The Feynman Path Integral: An Historical Slice

On Feynman's Discussion of Classical Physics Failing at Specific Heat

I provide the backstory on how a historical error in the Feynman Lectures on Physics was corrected.

Noncommutative quantum mechanics: uniqueness of the functional description

The generalized Weyl transform of index $α$ is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation for the Feynman kernel is not unique but labeled by the real parameter $α$. We succeed in proving that the $α$-dependent contributions disappear at the limit where the time slice goes to zero. This proof of consistency turns out to be intricate because the Hamiltonian involves products of noncommuting operators originating from the non-commutativity. The antisymme…

费曼通往薛定谔方程之路（及其他若干问题）

Feynman's path to Schrödinger (and various other things)

本文梳理费曼如何受狄拉克类比启发，将拉格朗日框架引入量子力学并建立路径积分表述，进而从路径积分推导出薛定谔方程并证明概率守恒，为本科生连接这一方法与标准课程内容。

费曼1947年关于狄拉克方程路径积分的信

Feynman 1947 letter on path integral for the Dirac equation

本文转录并评述费曼1947年致韦尔顿的信，该信记录了他为狄拉克粒子传播构建路径积分的未成功尝试及其历史与科学意义。

Classical and Fluctuating Paths in Spaces with Curvature and Torsion

This conference talk elaborates on a recently discovered mapping procedure by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed correctly into those in curved space. This procedure evolved from well established methods in the theory of plastic deformations where crystals with defects are described mathematically by applying nonholonomic coordinate transformations to ideal crystals. In the context of time-sliced path integrals, there seems to exists a quantum equivalence principle which determines the measures of fluctating orbits in s…

HSF-S：用于混合薛定谔 - 费曼量子电路仿真的速度优化编译与加速

HSF-S: Speed-Optimized Compilation and Acceleration for Hybrid Schrodinger-Feynman Quantum Circuit Emulation

研究针对混合薛定谔 - 费曼量子电路仿真实际运行时间受跨边界双量子比特门指数级路径增长主导的问题，提出HSF-S框架，通过特定方法抑制跨边界相互作用，降低路径成本，在基准电路上大幅提高可处理性并实现加速。