All Questions
Tagged with locality field-theory
36
questions
2
votes
1
answer
89
views
How to interpret Poisson bracket of fields in terms of causality?
In quantum field theory, the fact that space-like separated observables commute, i.e. $[\hat {\phi (x)}, \hat{\phi(y)}]=0$, is taken as the test for causality. The equivalent statement for classical ...
- 519
2
votes
1
answer
78
views
Are field theories where free energy density depends on 2nd-order derivative non-local?
It is accepted that infinite order of derivatives in field theory lead to non-local effects while finite number of them local.
reference within physics stack exchange
Let’s take a lattice with next-...
- 134
16
votes
6
answers
3k
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Are field theories necessary to make accurate predictions or do they just make calculations easier?
For example, if we really wanted to, could we, at least in principle, model electromagnetism just considering interactions between charged particles without using the EM field? That is, is it ...
- 2,327
1
vote
0
answers
53
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Ostrogradsky instability and fractional derivatives
Are fractional derivatives (or even more generally differentegrals) also under the scope of the Ostrogradsky instability theorem?
- 6,611
2
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1
answer
87
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Locality and local gauge invariance
I was reading this question on the Physics Stack Exchange, and I'm still not quite sure how I can understand the relationship between locality and local gauge invariance using this example. Consider ...
- 1,783
0
votes
2
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57
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Must all field theories depend on the spatial derivate of the fields?
For instance, if I have encountered
\begin{equation}
\label{eqq2}
\frac{\partial \mathcal{L}}{\partial (\partial_i \phi)} = 0
\end{equation}
This tells us that $\mathcal{L}$ cannot depend on $\...
- 1,031
3
votes
2
answers
692
views
Why does one work with the Lagrangian density in field theory?
Why is it necessary to introduce the Lagrangian density (integral of the Lagrangian over volume) when describing the dynamics of fields? Is there a specific reason for that or just for convenience?
- 363
4
votes
5
answers
114
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Is Electrostatics Local?
We can solve uniquely for the electrostatic potential $\phi(x)$ of some given charge distribution if we set the boundary condition that $$\lim_{|x|\to\infty}\phi(x) = 0$$ (or whatever boundary ...
- 1,647
1
vote
1
answer
259
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Non-analytic functions and non-local Lagrangians
Infinite sums of increasingly higher-order derivatives, when present in Lagrangians, are typically taken as a sign of nonlocality. This is supposed to rule out fractional, negative and exotic (for ...
- 519
3
votes
0
answers
64
views
Lattice differentiation and Locality
Assume we define the locality of a theory in the following way:
Assume we have a theory of real scalars, so this theory is non local if the action has terms like
$$\int d^dx\,\phi(x)V(x-y)\phi(y).$$
...
- 1,369
4
votes
1
answer
563
views
What is a "quasi-local" charge?
Could someone please tell me what is a quasi-local charge? For instance, why are Brown-York charges called quasi-local?
- 700
1
vote
1
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428
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QFTs without Lagrangian
I have been reading other questions in this site, but I have not found answers to all my questions about theories without Lagrangians.
What do we mean exactly when we say that they do not have a ...
- 431
4
votes
2
answers
165
views
What is locality?
In QFT and statistical mechanics, one is usually interested in studying integrals of the form:
$$Z(\phi) =\int d\mu_{C}(\phi')e^{-V(\phi+\phi')}$$
where $\mu_{C}$ is Gaussian measure with mean zero ...
- 585
3
votes
2
answers
232
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Could there exist a "locality" field? [closed]
What I mean is (and I'm a layperson on the subject), can there exist a field that pervades the universe - like the Higgs field - that interacts with particles to give them "distance" or "space" ...
- 41
2
votes
1
answer
200
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Why does the Lagrangian Density have to be a polynomial of the field?
In a lecture, a professor appeared to have said that the Lagrangian can only contain terms that have powers of $\phi$ and a term with $\partial_\mu \partial^\mu \phi$ . I imagine this would make any ...
- 305