Basic question: Propagator of a scalar boson

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Discussion Overview

The discussion revolves around the concept of the propagator of a scalar boson, with participants exploring its definition and representation in theoretical physics. The scope includes theoretical aspects and references to existing literature.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about the propagator of a scalar boson, noting difficulty in finding information online.
  • Another participant suggests that scalar propagators are typically discussed in textbooks and provides a link to Wikipedia as a starting point.
  • A participant expresses frustration that the specific section on scalar propagators does not contain the information they seek.
  • A mathematical representation of the scalar propagator is provided, indicating it is expressed as \(\sim \frac{1}{k^2 - m^2}\) in momentum space.
  • Further discussion highlights that the section on scalar propagators includes a debate on the correct propagator from a causality perspective, suggesting that confusion may arise from the interpretation of propagators as Green's functions of the free theory.
  • A participant thanks another for their input, indicating engagement with the discussion.

Areas of Agreement / Disagreement

The discussion reflects a lack of consensus, with participants expressing differing views on the availability and clarity of information regarding scalar boson propagators.

Contextual Notes

There are indications of missing assumptions regarding the understanding of propagators and their representations, as well as potential confusion stemming from the interpretation of propagators in the context of Green's functions.

physciencer
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I have a question that is very basic and could not seem to find it online or I have not searched the right way. What is the propagator of a scalar boson? I found that of a fermion line and that of a vector boson but could not find that of a scalar boson.
 
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Scalar propagators are usually the first to be discussed in any textbook and it is usually taken as the first example because it is free from the finer details in fermion or vector boson propagators. Try http://en.wikipedia.org/wiki/Propagator to start with.
 
But the very section that contains scalar propagator does not practically have it written there.
 
The propagator is written:

\sim \frac{1}{k^2 - m^2}

In momentum space.
 
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physciencer said:
But the very section that contains scalar propagator does not practically have it written there.
It contains a long discussion about which propagator is the correct one from a causality point of view and it is written explicitly several times and in different representations. Perhaps the confusion stems from not being used to seeing propagators as what they really are, i.e., Green's functions of the free theory? This is all discussed under "relativistic propagators".
 
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