All Questions
Tagged with renormalization operators
29
questions
4
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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
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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
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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
52
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Can a relevant operator's OPE with itself only include the identity and irrelevant operators?
I am interested in correlation functions in critical spin chains, and I'm trying to understand the consequences of conformal field theory for these correlation functions. I should warn that I do not ...
- 2,292
0
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46
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How to build up the creation/anihilation operators in Numerical Renormalization group?
Let's define a simple 1D linear tight-binding model (no matter that NRG is trivial here or even fails, this is just an simple example to illustrate my point)
$$H = \sum t_j \hat{c}^\dagger_{j}\hat{c}_{...
- 1,262
2
votes
0
answers
307
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2-loop correction to renormalized operator in $\phi^4$
I have a particular question with respect to renormalized operators of $\phi^4$ theory, namely the mass operator $\phi^2$ but at two-loop order. With respect to Peskin and Schroeder's text, chapter 12,...
- 704
1
vote
0
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43
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Normal ordering in Sine-Gordon model [duplicate]
I am studying Bosonization from Giamarchi's book (Quantum Physics in 1D), in Appendix E while doing RG analysis at second order he says (Eq. E.18) that we can NOT expand cosine directly because field $...
- 366
3
votes
1
answer
120
views
Renormalization of quark bilinears
I'm looking at the one-loop corrections to the amputated quark two-point functions ($\Gamma_i$) with insertions of quark bilinears (indexed by $i\in\{S,P,V,A,T\}$) with off-shell legs in Euclidean QCD....
- 71
3
votes
1
answer
76
views
Energy-momentum tensor normal ordering in Polchinski
In Volume 1 of Polchinski's String Theory book, the author works with energy--momentum tensor of CFTs till chapter 3 in a normal ordered mode, i.e. $T(z)= : \text{something}: (z)$. However, in ...
- 1,290
1
vote
0
answers
42
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When should UV regulators be removed?
I have been working in QFT for a few years now, and I cannot believe I've never come across this problem. When considering an effective field theory, the allowed operators mix under renormalization:
$$...
- 71
3
votes
0
answers
94
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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
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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