The Maslov correction in the semiclassical Feynman integral

Horváthy, P. A.

doi:10.2478/s11534-010-0055-3

Cited by 13 publications

(18 citation statements)

References 34 publications

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“…We have introduced the Morse index ν q which arises naturally for functional determinants with q negative modes [46], and can be interpreted as an analog of the intersection numbers arising in the Lefschetz thimble decomposition of ordinary integrals. In our computation, it is related to the fact that Gaussian integrals for negative modes have a two-fold ambiguity in their analytic continuation:…”

Section: Jhep05(2021)035mentioning

confidence: 99%

Resurgence of the large-charge expansion

Dondi

Kalogerakis

Orlando

et al. 2021

J. High Energ. Phys.

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We study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the non-perturbative corrections and to extend the validity of the eft to any value of the charge. We conjecture the general form of the non-perturbative behavior of the conformal dimensions for any value of N and find very good agreement with previous lattice data.

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Section: Jhep05(2021)035mentioning

confidence: 99%

Resurgence of the large-charge expansion

Dondi

Kalogerakis

Orlando

et al. 2021

J. High Energ. Phys.

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“…As stated in [10], we can observe clearly that when time passes over every caustic point, number of negative eigenvalues increases and the phase correction is multiplied in the Feynman formula. As pointed out in [11], if we integrate (6) formally to…”

Section: Discussionmentioning

confidence: 99%

Extended Feynman Formula for the Harmonic Oscillator by the Discrete Time Method

Funahashi

2010

Mod. Phys. Lett. A

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We calculate the Feynman formula for the harmonic oscillator beyond and at caustics by the discrete formulation of path integral. The extension has been made by some authors, however, it is not obtained by the method which we consider the most reliable regularization of path integral. It is shown that this method leads to the result with, especially at caustics, more rigorous derivation than previous.

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“…17 For an account of this phenomenon, see Ref. 15 and references therein, where the computation of the propagator in the path integral approach for the standard harmonic oscillator is discussed. As a consequence of this singular behavior, if analytic expressions for the solutions u 1 and u 2 are not available, then gi(t) have to be computed numerically from Eqs.…”

Section: Articlementioning

confidence: 99%

“…This problem is not specific of the WN method but appears also in other approaches such as Feynman's path integral method for computing the propagator. 15,16 The singular values of the functions gi(t) are related to the caustics appearing in the path integral method and are also related to the caustics appearing in Morse theory. 17 They are also related to the focal points appearing in Fourier optics.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, the phase jumps of the propagator in the path integral method 15,16 appearing when passing through a caustic, which are ultimately related to the Maslov index and the Maslov correction, and with the Guoy phase in optics, 19 are also easily obtained in the WN method. In summary, the existence of singularities in the functions gi(t) can be easily handled within the WN method and does not prevent the computation of the evolution operator for all times.…”

Section: Introductionmentioning

confidence: 99%

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Semiclassical interpretation of Wei–Norman factorization for SU(1, 1) and its related integral transforms

Guerrero

Berrondo

2020

Journal of Mathematical Physics

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We present an interpretation of the functions appearing in the Wei-Norman factorization of the evolution operator for a Hamiltonian belonging to the SU(1,1) algebra in terms of the classical solutions of the Generalized Caldirola-Kanai (GCK) oscillator (with time-dependent mass and frequency). Choosing P 2 , X 2 , and the dilation operator as a basis for the Lie algebra, we obtain that, out of the six possible orderings for the Wei-Norman factorization of the evolution operator for the GCK Hamiltonian, three of them can be expressed in terms of its classical solutions and the other three involve the classical solutions associated with a mirror Hamiltonian obtained by inverting the mass. In addition, we generalize the Wei-Norman procedure to compute the factorization of other operators, such as a generalized Fresnel transform and the Arnold transform (and its generalizations), obtaining also in these cases a semiclassical interpretation for the functions in the exponents of the Wei-Norman factorization. The singularities of the functions appearing in the Wei-Norman factorization are related to the caustic points of Morse theory, and the expression of the evolution operator at the caustics is obtained using a limiting procedure, where the Fourier transform of the initial state appears along with the Guoy phase.

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The Maslov correction in the semiclassical Feynman integral

Cited by 13 publications

References 34 publications

Resurgence of the large-charge expansion

Resurgence of the large-charge expansion

Extended Feynman Formula for the Harmonic Oscillator by the Discrete Time Method

Semiclassical interpretation of Wei–Norman factorization for SU(1, 1) and its related integral transforms

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