2 |\Omega\right>\tag{1}
$$
where $\langle\lambda_{\vec{p}}|$ is ...
- 78
0
votes
0
answers
53
views
What is the allowed operator in a global/ local theory?
While I'm reading Hong Liu's notes, it says:
Now we have introduced two theories:
(a)$$\mathcal{L}=-\frac{1}{g^2}Tr[\frac{1}{2}(\partial \Phi )^2+\frac{1}{4}\Phi^4]$$
(b)$$\mathcal{L}=\frac{1}{g^2_{...
- 368
1
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0
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75
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What does a quantized field in QFT do? [duplicate]
I'm studying for an exam called Introduction to QFT. One of the main topics in this class is the quantized free fields.
I can now find the fields that solve the Klein-Gordon equation and the Dirac ...
- 19
0
votes
0
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52
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On discretization in QFT and second quantization
Some time ago i saw in a QFT lecture series by the IFT UNESP that in QFT we need to discretize space by dividing it into tiny boxes of an arbitrary Volume $ \Delta V $ and then define canonical ...
- 309
0
votes
0
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64
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Naive approach to a path-ordered functional
For analytic functions, we know that
$$ \langle q'|F(\hat{q})|q\rangle = F[q]\,\langle q'|q\rangle\tag{1} $$
Now, suppose that $q$ depends on $\tau$, promote $F[\hat{q}]$ to a functional, and ...
- 266
0
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0
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35
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Lorentz invariance (LI) of time ordering operation
At Srednicki after eq. (4.10), we have a discussion about that the time ordering operation. Have to be frame inv. I.e it has to be LI.
He wrote that for timelike separation we don't have to worry ...
1
vote
1
answer
94
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Why does we quantize fields $\phi(t,x)$ and not $\phi$?
In classical mechanics, the action of a theory is determined by its Lagrangian:
$$S(q) := \int L(q(t),\dot{q}(t),t)dt $$
In the following, let us assume that $L$ does not depend explicitly on time. ...
- 1,131
-3
votes
2
answers
107
views
Multi-particle Hamiltonian for the free Klein-Gordon field
The text I am reading (Peskin and Schroeder) gives the Hamiltonian for the free Klein-Gordon field as:
$$H=\int {d^3 p\over (2\pi)^3}\; E_p\; a^{\dagger}_{\vec p}a_{\vec p}$$
This does not seem to be ...
- 4,399
-2
votes
1
answer
74
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On creation annihilation operators of the free Klein-Gordon field [closed]
I want to calculate multiparticle states like $|\vec p,\vec p\rangle$ from $|0\rangle$. It seems that I would need to compute from things like: $a^{\dagger}_{\vec p}a^{\dagger}_{\vec p}|0\rangle$?
It ...
- 4,399
0
votes
0
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63
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Questions about computing the commutator of the Lorentz generator
I am computing the commutator of the Lorentz generators, from the Eqn (3.16) to Eqn (3.17) in Peskin & Schroeder.
$$
\begin{aligned}
J^{\mu\nu} &= i(x^\mu \partial^\nu - x^\nu \partial^\mu ) &...
- 41
2
votes
2
answers
132
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Commutator of conjugate momentum and field for complex field QFT
In Peskin & Schroeder's Introduction to QFT problem 2.2a), we are asked to find the equations of motion of the complex scalar field starting from the Lagrangian density. I want to show that:
$$i\...
- 538