A physical basis for the phase in Feynman path integration

量子计算机上的圈费曼图积分

Loop Feynman integration on a quantum computer

本文提出新型量子蒙特卡洛积分器 QFIAE，通过引入量子神经网络将多维被积函数分解为傅里叶级数以实现二次加速，首次在量子计算机和模拟器上成功计算单圈费曼积分，验证了方法的有效性及跨领域应用潜力。

Feynman Functional Integral in the Fokker Theory

The equivalence of two formulations of Fokker's quantum theory is proved - based on the Feynman functional integral representation of the propagator for a system of charges with direct electromagnetic interaction and the quantum principle of least action as an analogue of the Schrödinger wave equation. The common basis for the two approaches is the generalized canonical form of Fokker's action.

Algebraic structure of the Feynman propagator and a new correspondence for canonical transformations

We investigate the algebraic structure of the Feynman propagator with a general time-dependent quadratic Hamiltonian system. Using the Lie-algebraic technique we obtain a normal-ordered form of the time-evolution operator, and then the propagator is easily derived by a simple ``Integration Within Ordered Product" (IWOP) technique.It is found that this propagator contains a classical generating function which demonstrates a new correspondence between classical and quantum mechanics.

Bayesian Approach to Inverse Quantum Statistics: Reconstruction of Potentials in the Feynman Path Integral Representation of Quantum Theory

The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the classical and semiclassical limits and provides a unified description in terms of functional integrals: the Feynman path integral for the statistical operator, and the integration over the space of potentials for calculating the predictive density. The latter is treated in maximum a posteriori approximation, and various approximation schemes for the former are devel…

Father time. II. A physical basis behind Feynman's idea of antiparticles moving backward in time, and an extension of the CPT theorem to include non-local gauge fields

It has been demonstrated in a recent paper (Mod.Phys.Lett. A13, 1265 (1998); hep-th/9902020) that the existence of a non-thermodynamic arrow of time at the atomic level is a fundamental requirement for conservation of energy in matter-radiation interaction. Since the universe consists of two things only --- energy and massive matter --- we argue that as a consequence of this earlier result, particles and antiparticles must necessarily move in opposite directions in time. Our result further indicates that the CPT theorem can be extended to cover non-local gauge fields.

Derivation of quantum work equalities using quantum Feynman-Kac formula

On the basis of a quantum mechanical analogue of the famous Feynman-Kac formula and the Kolmogorov picture, we present a novel method to derive nonequilibrium work equalities for isolated quantum systems, which include the Jarzynski equality and Bochkov-Kuzovlev equality. Compared with previous methods in the literature, our method shows higher similarity in form to that deriving the classical fluctuation relations, which would give important insight when exploring new quantum fluctuation relations.

用量子自适应重要性采样解锁多维积分

Unlocking Multidimensional Integration with Quantum Adaptive Importance Sampling

提出混合量子-经典算法QAIS，利用参数化量子电路编码非可分概率密度函数，高效评估多维积分，在尖峰圈费曼积分和多峰基准积分上实现高精度。

形变量子化中的费曼-卡茨公式

The Feynman-Kac formula in deformation quantization

本文将费曼-卡茨公式引入形变量子化框架，证明经维克旋转后可由哈密顿算符星指数的相空间积分渐近极限求得基态能量，并给出高效计算实例。

A History of Feynman's Sum over Histories in Quantum Mechanics

A history of Feynman's sum over histories is presented in brief. A focus is placed on the progress of path-integration techniques for exactly path-integrable problems in quantum mechanics.

Monte Carlo evaluation of the equilibrium isotope effects using the Takahashi-Imada factorization of the Feynman path integral

The Feynman path integral approach for computing equilibrium isotope effects and isotope fractionation corrects the approximations made in standard methods, although at significantly increased computational cost. We describe an accelerated path integral approach based on three ingredients: the fourth- order Takahashi-Imada factorization of the path integral, thermodynamic integration with respect to mass, and centroid virial estimators for relevant free energy derivatives. While the frst ingredient speeds up convergence to the quantum limit, the second and third improve statistical convergence…

On p-Adic Functional Integration

p-Adic generalization of the Feynman path integrals in quantum mechanics is considered. The probability amplitude for a particle in a constant field is calculated. Path integrals over p-adic space have the same form as those over R.

Three useful bounds in quantum mechanics - easily obtained by Wiener integration

In a reasonably self-contained and explicit presentation we illustrate the efficiency of the Feynman-Kac formula for the rigorous derivation of three inequalities of interest in non-relativistic quantum mechanics.