scholarly journals Harmonic-phase path-integral approximation of thermal quantum correlation functions

2018 ◽  
Vol 148 (10) ◽  
pp. 102316 ◽  
Author(s):  
Christopher Robertson ◽  
Scott Habershon
Keyword(s):  
Path Integral ◽  
Correlation Functions ◽  
Quantum Correlation ◽  
Integral Approximation ◽  
Harmonic Phase ◽  
Phase Path

scholarly journals Quantum-classical limit of quantum correlation functions

2004 ◽  
Vol 121 (16) ◽  
pp. 7565 ◽  
Author(s):  
Alessandro Sergi ◽  
Raymond Kapral
Keyword(s):  
Correlation Functions ◽  
Classical Limit ◽  
Quantum Correlation

Euclidean path integrals and quantum mechanics (QM)

2021 ◽  
pp. 18-41
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Quantum Mechanics ◽  
Path Integral ◽  
Correlation Functions ◽  
Path Integrals ◽  
Continuous Phase ◽  
Functional Integral ◽  
Smooth Transition ◽  
Path Integral Representation ◽  
The Matrix ◽  
Functional Measure

Functional integrals are basic tools to study first quantum mechanics (QM), and quantum field theory (QFT). The path integral formulation of QM is well suited to the study of systems with an arbitrary number of degrees of freedom. It makes a smooth transition between nonrelativistic QM and QFT possible. The Euclidean functional integral also emphasizes the deep connection between QFT and the statistical physics of systems with short-range interactions near a continuous phase transition. The path integral representation of the matrix elements of the quantum statistical operator e-β H for Hamiltonians of the simple separable form p2/2m +V(q) is derived. To the path integral corresponds a functional measure and expectation values called correlation functions, which are generalized moments, and related to quantum observables, after an analytic continuation in time. The path integral corresponding to the Euclidean action of a harmonic oscillator, to which is added a time-dependent external force, is calculated explicitly. The result is used to generate Gaussian correlation functions and also to reduce the evaluation of path integrals to perturbation theory. The path integral also provides a convenient tool to derive semi-classical approximations.

scholarly journals Construction of Free Energy of Calabi–Yau Manifold Embedded in CPN-1 via Torus Actions

1997 ◽  
Vol 12 (32) ◽  
pp. 5775-5802 ◽  
Author(s):  
Masao Jinzenji
Keyword(s):  
Free Energy ◽  
Integral Representation ◽  
Path Integral ◽  
Correlation Functions ◽  
Sigma Model ◽  
Torus Action ◽  
Torus Actions ◽  
Path Integral Representation

We calculate correlation functions of topological sigma model (A-model) on Calabi–Yau hypersurfaces in CPN-1 using torus action method. We also obtain path-integral representation of free energy of the theory coupled to gravity.

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