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arxiv: 1906.10180 · v1 · pith:P54YEQAZnew · submitted 2019-06-24 · ✦ hep-th

Renormalisation in Open Quantum Field theory II: Yukawa theory and PV reduction

Avinash , Chandan Jana , Arnab Rudra This is my paper

Pith reviewed 2026-05-25 17:03 UTC · model grok-4.3

classification ✦ hep-th
keywords open quantum field theoryYukawa theoryPassarino-Veltman reductionnon-local divergencesfermionic self-energyrenormalisationdensity matrixtrace preservation
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The pith

Non-local divergences appear in the one-loop fermionic self-energy of open Yukawa theory and persist even when the tree level satisfies trace preservation.

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

The paper extends Passarino-Veltman reduction methods to tensor loop integrals that arise in open quantum field theories. It applies the adapted reduction to open Yukawa theory and calculates the one-loop self-energy corrections for the fields. The calculation produces non-local divergences in the fermionic self-energy. These non-local terms remain after the tree-level theory is adjusted to obey the trace-preserving condition on the density matrix. The outcome indicates that standard renormalization procedures encounter new obstacles when applied to open systems.

Core claim

We compute Passarino-Veltman (PV) reduction for tensor loop integrals that appear in open field theories. We apply these results to open-Yukawa theory and compute the self-energy correction of the fields. We found that non-local divergences show up in the one loop correction to the fermionic self-energy. These non-local divergences do not disappear even if the tree level theory is chosen to satisfy the trace preserving condition of the density matrix.

What carries the argument

Passarino-Veltman reduction for tensor loop integrals adapted to open field theories and used to extract self-energy corrections.

If this is right

  • Non-local divergences must be classified and subtracted when renormalizing open Yukawa theory.
  • The trace-preserving condition imposed at tree level fails to remove non-local one-loop terms.
  • Adapted PV reduction is required to distinguish local from non-local divergence structures in open theories.
  • Self-energy corrections in open Yukawa theory contain divergence patterns absent from the corresponding closed theory.

Where Pith is reading between the lines

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

  • Similar non-local divergences may appear when the same reduction is applied to other open models such as scalar or gauge theories.
  • Open quantum field theories could require additional counterterms or modified regularization to restore locality at loop level.
  • The persistence of these terms suggests that renormalization group flow in open systems may differ from the closed case in its ultraviolet structure.

Load-bearing premise

Standard Passarino-Veltman reduction techniques for tensor integrals apply without modification to open quantum field theories while preserving the validity of the loop expansion and divergence classification.

What would settle it

An explicit one-loop calculation of the fermionic self-energy in open Yukawa theory performed with cutoff regularization instead of dimensional regularization that shows the non-local divergences either cancel or remain.

read the original abstract

We compute Passarino-Veltman (PV) reduction for tensor loop integrals, that appear in open field theories. We apply these results to open-Yukawa theory and compute the self-energy correction of the fields. We found that non-local divergences show up in the one loop correction to the fermionic self-energy. These non-local divergences do not disappear even if the tree level theory is chosen to satisfy the trace preserving condition of the density matrix.

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

1 major / 0 minor

Summary. The manuscript computes Passarino-Veltman reductions for tensor loop integrals appearing in open quantum field theories and applies the results to open Yukawa theory. It reports that non-local divergences appear in the one-loop fermionic self-energy correction and that these divergences persist even after the tree-level theory is chosen to satisfy the trace-preserving condition on the density matrix.

Significance. If the explicit computation holds, the result identifies a structural difference between renormalization in open versus closed QFTs: non-local divergences that are not removed by the trace-preserving condition. This supplies a concrete, falsifiable example in Yukawa theory and strengthens the case that open-system renormalization requires dedicated techniques beyond standard closed-system methods.

major comments (1)
  1. The central claim rests on the direct application of unmodified Passarino-Veltman reduction to the tensor integrals of open Yukawa theory. The manuscript must explicitly verify that the open-system modifications (e.g., to the propagator or vertex structure) do not alter the reduction identities or the subsequent classification of divergences as local versus non-local; without this justification the reported non-local terms cannot be taken as established.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and the constructive comment on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: The central claim rests on the direct application of unmodified Passarino-Veltman reduction to the tensor integrals of open Yukawa theory. The manuscript must explicitly verify that the open-system modifications (e.g., to the propagator or vertex structure) do not alter the reduction identities or the subsequent classification of divergences as local versus non-local; without this justification the reported non-local terms cannot be taken as established.

    Authors: The Passarino-Veltman reduction identities follow from Lorentz covariance and the algebraic decomposition of tensor structures in the loop momentum; these identities are independent of the specific form of the propagators and vertices. The open-system modifications in Yukawa theory enter only through the explicit integrands, not through the reduction coefficients or the local/non-local classification of the resulting divergences. We agree, however, that an explicit statement confirming this applicability would strengthen the presentation and will add a short clarifying paragraph in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The manuscript executes an explicit one-loop computation of tensor integrals via Passarino-Veltman reduction in open Yukawa theory, then reports the resulting non-local divergences in the fermionic self-energy after imposing the tree-level trace-preserving condition on the density matrix. All load-bearing steps consist of direct algebraic reduction of the loop integrals and classification of divergences; none reduce by construction to fitted parameters, self-definitions, or unverified self-citations. The central claim is therefore a computational output rather than an input renamed as a prediction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no information on free parameters, axioms, or invented entities; ledger left empty.

pith-pipeline@v0.9.0 · 5595 in / 931 out tokens · 21712 ms · 2026-05-25T17:03:04.775352+00:00 · methodology

discussion (0)

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Reference graph

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