# Tagged Questions

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### How to replace $T$-product with retarded commutator in LSZ formula?

I am reading Itzykson and Zuber's Quantum Field Theory book, and am unable to understand a step that is made on page 246: Here, they consider the elastic scattering of particle $A$ off particle $B$: ...
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### Commutation relations of the generators of the conformal group

My question is from P.98 of the book by Di Francesco on Conformal Field theory. He gives the six non-vanishing commutation relations between the elements $P_{\mu}, D, L_{\mu \nu}$ and $K_{\mu}$ ...
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### Finding the creation/annihilation operators

Using Minkowski signature $(+,-,-,-)$, for the Lagrangian density $${\cal L}=\partial_{\mu}\phi\partial^{\mu}\phi^{\dagger}-m^2\phi \phi^{\dagger}$$ of the complex scalar field, we have the field ...
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### Deriving commutation relations in second quantisation

I am trying to start from: \begin{align*} [\phi(x),\pi(x')] = i\hbar\delta(x-x') \\ [\phi(x),\phi(x')] = [\pi(x),\pi(x')]=0 \end{align*} to derive: \begin{align*} [a(k),a(k')^\dagger]=\delta_{kk'}\\ ...
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### Causality in QFT from vanishing commutator and the EPR paradox

The question relates to this post. As shown in Peskin and Schroeder's introduction to quantum field theory p. 28., $$[\phi(x),\phi(y)] = 0 \;\;\mathrm{if}\;\; (x-y)^2<0$$, which implies the ...
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### Does This Really “Prove” Spin-statistics Theorem?

In quantization of scalar field theory we impose commutation relation between the field operators by hand and similarly we impose anti-commutation relation between Dirac field operators by hand. As a ...
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### EQUAL TIME commutation relations

Why is equal time commutation relation used in canonical quantization of free fields?
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### Schroedinger field operators and their commutation relations

I've got several questions regarding the so called second quantization of the Schroedinger equation. My professor introduced the field operators for the Schroedinger field by simply stating them as ...
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### Observables still commute even if fields only anti-commute

In Peskin & Schroeder page 56, after introducing anti commutation relations for the fields instead of commutation relations (in order to fix the negative energy problem as well as to have proper ...
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### Quantizing the Dirac Field: which commutation relations are more fundamental?

When quantizing a system, what is the more (physically) fundamental commutation relation, $[q,p]$ or $[a,a^\dagger]$? (or are they completely equivalent?) For instance, in Peskin & Schroeder's ...
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### Fock state and corresponding relations for continuous momentum label

In Wikipedia I found following relation for Fock state: $$\hat {a}_i| \{n_j\}_j\rangle ~=~ \sqrt{n}_i| \{n_j-\delta_{ij}\}_j\rangle,$$ where $n_j$ refers to the number of $j$'th particles. This ...
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### Commutator problem

I am trying to calculate the following commutator $$[\mathcal{H}_0(r',t'),\psi(r,t)]_-$$ where $\mathcal{H}_0 = (\frac{1}{2m}\nabla^2 + e\mathbf{A}(r',t'))^2 + e\phi(r',t') - \mu$, and $\mu$ is the ...
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### Do commutation relations exist between superfields?

To quantize a theory, Klein gordon field for example, commutation relations are stablished. Or anticommuting ones in the fermionic case. If I have the Wess.Zumino model or the free model: ...
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Srednicki writes: We can make this a little fancier by defining the unitary spacetime translation operator $$T(a) \equiv \exp(-iP^\mu a_\mu/ \hbar)$$ Then we have $$T(a)^{-1} \phi(x) T(a) = ... 2answers 282 views ### Imposing anti-commutation relations on fermionic quasi-particles In many theories of CMT, we assume the nature of quasi-particles (without giving proper justifications). For example, we assume nature of quasi-particles to be fermionic in case of a interacting ... 0answers 123 views ### QFT basics for Klein-Gordon fields I am teaching myself QFT from Peskin for next years maths course and I have two questions: What is a c-number? Is it a complex number, and if so why does it mean, ... 1answer 255 views ### Klein-Gordon Canonical Commutation Relation (CCR) In the complex Klein-Gordon field we regard as dynamical variables the field \phi, the complex conjugate of the field \phi^*, and the momenta \pi, \pi^*. I can't see how should arise the ... 1answer 141 views ### State space of QFT, CCR and quantization, and the spectrum of a field operator? In the canonical quantization of fields, CCR is postulated as (for scalar boson field ):$$[\phi(x),\pi(y)]=i\delta(x-y)\qquad\qquad(1)$$in analogy with the ordinary QM commutation relation: ... 2answers 386 views ### Causality and Quantum Field Theory I have a problem with proof of causality in Peskin & Schroeder, An Introduction to QFT, page 28. To avoid confusion I use three vectors notation, rewriting the Eq. (2.53) for y=0 as follows: ... 2answers 794 views ### In QFT, why does a vanishing commutator ensure causality? In relativistic quantum field theories (QFT),$$[\phi(x),\phi^\dagger(y)] = 0 \;\;\mathrm{if}\;\; (x-y)^2<0$$On the other hand, even for space-like separation$$\phi(x)\phi^\dagger(y)\ne0.$$... 1answer 257 views ### Theories with non-vanishing commutators outside the lightcone I'm reading Weinberg's new book on Quantum Mechanics, and in Chapter 8.7 "Time-Dependent Perturbation Theory" he derives the usual Dyson series for the S matrix when the interaction Hamiltonian ... 1answer 138 views ### QED Commutation Relations Implications In Brian Hatfield's book on QFT and Strings there is the following quote: In particular$$ [A_i (x,t), E_j(y,t)] = -i \delta_{ij}\delta(x-y) $$implies that$$ [A_i(x,t),\nabla \cdot E(y,t)] = ...
I've seen it written many times that the commutation relation $[M^{I-},M^{J-}]=0$ is required for Lorentz invariance in the light cone gauge quantisation of the bosonic string. This follows ...