All Questions
Tagged with locality lagrangian-formalism
32
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How does locality on space time manifold M put constraints on functions on configuration space of fields?
I am reading David Skinner's notes on AQFT. In Chapter 1 page 3, he mentioned that "purely from the point of view of functions on $C$, locality on $M$ is actually a very strong restriction", ...
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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-...
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Understanding this abstract Lagrangian of effective field theory
I'm learning Wilson's approach to renormalization and the Effective Field Theory. Typically, the theory is defined by a Lagrangian valid up to some scale $Λ$. I saw these two definitions for 4-...
- 1,783
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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 ...
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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?
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How constraint to first-order derivative in Lagrangian is a consequence of demand to get local theory?
In Physics From Symmetry Section 4.2 Restriction, the Author said that
It is sometimes claimed that the constraint to first-order derivatives is a consequence of our demand to get a local theory, but ...
- 11.9k
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On the computation of functionals in QFT
Using the Gaussian (path)-integral
$$
\int \mathcal{D}\eta e^{i\int_{t_i}^{t_f} dt \eta(t) O(t) \eta(t)} = N [\operatorname{det} O(t)]^{-1/2}
$$
my book claims that we can compute the following ...
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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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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
$$\int d^dx\,\phi(x)V(x-y)\phi(y).$$
...
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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 ...
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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
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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 ...
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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}^{...
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Infinite derivatives, Locality and Lagrangian
Providing the derivative of a single valued function $f(x)$ is like providing its value at two infinitesimally close points.
My question consists of two parts:
Can Higher derivatives be thought of as ...
- 1,182
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Under what circumstances is the functional derivative (of an action functional) an actual function?
In general, for a functional $F[\phi]$, the functional derivative is
$$\frac{\delta F[\phi]}{\delta \phi} [f(x)] = \lim_{\varepsilon \to 0} \frac{F[\phi + \varepsilon f ] - F[\phi]}{\varepsilon}$$
...
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