All Questions
20
questions
4
votes
0
answers
107
views
Canonical commutation relation in QFT
The canonical commutation relation in QFT with say one (non-free) scalar real field $\phi$ is
$$[\phi(\vec x,t),\dot \phi(\vec y,t)]=i\hbar\delta^{(3)}(\vec x-\vec y).$$
Is this equation satisfied by ...
- 2,226
0
votes
0
answers
64
views
Renormalization of the composite operator $\exp(\phi(x))$
I'd like to calculate $\langle\Omega|\exp(\phi(x))|\Omega\rangle$ for quartic scalar field theory (where $|\Omega\rangle$ is the interacting vacuum) and then renormalize to first order in the coupling ...
- 51
4
votes
1
answer
121
views
How do we know at the operator-level that the tadpole $\langle\Omega|\phi(x)|\Omega\rangle=0$ vanishes in scalar $\phi^4$ theory?
I'm a mathematician slowly trying to teach myself quantum field theory. To test my understanding, I'm trying to tell myself the whole story from a Lagrangian to scattering amplitudes for scalar $\phi^...
- 421
0
votes
1
answer
154
views
Peskin & Schroeder equation (7.2)
I found this completeness relation of momentum eigenstate $|\lambda_p\rangle$
Here $|\Omega\rangle$ is the vacuum, and $|\lambda_p\rangle$ represents the state with one particle labeled by $\lambda$ ...
- 1
2
votes
0
answers
307
views
2-loop correction to renormalized operator in $\phi^4$
I have a particular question with respect to renormalized operators of $\phi^4$ theory, namely the mass operator $\phi^2$ but at two-loop order. With respect to Peskin and Schroeder's text, chapter 12,...
- 704
1
vote
0
answers
43
views
Normal ordering in Sine-Gordon model [duplicate]
I am studying Bosonization from Giamarchi's book (Quantum Physics in 1D), in Appendix E while doing RG analysis at second order he says (Eq. E.18) that we can NOT expand cosine directly because field $...
- 366
3
votes
0
answers
94
views
Are non-covariant Schwinger terms related to the renormalization of composite operators?
In Section 5.5 of Duncan's The Conceptual Framework of Quantum Field Theory, he shows that theories that are not ultra-local has Schwinger terms:
$$
[\mathcal H_\text{int}(\mathbf x_1,t),\mathcal H_\...
- 213
5
votes
0
answers
251
views
QFT: Normal Ordering Interaction Hamiltonian Before Using Wick's Theorem
It has recently come to my attention, though reading the notes of a course on QFT that I've started, that there seems to be an "ambiguity" in, or at least two distinct ways of, calculating ...
- 737
1
vote
0
answers
99
views
In the derivation of LSZ formula, why do we need $\langle k| \phi(0)|0 \rangle =1$? (Srednicki's book)
In the section 5 of the book, it says
The LSZ formula is valid provided that the field obeys
$$\langle 0|\phi(x)|0\rangle=0, \langle k|\phi(x)|0\rangle=1.$$
The second one is needed to ensure one-...
- 995
1
vote
0
answers
114
views
Renormalization of non-local product of operators
In Unraveling hadron structure with generalized parton distributions by Belitsky and Radyushkin, appendix G, eq. (G.47) it is said that for renormalization of an on-local product of operators such as ...
- 1,597
6
votes
1
answer
558
views
Operator mixing in dimensional regularization of EFTs
When renormalizing "non-renormalizable" operators within an effective field theory (EFT) one usually has to introduce additional (higher-dimensional) operators to the Lagrangian which act as ...
- 765
2
votes
0
answers
219
views
Background field method for QED
I want to evaluate the 1-loop beta function for massless QED using background field method. This is my trying. First we separate the gauge field into
$$A_\mu(x)=\bar{A}_\mu(x)+\delta A_\mu(x)$$
\begin{...
- 1,863
4
votes
1
answer
1k
views
Interpretation of renormalisation of composite operators
The notion of renormalization is probably one of the most difficult to understand and bizarre properties of the QFT. As for the renormalisation of couplings it ...
- 4,883
0
votes
1
answer
152
views
Do vacuum bubbles exist in theories with normal ordered Hamiltonian? [duplicate]
When we calculate the Hamiltonian in the free theory, we notice that it contains an infinitely large term
\begin{align}
H
&= \int_V \mathrm{d }k^3 \frac{\omega_k}{(2\pi)^3 } a^\dagger(\vec ...
- 10.1k
5
votes
0
answers
929
views
Normal ordering in path integral of QFT
In QFT, we use normal ordering to eliminate infinity from hamiltonian. In path integral formulation of QFT though, since what we integrate over is "classical field configuration", instead of operators,...
- 327