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Path integrals: From quantum mechanics to photonics
APL Photonics, 2021 The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its dynamical evolution,
Charles W. Robson +3 more
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Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts
Journal of High Energy Physics, 2021 We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external momenta.
Guy R. Jehu
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Semiclassical Series from Path Integrals [PDF]
, 1999 We derive the semiclassical series for the partition function in Quantum Statistical Mechanics (QSM) from its path integral representation. Each term of the series is obtained explicitly from the (real) minima of the classical action. The method yields a
Cavalcanti, R. M., de Carvalho, C. A. A.
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User's guide to Monte Carlo methods for evaluating path integrals [PDF]
, 2018 We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the ...
Dürr, S +3 more
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Three dimensional Green's function for ship motion at forward speed
International Journal of Mathematics and Mathematical Sciences, 1990 The Green's function formulation for ship motion at forward speed contains double integrals with singularities in the path of integrations with respect to the wave number.
Matiur Rahman
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Coordinate-free quantization of first-class constrained systems [PDF]
, 1996 The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include ...
Ashtekar +17 more
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Feynman formulae for solutions of Schrodinger-type equations with fourth-power polinomial potentials [PDF]
Компьютерные исследования и моделирование, 2012 The conditions for the existence of Feynman integrals in a sense of analytic continuation of the exponential functionals with a fourth-power polynomial in the index are studied, their presentations by Gaussian integrals are constructed in the paper.
Anna Konstantinovna Kravtseva
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Damage Creep Model of Viscoelastic Rock Based on the Distributed Order Calculus
Applied Sciences, 2023 In this paper, the distributed order calculus was used to establish a creep damage theoretical model to accurately describe the creep properties of viscoelastic materials.
Ming Li +6 more
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Chern-Simons Path Integrals in S2 × S1
Mathematics, 2015 Using torus gauge fixing, Hahn in 2008 wrote down an expression for a Chern-Simons path integral to compute the Wilson Loop observable, using the Chern-Simons action \(S_{CS}^\kappa\), \(\kappa\) is some parameter.
Adrian P. C. Lim
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Classification of Solvable Feynman Path Integrals
, 1992 A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last ten years or so, including, of course, the main contributions since ...
Grosche, Christian, Steiner, Frank
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