All Questions
Tagged with locality commutator
10
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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 ...
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Well-definedness of commutation relation in commuting local Hamiltonians
I'm reading the famous paper by Haah: Local stabilizer codes in three dimensions without string logical operators. In the last sentence of the introduction, he wrote:
A logical operator is a Pauli ...
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How do Lieb-Robinson Bounds talk about locality without the position operator?
So we know when one goes from QM to QFT Lieb Robinson bounds become micro causality. But micro causality is a statement on the commutators assuming they are space-like, time-like or light-like. ...
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Why Locality meant jointly observable?
Tobias Osborne's lecture around 20:00, he mentioned that the ideal of "Locality" could be expressed as such
If $x-y$ were space-like, then for all observable $A_{j,x}$ and $A_{k,y}$ were ...
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Particle picture in position space in quantum field theory
When I operate $a^{\dagger}_k$ on vacuum, $|0\rangle$, I get a particle created in momentum space with a 4-momentum equal to $(\omega_k, \vec{k})$ where $\omega_k=\sqrt{m^2+\vec{k}^2}$ here I'm only ...
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Is the vanishing commutator of observables outside the light cone only a necessary or also a sufficient condition for causality?
The equal-time commutator of observables in QFT has to vanish outside the light cone in order to ensure causality. Mathematically spoken, $[ \bar{\psi}(x)\Gamma_1\psi(x),\bar{\psi}(y)\Gamma_2\psi(y)]|...
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Does Microcausality follow from Lorentz Invariance?
In a Lorentz Invariant theory, does microcausality automatically hold?
In a free theory this is obvious. In an interacting theory I found some 'proof's in this paper: http://arxiv.org/abs/0709.1483
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Commutation relations in QFT and the principle of locality
My question is, given two space-time points $x^{\mu}$ and $y^{\mu}$, if the events that occur at these points are simultaneous, i.e. $x^{0}=y^{0}$, are the two events necessarily space-like separated? ...
- 3,063
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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, $[\hat{\phi}(x),\hat{\phi}(y)]~=~<...
user73685
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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 $V_I(...
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