All Questions
Tagged with quantum-field-theory operators
715
questions
2
votes
0
answers
65
views
Calculating LSZ reduction for higher order in fields terms
Consider a theory with only a single massless scalar field $\phi(x)$ and a current $J^\mu(x)$ which can be polynomially expanded as fields and their derivatives and spacetime
\begin{align}
J^\mu(x) = ...
- 78
2
votes
1
answer
93
views
Equivalent definitions of Wick ordering
Let $\phi$ denote a field consisting of creation and annihilation operators. In physics, the Wick ordering of $\phi$, denoted $:\phi:$, is defined so that all creation are to the left of all ...
- 3,350
3
votes
0
answers
57
views
Is there any difference between Wick time order and Dyson time order?
Reading A Guide to Feynman Diagrams in the Many-Body Problem by R. Mattuck, I am getting the feeling that I missed something subtle related to time order. When deriving the Dyson series for the ...
- 5,578
3
votes
1
answer
129
views
What are single-, double- and multi-trace operators in AdS/CFT?
Can someone explain what are single-, double- and multi-trace operators are in AdS/CFT? I am a senior undergrad and only recently started studying AdS/CFT from TASI lectures and could not make much ...
- 904
0
votes
0
answers
44
views
Picture Number in String Vertex Operator
How can I know what is the Picture of a particular vertex operator?
For example in 8.3.15 in Polchinski's book Vol.1, the Vertex Operators for the Enhanced Gauge symmetry are given by
\begin{equation}...
- 11
1
vote
1
answer
54
views
Choice of spacetime foliation while quantising a conformal field theory
I was reading Rychkov's EPFL lectures on $D\geq 3$ CFT (along with these set of TASI lectures) and in chapter 3, he starts discussing radial quantisation and OPE (operator product expansion). I ...
- 904
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
2
votes
2
answers
124
views
Dictionary between interpretations of field operators
For now, let $\hat{\phi}(x)$ be a quantization of a classical, real scalar field $\phi(x)$.
My understanding is that, for fixed $x$, there are three ways to regard the operator $\hat{\phi}(x)$:
The ...
1
vote
1
answer
55
views
Total momentum operator of the Klein-Gordon field (before limit to the continuum)
I'm following K. Huang's QFT: From Operators to Path Integrals book. In the second chapter, he introduces the Klein-Gordon equation (KGE), and its scalar field $\phi(x)$, which satisfies this equation....
- 11
0
votes
2
answers
88
views
Ladder operators and creation & annihilation operators - different between $a$, $b$ and $c$ [closed]
Usually, the ladder operator denoted by $a$ and $a^\dagger$. In some case, people talk about the creation operator and denote it by $c$ and $c^\dagger$. Recently I see another notation, $b$ and $b^\...
- 23
2
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0
answers
113
views
Confused about square of time-reversal operator $T$
I am reading An Introduction to Quantum Field Theory by Peskin & Schroeder, and I am confused about what is the square $T^2$ of time reversal operator $T$.
My guess is that for $P^2$, $C^2$ and $T^...
- 613
1
vote
0
answers
43
views
Conjugate momenta in Radial Quantization
When we radially quantize a conformal field theory, is there at least formally a notion of a conjugate momentum $\Pi$ to the primary fields $O$ which would satisfy an equal radius commutation relation ...
- 482
2
votes
1
answer
88
views
Why reasonable observables are made of an even number of fermion fields?
On Michele Maggiore book on QFT (page 91) is stated, out of nothing, that "observables are made of an even number of fermionic operator" and similar sentences is in Peskin book (page 56).
Is ...
- 613
6
votes
4
answers
623
views
How can a QFT field act on particle states in Fock space?
Recently I asked a question that was considered a duplicate. However I felt that the related question didn't answer my doubts. After a bit of pondering I have realized the core of my discomfort with ...
- 4,577
0
votes
1
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67
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Is integral of energy-momentum tensor in QFT over a region $R$ self-adjoint?
Consider a quantum field theory in flat 1+1D spacetime for simplicity. Let $T_{\mu\nu}$ be the conserved symmetric stress tensor. One writes operators by integrating the tensor over the whole space, ...
- 184