I was reading this article Scalar propagators on AdS Space by Harold Erbin, where the author attempts to find the classical solution of the massive scalar field in AdS space. To discard one of the solutions in Eqn. 2.13, author argues that the solution has to be regular everywhere and omits out the solution related to first order modified Bessels since they blow up in the center of the AdS space. My question might be naive, I was trying to understand why fields can not assume infinite values. Does it have to do anything with the bounded-ness and stability of the action?

  • $\begingroup$ Well, these fields do need to minimize the action in Eq. (1.1). $\endgroup$
    – J.G.
    Jun 25, 2022 at 20:43
  • $\begingroup$ That's a classical statement, no? In the path integral representation, is there any restriction? $\endgroup$
    – Anyon
    Aug 9, 2022 at 17:22
  • $\begingroup$ Link dead: "404 Error: the page you requested cannot be found." $\endgroup$
    – Qmechanic
    Mar 3 at 11:56


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