PolyDet

Renormalised one-loop fluctuation determinant around a polygonal bounce (false-vacuum decay) — a Wolfram Language paclet and companion to FindBounce. It consumes a polygonal bounce (segment masses + matching radii) and returns ln det_ren via the transfer-matrix multipole sum with optimal-truncation acceleration and MS-bar renormalisation (D = 3, 4). It is the next factor after FindBounce's action, Gamma ~ (...) (det S'')^{-1/2} e^{-S}.

Sectors: single scalar, coupled multi-scalar (mass matrices, zero-mode removal, nucleation-rate assembly), Dirac fermion (Yukawa), and Abelian gauge boson (U(1) Higgs, ghost collapse).

The paclet source lives in PolyDet/; Build.wls packs it into a distributable .paclet archive.

Install

Download the built PolyDet-<version>.paclet from the latest release — it bundles the indexed Documentation Center pages (guide, reference pages, tutorials) — then:

PacletInstall["/path/to/PolyDet-0.4.0.paclet", ForceVersionInstall -> True]
Needs["PolyDet`"]

Then restart the front end (or quit and relaunch Mathematica) so the Documentation Center rebuilds its list of installed paclets — the PolyDet guide and ?PolyDet* >> links appear after the restart.

For development from a source checkout — gives the kernel functions but not the Documentation Center pages (the source tree has no search index; that is generated only by the .paclet build):

PacletDirectoryLoad["/path/to/PolyDet-checkout"];  (* the repo root, containing PolyDet/ *)
Needs["PolyDet`"]

Quick start

(* per-multipole Gel'fand-Yaglom log-ratio *)
PolyDetLnR[3, {1., 2., 1.5}, {2., 3.}]

(* renormalised determinant on a thin-wall polygon (segment masses^2, radii) *)
PolyDetRen[masses2, radii, "Dimension" -> 4]

(* straight from a FindBounce BounceFunction bf *)
{masses2, radii} = PolyDetInputs[Vpp, bf];
PolyDetRen[masses2, radii]

See the PolyDet guide page (Documentation Center, search "PolyDet") for the full symbol list across all four sectors, and the reference pages for the main entry points PolyDetRen, PolyDetSigma, PolyDetLnR, PolyDetInputs, PolyDetRenMat, PolyDetRenPsi, PolyDetSigmaGauge, PolyDetRate.

Build from source

wolframscript -file Build.wls            # build docs + pack PolyDet-<ver>.paclet
wolframscript -file PolyDet/Tests/run.wls  # run the test suite

License

Released under the MIT License.

Author

Miha Nemevšek — miha.nemevsek@ijs.si