Question

My question seems simple but I am having trouble finding resources/papers on the topic (I am guessing my wording is poor). I am trying to find material (and perhaps a physical proof even) that in a relativistic field theory, the highest order corrections to the theory dictate causality.

Getting specific, I know there is a paper by Maldacena (can't find it at the moment) stating that the κ3(Riem)3⊂L
correction of the Einstein-Hilbert action gives acausal physics. However, if you include the κ4(Riem)4
term, then the theory becomes causal again and everything is fine (I know this after talking to a few friends/colleagues and we argued about it).

But what I would like to fine is someone discussing the physics of a general field theory that does not need to include (but can include) gravitational terms.

If we want to discuss how to define causality for such a general case, then perhaps starting with, "the input can not exceed the output," maybe an ok place to start (I really am just shooting in the dark here since my knowledge of what it means to be causal is slim to none).

Answer 1

High-order corrections in relativistic field theories, such as those considered by Maldacena in the context of gravity, are also important in general field theories where they help to maintain causality, the principle that causes precede effects and nothing travels faster than light.

These corrections ensure that the theory remains consistent with causality at all levels of perturbation.

Step-by-step explanation:

The question you've raised pertains to high-order corrections in relativistic field theories and their impact on causality, particularly outside of gravitational contexts.

The paper by Maldacena you're referring to likely discusses the implications of higher curvature corrections to the Einstein-Hilbert action, which illustrates how additional terms in a field theory can resolve acausal behaviors that emerge at certain correction levels.

For a general field theory, causality often refers to the principle that the cause precedes its effect, and no signal or information can propagate faster than the speed of light, ensuring that the input does not exceed the output in terms of causality.

Understanding how these higher-order corrections enforce causality may require a look into the principles of quantum field theory (QFT) and the properties of the effective action, which incorporates all quantum corrections.

Since you are interested in general concepts outside of gravitational terms, you might want to explore resources on QFT, renormalization group flows, and the role of local counterterms. These are concepts that allow field theories to maintain causality and unitarity at high energies or correction orders.