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arxiv: 2606.30965 · v1 · pith:RUQ2FWN3new · submitted 2026-06-29 · 🧮 math-ph · hep-th· math.DG· math.MP· math.SG

Homotopies in Batalin-Vilkovisky Formalism

Branislav Jur\v{c}o , J\'an Pulmann , Martin Zika This is my paper

Pith reviewed 2026-07-01 00:42 UTC · model grok-4.3

classification 🧮 math-ph hep-thmath.DGmath.MPmath.SG
keywords Batalin-Vilkovisky formalismquantum master equationhomotopiesrenormalization group flowgauge fixingfield redefinitionseffective actions
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The pith

Homotopies induced by renormalization group flow and non-infinitesimal gauge fixing changes yield field redefinitions that produce spans of quantum master actions with isomorphic effective actions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews the notion of homotopy between quantum master actions in the geometric Batalin-Vilkovisky formalism. It constructs new examples of such homotopies that arise from renormalization group flow and from finite changes of gauge fixing. These homotopies supply explicit field redefinitions that connect different quantum master actions. The resulting spans have effective actions that are isomorphic, so the physical content extracted from the actions remains the same. A reader would care because the construction shows how the geometric structure of the formalism accommodates these flows and changes while preserving the quantum master equation.

Core claim

The paper shows that homotopies of quantum master actions coming from renormalization group flow and non-infinitesimal gauge fixing changes induce field redefinitions; these redefinitions can be used to build spans of quantum master actions whose effective actions are isomorphic.

What carries the argument

Homotopy of quantum master actions in geometric Batalin-Vilkovisky formalism, which supplies field redefinitions that preserve the quantum master equation.

If this is right

  • Spans of quantum master actions can be constructed whose effective actions are isomorphic.
  • Renormalization group flow supplies a homotopy between quantum master actions.
  • Non-infinitesimal changes of gauge fixing supply another class of such homotopies.
  • The field redefinitions induced by the homotopies preserve the quantum master equation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same homotopies could be applied to relate different perturbative expansions of a single theory.
  • The construction may extend to finite renormalization group transformations that are not infinitesimal.
  • Spans built this way could be used to compare different gauge choices while keeping the same observables.

Load-bearing premise

The homotopies induced by renormalization group flow and non-infinitesimal gauge fixing changes are compatible with the geometric structure of the Batalin-Vilkovisky formalism and induce valid field redefinitions that preserve the quantum master equation.

What would settle it

An explicit computation for a concrete field theory in which a field redefinition coming from one of these homotopies produces a new action that fails to satisfy the quantum master equation.

read the original abstract

We review the notion of homotopy of quantum master actions in geometric Batalin-Vilkovisky formalism. Then we construct new examples of such homotopies, coming from renormalization group flow and non-infinitesimal changes of gauge fixing. Finally, we use the field redefinitions given by these homotopies to construct spans of quantum master actions with isomorphic effective actions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 0 minor

Summary. The manuscript reviews the notion of homotopy of quantum master actions in the geometric Batalin-Vilkovisky formalism. It constructs new examples of such homotopies coming from renormalization group flow and non-infinitesimal changes of gauge fixing. Finally, it uses the field redefinitions given by these homotopies to construct spans of quantum master actions with isomorphic effective actions.

Significance. If the constructions are valid, the work supplies concrete new examples of homotopies in the geometric BV setting and a method for relating quantum master actions via spans whose effective actions are isomorphic. This could clarify structural aspects of renormalization and gauge fixing within the formalism. The abstract does not indicate machine-checked proofs, reproducible code, or parameter-free derivations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for reviewing our manuscript on homotopies in the geometric Batalin-Vilkovisky formalism. We appreciate the recognition that the work supplies concrete new examples from renormalization group flow and gauge fixing, along with a method for relating quantum master actions via spans. We address the overall assessment below, noting that no specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The provided abstract and context describe a review of homotopies in geometric BV formalism followed by construction of new examples from RG flow and gauge-fixing changes, then application to spans of quantum master actions. No equations, definitions, or claims are supplied that reduce a derived result to an input by construction, nor any load-bearing self-citation chains or fitted parameters renamed as predictions. The work is presented as building on standard BV structures with independent constructions, consistent with a self-contained mathematical development.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are identifiable.

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Reference graph

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