Straight-line path approximation for studying Planckian-energy scattering in quantum gravity

Han, Nguyen Suan; Ponna, Eap

doi:10.1007/bf03035893

Cited by 4 publications

(4 citation statements)

References 25 publications

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“…In the present Letter we show that this is feasible by using a method which has been introduced by Barbashov and coworkers [2,3,4] nearly 40 years ago. They showed how one can amputate exact Green functions in Quantum Field Theory without using perturbation theory but their work doesn't seem to have received much attention apart from the (rather specialized) field of quantum gravity where Fabbrichesi, Han and others [5,6,7,8] have extensively used the Barbashov method to describe gravitational scattering. Our main aim in this work is to transcribe their method to the nonrelativistic case and to use the result for an approximate variational calculation similar to the one investigated in Refs.…”

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confidence: 99%

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A new path-integral representation of the T-matrix in potential scattering

Carron¹,

Rosenfelder²

2011

Physics Letters A

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We employ the method used by Barbashov and collaborators in Quantum Field Theory to derive a pathintegral representation of the T -matrix in nonrelativistic potential scattering which is free of functional integration over fictitious variables as was necessary before. The resulting expression serves as a starting point for a variational approximation applied to high-energy scattering from a Gaussian potential. Good agreement with exact partial-wave calculations is found even at large scattering angles. A novel path-integral representation of the scattering length is obtained in the low-energy limit.

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confidence: 99%

“…Since the algebra in Ref. [6] (which we follow with several corrections) is somewhat sketchy and involved we list in more detail the steps to be taken in the following:…”

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A new path-integral representation of the T-matrix in potential scattering

Carron¹,

Rosenfelder²

2011

Physics Letters A

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“…The eikonal approximation here is equivalent to the straight line approximation [6][7][8][9][10][11][12][13], which is used to compute the functional integrals as it occurs. The advantage of this approach is that, it can be extended to compute the leading term and the first-order correction term in the asymptotic scattering amplitude at Planck energies and the first-order correction in quantum linear gravity theory [14][15][16][17][18] and effective quantum gravity theory [19].…”

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confidence: 99%

“…The amplitude of the particle scattering in the external field can be found through solving Schrodinger equation. First, we solve the integral equation corresponding to Schrodienger equation to find the Green function of the particle in the external field [5][6][7][8][9][10][11][12][13][14].…”

Section: Two-particle Quasi-potential Equation In An Operator Formmentioning

confidence: 99%

Functional Integral Method for Potential Scattering Amplitude in Quantum Mechanics

Ba¹,

Ha²,

Xuan³

2022

MaP

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The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We obtained the potential scattering amplitude from the complete Green function in the corresponding external field through solving the Schrodinger equation, after being separated from the poles on the mass shell, which takes the form of an eikonal (Glauber) representation in the high energy region and the small scattering angles. Considering specific external potentials such as the Yukawa or Gaussian potential, we found the corresponding differential scattering cross-sections.

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The contribution of effective quantum gravity to the high energy scattering in the framework of modified perturbation theory and one loop approximation

Han

Xuan

2019

Eur. Phys. J. C

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The asymptotic behavior of the scattering amplitude for two scalar particles at high energies with fixed momentum transfers is studied. The study is done within the effective theory of quantum gravity based on quasi-potential equation. By using the modified perturbation theory, a systematic method is developed to find the leading eikonal scattering amplitudes together with corrections to them in the one-loop gravitational approximation. The relation is established and discussed between the solutions obtained by means of the operator and functional approaches applied to quasi-potential equation. The first non-leading corrections to the leading eikonal amplitude are found.

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Straight-line path approximation for studying Planckian-energy scattering in quantum gravity

Cited by 4 publications

References 25 publications

A new path-integral representation of the T-matrix in potential scattering

A new path-integral representation of the T-matrix in potential scattering

Functional Integral Method for Potential Scattering Amplitude in Quantum Mechanics

The contribution of effective quantum gravity to the high energy scattering in the framework of modified perturbation theory and one loop approximation

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