Canonical derivation of effective potentials

Martin Bojowald; Suddhasattwa Brahma

RECORD

Canonical derivation of effective potentials

Martin Bojowald, Suddhasattwa Brahma

High Energy Physics - Theory · Submitted 13 Nov 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim A comparison with the standard Coleman-Weinberg potential shows that the new methods correctly include all relevant quantum corrections.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,159 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.13 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.37 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.97 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

A canonical formulation of effective equations describes quantum corrections by the back-reaction of moments on the dynamics of expectation values of a state. As a first step toward an extension to quantum-field theory, these methods are applied here to the derivation of effective potentials around a homogeneous vacuum expectation value of scalar fields. A comparison with the standard Coleman-Weinberg potential shows that the new methods correctly include all relevant quantum corrections. At the same time, the effective potential is shown to be correct also for non-Fock and mixed states. Several explicit results are derived in models of interacting scalars and fermions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A canonical formulation of effective equations describes quantum corrections by the back-reaction of moments on the dynamics of expectation values of a state.	background 0.80	0.21	0.12	asserted 1.00
s1	As a first step toward an extension to quantum-field theory, these methods are applied here to the derivation of effective potentials around a homogeneous vacuum expectation value of scalar fields.	contribution 0.86	0.91	0.07	asserted 0.96
s2	A comparison with the standard Coleman-Weinberg potential shows that the new methods correctly include all relevant quantum corrections.	result 0.91	0.89	0.47	asserted 1.00
s3	At the same time, the effective potential is shown to be correct also for non-Fock and mixed states.	result 1.00	0.93	0.18	asserted 1.00
s4	Several explicit results are derived in models of interacting scalars and fermions.	result 0.52	0.95	0.08	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 0.58 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

A canonical formulation of effective equations describes quantum corrections by the back-reaction of moments on the dynamics of expectation values of a state. As a first step toward an extension to quantum-field theory, these methods are applied here to the derivation of effective potentials around a homogeneous vacuum expectation value of scalar fields. A comparison with the standard Coleman-Weinberg potential shows that the new methods correctly include all relevant quantum corrections. At the same time, the effective potential is shown to be correct also for non-Fock and mixed states. Several explicit results are derived in models of interacting scalars and fermions.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

17 arXiv papers cite this in 31 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 23 sentences without a confident label

Builds on it 1 paper

The back-reaction equations of [ref] can therefore be embedded in a canonical effective theory by a suitable extension of [ref] .

Canonical description of cosmological backreaction · Field theory model · 0.93

Uses its method or tool 2 papers

In this last form, the effective potential is directly obtained by canonical methods [ref] , briefly reviewed below.

Minisuperspace models as infrared contributions · Introduction · 0.87
Following the methods of [ref] , we can compute the relevant state properties without using a wave function.

Testing non-associative quantum mechanics · Introduction · 1.00

Compares with it 2 papers

The full theory ([ref]), from which we derived the minisuperspace model, also has an effective potential: the Coleman–Weinberg potential [ref] [equation] It looks very different from the minisuperspace effective potential, but, as noticed in [ref] , performing the $k^0$-integration in closed form reveals their similarity: The Coleman–Weinberg potential then equals [equation]

The BKL scenario, infrared renormalization, and quantum cosmology · Infrared contributions · 0.88
Let us remark on the comparison with the past derivations of effective potentials using fluctuations [ref] .

Effective dynamics of quantum fluctuations in field theory: with applications to cosmology · Uncertainty principle and energy-minimization · 0.98

Cites it as support 1 paper

Both assumptions have been shown to lead to correct results for anharmonic oscillators in quantum mechanics [ref] and, in the context of the Coleman–Weinberg potential, for quartic self-interactions of a scalar field [ref] .

Minisuperspace models as infrared contributions · Minisuperspace model · 0.99

Cites it as background 1 paper

This part of the paper is largely a review of [ref] .

Effective dynamics of quantum fluctuations in field theory: with applications to cosmology · Review of effective dynamics in quantum mechanics · 0.85

What it cites · 6 sentences without a confident label

Cites as background 1 paper

Canonical effective methods [ref] have so far produced several results in quantum-mechanical systems which can serve as analogs of effective potentials in quantum field theory.

Higher time derivatives in effective equations of canonical quantum systems · Introduction · 0.81

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.