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emanaly
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As I have read, the effective Lagrangian are non local sometimes, does that mean they break causlaity ? Are they non local because the heavy particles ( propagators) are integrated out?
See e.g. Schwartz, QFT and the Standard Model, Eqs. (22.2), (22.3), (22.6), (33.5).vanhees71 said:Do you have a reference? All effective relativistic models I know of are local in the usual sense (the Hamilton density depends only on one spacetime argument).
They are derived from local causal Lagrangians, so their physical effect should not break causality. Typically the effective theory of this kind contains an infinite number of terms with higher and higher derivatives. If you truncate the series by retaining only a finite number of terms, then you may get a violation of causality at high energies, but this may be irrelevant when you apply the effective theory at low energies only. In any case, if you do a resummation of the whole series, the acausality problems should go away.emanaly said:As I have read, the effective Lagrangian are non local sometimes, does that mean they break causlaity ?
Generally, an infinite series in higher and higher derivatives is an indication of possible non-locality. And even without infinite derivatives, an equation of motion with higher than second derivatives may lead to serious problems http://www.scholarpedia.org/article/Ostrogradsky's_theorem_on_Hamiltonian_instabilityvanhees71 said:And what this has to do with "non-locality"?
An effective Lagrangian is a mathematical tool used in quantum field theory to describe the behavior of a system at low energies. It is a simplified version of the full Lagrangian, which takes into account all possible interactions between particles, but is often too complex to be used in practical calculations.
An effective Lagrangian does not necessarily break causality. Causality is a fundamental principle in physics that states that an effect cannot occur before its cause. In the context of an effective Lagrangian, causality can be violated if the theory is not renormalizable, meaning that it cannot be used to make meaningful predictions.
Yes, an effective Lagrangian can lead to non-local effects. Non-locality refers to interactions between particles that are not localized in space and time. This can happen in theories that involve higher-order derivatives or non-local operators in the Lagrangian. However, these non-local effects are typically negligible at low energies and are only relevant in extreme conditions, such as in high energy particle collisions.
An effective Lagrangian is used in practical calculations by making approximations and truncations to the full Lagrangian. This allows for simpler calculations and predictions to be made for low-energy phenomena. However, the validity of these calculations depends on the specific context and assumptions made in the effective Lagrangian.
The limitations of using an effective Lagrangian include the fact that it is only applicable at low energies and does not account for all possible interactions between particles. It also relies on certain assumptions and approximations, which may not hold in all situations. Additionally, the effective Lagrangian may not be renormalizable, leading to potential issues with causality and non-locality.