What is the meaning of manifest locality in Lagrangian formalism?

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In summary, "manifest locality" is a term used in Hamiltonian QFT to refer to the implementation of Lorentz invariance by requiring that spacelike field operators commute. In the Lagrangian formalism, it means that the Lagrangian consists of sums and products of fields at the same place and time, and the action is Lorentz covariant. This is achieved by writing the Lagrangian as the integral of a Lagrangian density, which has a finite number of derivatives. However, it is possible to have locality without Lorentz covariance.
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atyy
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The term "manifest locality" keeps being used, eg. in talks by Cachazo http://pirsa.org/10080013/ and Arkani-Hamed http://online.kitp.ucsb.edu/online/bblunch/arkanihamed/ .

In Hamiltonian QFT, "locality" means Lorentz invariance, and is implemented by requiring that spacelike field operators commute.

Is "manifest locality" in the Lagrangian formalism the same thing? If so, I guess it means that (i) the Lagrangian consists of sums and products of fields at the same place and time, and (ii) the action is Lorentz covariant? (Seems maybe not, since they always talk about "manifest locality" of the Feynman diagrams - what does that mean?)
 
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I'm pretty sure that it just means your point (i).
Manifest locality means that your lagrangian can be written as the integral of a lagrangian density, which is a sum of products of fields at the same space-time point. You also need to have only a finite number of derivatives.

You can have locality without Lorentz covariance, so I'm not sure about your Hamiltonian QFT statement.
 

1. What does manifest locality mean?

Manifest locality is a concept in physics that suggests that the outcome of an event can only be influenced by events or interactions that are in its immediate vicinity in space and time.

2. How is manifest locality different from non-locality?

Manifest locality and non-locality are two opposing ideas in physics. Non-locality suggests that events can be influenced by events that are not in its immediate vicinity, while manifest locality suggests the opposite - that events can only be influenced by nearby events.

3. Is manifest locality a proven concept?

Manifest locality is a widely accepted concept in physics, and has been supported by various experiments and theories such as the theory of relativity. However, it is still a subject of ongoing research and debate in the scientific community.

4. What are the implications of manifest locality?

The concept of manifest locality has important implications for our understanding of causality and the nature of reality. It suggests that the universe operates in a predictable and orderly manner, and that events are not influenced by mysterious or unknowable forces.

5. Does manifest locality apply to all levels of reality?

Manifest locality is a fundamental concept in physics and applies to all levels of reality, from the microscopic world of particles to the macroscopic world of everyday objects. However, it may not fully explain some phenomena such as quantum entanglement, which is still a subject of research and debate.

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