All Questions
Tagged with non-locality field-theory
14
questions
2
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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
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0
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Non-local Euler-Lagrange equations and Noether theorems
Following up my Noether theorem issues: how can Euler-Lagrange and Noether theorems be formulated for non-local lagrangians?
Two examples from the literature:
Example 1. Let $L(\phi, F(\phi))=-\dfrac{...
- 6,611
1
vote
1
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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 ...
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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
2
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1
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Energy and canonical momentum conservation in non-local classical field theory
Assume we have the following Lagrangian field density where $x, x'$ both three dimensional real vectors are coordinates and $t$ represents time, field is given by $\phi$. Assume for the sake of ...
4
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Decomposition of rank-2 field and local interactions
Any rank-2 tensor can be decomposed in the following way
$$
\phi_{\mu\nu} =\phi_{\mu\nu}^{TT} + \partial_{(\mu}\xi_{\nu)} +\frac{1}{4}T_{\mu\nu}s+\frac{1}{4}L_{\mu\nu}(w-3s)
$$
where $\phi_{\mu\nu}^{...
- 2,197
4
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Why infinite order derivative in Lagrangian density implies non-local?
There is a homework in field theory. It says that negative order of derivative( such as $\frac{1}{\nabla^2}$), fraction order of derivative ( such as $\nabla^{2/3}$ ) and infinite order derivative in ...
user153663
0
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2
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290
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Why can we always define the Lagrangian Density this way?
Learning some field theory, and many authors just claim "it is nice to express the Lagrangian as an integral $L = \int\mathcal{L}\,\mathrm{d}^3x$." Now I understand when dealing with fields, the sum's ...
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13
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1
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Local versus non-local functionals
I'm new to field theory and I don't understand the difference between a "local" functional and a "non-local" functional. Explanations that I find resort to ambiguous definitions of locality and then ...
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Non-local structure of field theory
Can someone explain what is non-local structure of field theory? I know you cannot have $\phi(x) \phi(y)$ term in Lagrangian which indicates the non-locality. However, why I cannot have the non-local ...
- 411
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What is meant by a local Lagrangian density?
What is meant by a local Lagrangian density?
How will a non-local Lagrangian look like?
What is the problem that we do not consider such Lagrangian densities?
- 26.8k
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Definition of Local Function
Now a days I am studying Srednicki's QFT book. In its third chapter it is written that
Any local function of φ(x) is a Lorentz scalar, [...] .
Now my question is: What is a local function?
- 3,023
7
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answer
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How to tell local and non-local in QFT?
I'm taking QFT course in this term. I'm quite curious that in QFT by which part of the mathematical expression can we tell a quantity or a theory is local or non-local?
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Why are infinite order Lagrangians called 'non-local'?
And in what sense are they 'non-local'?
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