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:1408.3210 · Physical Review A

Coherent-state path integrals in the continuum

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

Published Sep 3, 2014• 14 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.90.032104

Related papers

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

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

E. A. Kochetov

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.

arXiv:1811.10230•Physical Review A•Feb 13, 2019•6 citations

Functional integral representation of the dynamics of squeezed states

Gregg M. Gallatin

Functional integrals provide a powerful and useful formalism for deriving both perturbative and nonperturbative results in quantum theory. Here we consider their application to the problem of formulating the dynamics of coherent and squeezed states. We derive the functional integral representation of the coherent state density matrix by combining the closed time path representation of the density matrix in terms of functional integrals in configuration space with the projection of coherent states onto configuration space states. In this formalism the atomic variables can, without loss of generality, be integrated out exactly yielding a single functional integral which describes the combined quantum dynamics of both the atomic and the coherent states.

Annual Meeting Optical Society of America•Jan 1, 1989•0 citations

An investigation of coherent state path integrals as applied to a harmonic oscillator and a single spin

L. C. Lew Yan Voon

In this project two steps involved in the handling of path integrals are reexamined in detail for coherent state path integals. They concern the continuum limit approximation and the regularization of the formal path integrals. Restricting oneself to the harmonic oscillator, the technique of time splitting is used to set up the coherent state path integrals and the proper way to pass to the continuum limit is demonstrated. The manipulation of these path integrals calls for regularization procedures and the validity of discrete, Riemann zeta function and 'derivative' regularization methods is observed. A modification to a fermionic theory is briefly mentioned and, finally, the above results are implemented in writing down a path integral for a single spin.

•Jan 1, 2010•2 citations

Coherent-state path integrals in the continuum via geometric de-quantization

Panagiotis Lykourgias, I. Lyris, A. I. Karanikas

We present a new method for the consistent construction of time-continuous coherent-state path integrals using the theory of half-form quantization. Through the inversion of the quantization procedure we construct a de-quantization map taking first order operators to their corresponding path integrals. We generalize our results using functional techniques, allowing for the consistent path integral study of more general operators, including higher orders and interactions.

arXiv:2006.13720•Jun 24, 2020•0 citations
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.
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.
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.
Functional integrals provide a powerful and useful formalism for deriving both perturbative and nonperturbative results in quantum theory. Here we consider their application to the problem of formulating the dynamics of coherent and squeezed states. We derive the functional integral representation of the coherent state density matrix by combining the closed time path representation of the density matrix in terms of functional integrals in configuration space with the projection of coherent states onto configuration space states. In this formalism the atomic variables can, without loss of generality, be integrated out exactly yielding a single functional integral which describes the combined quantum dynamics of both the atomic and the coherent states.
In this project two steps involved in the handling of path integrals are reexamined in detail for coherent state path integals. They concern the continuum limit approximation and the regularization of the formal path integrals. Restricting oneself to the harmonic oscillator, the technique of time splitting is used to set up the coherent state path integrals and the proper way to pass to the continuum limit is demonstrated. The manipulation of these path integrals calls for regularization procedures and the validity of discrete, Riemann zeta function and 'derivative' regularization methods is observed. A modification to a fermionic theory is briefly mentioned and, finally, the above results are implemented in writing down a path integral for a single spin.