Proper-time method for unequal masses

A.A. Osipov

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Proper-time method for unequal masses

A.A. Osipov

High Energy Physics - Theory · Submitted 21 Feb 2021

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

The authors' main claim We propose a new efficient tool to calculate the leading terms of this series based on the Schwinger proper-time method.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,610 input tokens.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.31 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

The result of removing of heavy non-equal mass particles from the theory can be described, at low energy, by the effective action, which is a series in inverse-square powers of the mass. We propose a new efficient tool to calculate the leading terms of this series based on the Schwinger proper-time method. Unequal masses give rise to a large number of effective vertices describing the explicit flavour symmetry breaking effects with well-defined coupling constants. Our method is pertinent to the theory with explicit and spontaneous chiral symmetry breaking, chiral gauge theory, standard and beyond standard model effective field theory, the theory of critical phenomena, cosmology, etc.

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	The result of removing of heavy non-equal mass particles from the theory can be described, at low energy, by the effective action, which is a series in inverse-square powers of the mass.	background 0.91	0.28	0.33	asserted 1.00
s1	We propose a new efficient tool to calculate the leading terms of this series based on the Schwinger proper-time method.	contribution 0.75	0.85	0.28	asserted 0.96
s2	Unequal masses give rise to a large number of effective vertices describing the explicit flavour symmetry breaking effects with well-defined coupling constants.	result 0.62	0.45	0.13	asserted 1.00
s3	Our method is pertinent to the theory with explicit and spontaneous chiral symmetry breaking, chiral gauge theory, standard and beyond standard model effective field theory, the theory of critical phenomena, cosmology, etc.	interpretation 0.77	0.21	0.08	asserted 0.91

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from proof or derivation 0.99.

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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

The result of removing of heavy non-equal mass particles from the theory can be described, at low energy, by the effective action, which is a series in inverse-square powers of the mass. We propose a new efficient tool to calculate the leading terms of this series based on the Schwinger proper-time method. Unequal masses give rise to a large number of effective vertices describing the explicit flavour symmetry breaking effects with well-defined coupling constants. Our method is pertinent to the theory with explicit and spontaneous chiral symmetry breaking, chiral gauge theory, standard and beyond standard model effective field theory, the theory of critical phenomena, cosmology, etc.

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2 arXiv papers cite this in 2 sentences

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Uses its method or tool 1 paper

In the Fourier space, the HK can be written as [ref] [equation] where [equation] and [equation] The Gaussian momentum integral over the $f_n(t,𝒜)$ in Eq. [ref] generates a polynomial in $t$, and that allows the HK to be written in the following form [equation] where $b̃_n$ are the Generalized Heat-Kernel Coefficients (g-HKC) which get contribution from $f_m(t,𝒜), m≤2n$[In case of derivative involved operators, this relation does not hold and $f_m(t,𝒜)$ with $m> 2n$ may also contribute to a specific order of $b̃_n$.

Renormalization of Scalar and Fermion Interacting Field Theory for Arbitrary Loop: Heat-Kernel Approach · Heat-Kernel and Scalar Green's Function: Encapsulating Self-interaction · 0.91

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