scholarly journals Exponential functions of perturbative series and elimination of secular divergences in time-dependent perturbation theory in quantum mechanics

2017 ◽  
Vol 7 ◽  
pp. 890-894
Author(s):  
Q.H. Liu ◽  
Z. Li ◽  
M.N. Zhang ◽  
Q. Li ◽  
B.J. Chen
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Time Dependent ◽  
Exponential Functions ◽  
Perturbative Series

A modification of the Dirac time-dependent perturbation theory

1984 ◽  
Vol 394 (1807) ◽  
pp. 345-361 ◽  
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Time Dependent ◽  
Static Case ◽  
Simple Route ◽  
Factors Associated ◽  
Perturbation Procedure ◽  
Variation Of Constants ◽  
Harmonic Perturbation ◽  
Secular Terms

Within the framework of the method of variation of constants, time-dependent perturbation theory is presented in a form that naturally eliminates the undesirable ‘secular ’ terms for a time-independent perturbation, permits an order-by-order calculation of the exact wavefunction for a ‘resonant’ harmonic perturbation and offers a simple route to establish the adiabatic hypothesis in quantum mechanics. The formulation rests on the introduction of a flexibility in the choice of the phase factors associated with the varying amplitudes, together with development of a perturbation procedure that closely resembles the Brillouin-Wigner formalism in the static case, and which exploits the flexibility of the phase factors at each order of the theory.

scholarly journals Critical behavior of the 2d scalar theory: resumming the N8LO perturbative mass gap

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Gustavo O. Heymans ◽  
Marcus Benghi Pinto
Keyword(s):  
Perturbation Theory ◽  
Critical Behavior ◽  
State Of The Art ◽  
Critical Coupling ◽  
Scalar Theory ◽  
Perturbative Series ◽  
Supercritical Region ◽  
Mass Gap ◽  
Perturbative Result ◽  
Symmetric Phase

Abstract We apply the optimized perturbation theory (OPT) to resum the perturbative series describing the mass gap of the bidimensional ϕ4 theory in the ℤ2 symmetric phase. Already at NLO (one loop) the method is capable of generating a quite reasonable non-perturbative result for the critical coupling. At order-g7 we obtain gc = 2.779(25) which compares very well with the state of the art N8LO result, gc = 2.807(34). As a novelty we investigate the supercritical region showing that it contains some useful complimentary information that can be used in extrapolations to arbitrarily high orders.

scholarly journals Stochastic computation of g − 2 in QED

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ryuichiro Kitano ◽  
Hiromasa Takaura ◽  
Shoji Hashimoto
Keyword(s):  
Perturbation Theory ◽  
Numerical Computation ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Stochastic Perturbation ◽  
Higher Order ◽  
Feynman Diagrams ◽  
Perturbative Series ◽  
Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

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