Tagged Questions
5
votes
2answers
208 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:
...
8
votes
2answers
243 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
$$\phi(x)\phi^\dagger(y)\ne0.$$
...
7
votes
1answer
144 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 ...
1
vote
2answers
131 views
Causality in a gedanken experiment on the hydrogen atom
Consider a gedanken(=thought) experiment where I am tracking the motion of the electron in a hydrogen atom with a time resolution of (say) $\Delta t = 10^{-20}$ seconds. Further assume (for ...
3
votes
2answers
125 views
Could we get rid of explicit fields derivatives in Quantum Field Theories?
For instance, if we choose the following scalar field Lagrangian, which is (I hope) Lorentz-invariant, where $l$ is a a length scale, and with a $(-1,1,1,1)$ metric:
$$ \mathfrak{L}(x) \sim ...
5
votes
2answers
287 views
The Lagrangian in Scalar Field Theory
This is perhaps a naive question, but why do we write down the Lagrangian
$$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2}m^2\phi^2$$
as the simplest ...
6
votes
3answers
240 views
Is the commutation of all possible operators sufficient to identify a spacelike interval?
It has been claimed (e.g. here) and apparently already been established, that the interval $x - y$ being (called) "spacelike" implies that $\bigl[\hat O (x),\, \hat O' (y)\bigr]=0$ for any two (not ...
4
votes
2answers
337 views
the causality and the anti-particles
How can I quantitatively and qualitatively understand the fact that there is a relevence between the existence of anti-particles and the causality?
