Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1811.10230 · Physical Review A

Comment on “Coherent-state path integrals in the continuum”

E. A. Kochetov

Published Feb 13, 2019• 6 citations
arXivHTMLPDF

Abstract

Kordas et al. [Phys. Rev. A 90, 032104 (2014)] claim to have established a time-continuous formulation of the path integration in the coherent-state (CS) basis free from the inconsistency first reported by Wilson and Galitski [Phys. Rev. Lett. 106, 110401 (2011)]. Since a few recent investigations consider the approach advocated by Kordas et al. as providing a remedy for the CS path-integral anomaly, I feel it is appropriate to show that the formulation proposed by Kordas et al. does not eliminate the anomaly. The Reply does not change the status of my criticism.

DOI
10.1103/physreva.99.026101

Related papers

Reply to “Comment on ‘Coherent-state path integrals in the continuum’”

G. Kordas, S. I. Mistakidis, A. I. Karanikas

In this Reply we briefly clarify the main points of our method to construct coherent-state path integrals in the continuum and we reply to the critique raised by in the preceding Comment by Kochetov [Phys. Rev. A 99, 026101 (2019)]. By using definite examples, we prove that our approach is capable of resolving the inconsistencies accompanying the standard coherent-state path-integral representation of interacting systems.

Physical Review A•Feb 13, 2019•3 citations

Coherent-state path integrals in the continuum

G. Kordas, S. I. Mistakidis, A. I. Karanikas

We discuss the time continuous path integration in the coherent-state basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set the basis to develop perturbative and nonperturbative approximations already known in the quantum-field-theory community. These techniques can be proven useful in a great variety of problems where bosonic Hamiltonians are used.

arXiv:1408.3210•Physical Review A•Sep 3, 2014•14 citations

Coherent-state path integrals in the continuum: The SU(2) case

G. Kordas, Dimitrios Kalantzis, A. I. Karanikas

We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.

arXiv:1605.06757•May 22, 2016•1 citation

Making the coherent state path integral great again: insights from stochastic calculus

Adam Rançon

Recently, doubts have been cast on the validity of the continuous-time coherent state path integral. This has led to controversies regarding the correct way of performing calculations with path integrals, and to several alternative definitions of what should be their continuous limit. Furthermore, the issue of a supposedly proper ordering of the Hamiltonian operator, entangled with the continuous-time limit, has led to considerable confusion in the literature. Since coherent state path integrals are at the basis of the modern formulation of many-body quantum theory, it should be laid on solid foundations. Here, we show that the standard coherent state path integral is fine as it is, and does not need any modification. We show that the issues raised above are coming from illegitimate use of the (standard) rules of calculus, which are not necessarily valid in path integrals. This is well known in the context of stochastic equations, in particular in their path integral formulation. This insight allows for solving these issues, and addressing the correspondence between the various orderings at the level of the path integral. We also use this opportunity to address the proper calculation of a functional determinant in the presence of a Hubbard-Stratonovich field, which shares in the controversies.

•Jun 6, 2019•0 citations

Hubbard–Stratonovich transformation and consistent ordering in the coherent state path integral: insights from stochastic calculus

Adam Rançon

Abstract Recently, doubts have been cast on the validity of the continuous-time coherent state path integral. This has led to controversies regarding the correct way of performing calculations with path integrals, and to several alternative definitions of what should be their continuous limit. Furthermore, the issue of a supposedly proper ordering of the Hamiltonian operator, entangled with the continuous-time limit, has led to considerable confusion in the literature. Since coherent state path integrals are at the basis of the modern formulation of many-body quantum theory, it should be laid on solid foundations. Here, we show that the issues raised above are coming from the illegitimate use of the (standard) rules of calculus, which are not necessarily valid in path integrals. This is well known in the context of stochastic equations, in particular in their path integral formulation. This insight allows for solving these issues and addressing the correspondence between the various orderings at the level of the path integral. We also use this opportunity to address the proper calculation of a functional determinant in the presence of a Hubbard–Stratonovich field, which shares in the controversies.

arXiv:1906.02571•Journal of Physics A Mathematical and Theoretical•Jan 17, 2020•4 citations

Reply to "Comment on 'Modifying the variational principle in the action-integral-functional derivation of time-dependent density functional theory'"

J. Schirmer

In a recent paper [Phys. Rev. A 77, 062511 (2008)], it was advocated to modify the variational principle for the action-integral functional in the Runge-Gross foundation of time-dependent density-functional theory. This was criticised in a subsequent paper [Phys. Rev. A 62, 052510 (2010)] by the present author. In a Comment [Phys. Rev. A 83, 046501 (2011)], it is argued that the criticism is unfounded. This is a response as given to the four specific points raised in the Comment, clarifying and confirming the essence of the original criticism.

arXiv:1105.2718•May 13, 2011•0 citations
Kordas et al. [Phys. Rev. A 90, 032104 (2014)] claim to have established a time-continuous formulation of the path integration in the coherent-state (CS) basis free from the inconsistency first reported by Wilson and Galitski [Phys. Rev. Lett. 106, 110401 (2011)]. Since a few recent investigations consider the approach advocated by Kordas et al. as providing a remedy for the CS path-integral anomaly, I feel it is appropriate to show that the formulation proposed by Kordas et al. does not eliminate the anomaly. The Reply does not change the status of my criticism.
Recently, doubts have been cast on the validity of the continuous-time coherent state path integral. This has led to controversies regarding the correct way of performing calculations with path integrals, and to several alternative definitions of what should be their continuous limit. Furthermore, the issue of a supposedly proper ordering of the Hamiltonian operator, entangled with the continuous-time limit, has led to considerable confusion in the literature. Since coherent state path integrals are at the basis of the modern formulation of many-body quantum theory, it should be laid on solid foundations. Here, we show that the standard coherent state path integral is fine as it is, and does not need any modification. We show that the issues raised above are coming from illegitimate use of the (standard) rules of calculus, which are not necessarily valid in path integrals. This is well known in the context of stochastic equations, in particular in their path integral formulation. This insight allows for solving these issues, and addressing the correspondence between the various orderings at the level of the path integral. We also use this opportunity to address the proper calculation of a functional determinant in the presence of a Hubbard-Stratonovich field, which shares in the controversies.
Abstract Recently, doubts have been cast on the validity of the continuous-time coherent state path integral. This has led to controversies regarding the correct way of performing calculations with path integrals, and to several alternative definitions of what should be their continuous limit. Furthermore, the issue of a supposedly proper ordering of the Hamiltonian operator, entangled with the continuous-time limit, has led to considerable confusion in the literature. Since coherent state path integrals are at the basis of the modern formulation of many-body quantum theory, it should be laid on solid foundations. Here, we show that the issues raised above are coming from the illegitimate use of the (standard) rules of calculus, which are not necessarily valid in path integrals. This is well known in the context of stochastic equations, in particular in their path integral formulation. This insight allows for solving these issues and addressing the correspondence between the various orderings at the level of the path integral. We also use this opportunity to address the proper calculation of a functional determinant in the presence of a Hubbard–Stratonovich field, which shares in the controversies.
In a recent paper [Phys. Rev. A 77, 062511 (2008)], it was advocated to modify the variational principle for the action-integral functional in the Runge-Gross foundation of time-dependent density-functional theory. This was criticised in a subsequent paper [Phys. Rev. A 62, 052510 (2010)] by the present author. In a Comment [Phys. Rev. A 83, 046501 (2011)], it is argued that the criticism is unfounded. This is a response as given to the four specific points raised in the Comment, clarifying and confirming the essence of the original criticism.