Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets

By H. Kleinert. 2006

1,322 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6a2e9e6d11695a0444722b7d39a1b390e43709fe

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Citations in the corpus

Multivalued Fields: In Condensed Matter, Electromagnetism, And Gravitation (2008, methodology): “Recall that the canonically conjugate momentum variable p(t) in an ordinary path integral [20]”
Path integrals and symmetry breaking for optimal control theory (2005, neutral): “This approach to approximating the path integral is also known as variational perturbation theory and gives an expansion of the path integral in terms of the anharmonic interaction terms and a variational function that is to be optimized [14].”
Worldline instantons and the fluctuation prefactor (2006, methodology): “13) The semiclassical approximation to quantum mechanical path integrals [41, 42] leads to the following simple result:”
Power-law out of time order correlation functions in the SYK model (2017, background): “The resulting fluctuation determinant is obtained by standard recipes [34]: consider any two independent solutions z1,2 of the differential equation [ −∂(2)τ + 2(1 − λ)2 cos2 (τ(1 − λ)) ] z1,2(τ) = 0.”
Functional determinants in quantum field theory (2007, background): “Mathematically, much is known for ordinary differential operators, especially through the work of Gel’fand–Yaglom [21, 22] and its extensions [24, 26, 28], but considerably less is known for partial differential operators with non-trivial potentials.”
Graphical Model Inference in Optimal Control of Stochastic Multi-Agent Systems (2008, methodology): “We will now discuss how this is done by taking a path integral approach (Kleinert, 2006).”
CHOMP: Covariant Hamiltonian optimization for motion planning (2013, background): “Modeling distributions over a space of paths is a problem of fundamental significance to a number of fields such as statistical physics (Chaichian and Demichev, 2001), finance (Kleinert, 2009), human behavior modeling (Ziebart et al.”