Equivalence between the real time Feynman histories and the quantum shutter approaches for the "passage time" in tunneling

The Logic behind Feynman's Paths

The classical notions of continuity and mechanical causality are left in order to refor- mulate the Quantum Theory starting from two principles: I) the intrinsic randomness of quantum process at microphysical level, II) the projective representations of sym- metries of the system. The second principle determines the geometry and then a new logic for describing the history of events (Feynman's paths) that modifies the rules of classical probabilistic calculus. The notion of classical trajectory is replaced by a history of spontaneous, random an discontinuous events. So the theory is reduced to …

一种用于量子比特的拉格朗日路径积分方法

A Lagrangian path integral approach to the qubit

该研究基于广群概念推广施温格量子力学图像，提出量子比特的拉格朗日路径积分方法，给出历史求和计算方式，揭示传播子幺正性带来的拉格朗日量量子化条件及特例。

The coevent formulation of quantum theory

Understanding quantum theory has been a subject of debate from its birth. Many different formulations and interpretations have been proposed. Here we examine a recent novel formulation, namely the coevents formulation. It is a histories formulation and has as starting point the Feynman path integral and the decoherence functional. The new ontology turns out to be that of a coarse-grained history. We start with a quantum measure defined on the space of histories, and the existence of zero covers rules out single-history as potential reality (the Kochen Specker theorem casted in histories form i…

The Spacetime Approach to Quantum Mechanics

Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schrödinger-Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. Sum-over-histories quantum mechanics can be generalized to deal with spacetime alternatives that are not "at definite moments of time". An example in field theory is the set of alternative ranges of values of a field averaged over a spacetime region. An example in particle mechanics …

Real-time correlators in chaotic quantum many-body systems

We study real-time local correlators $\langle\mathcal{O}(\mathbf{x},t)\mathcal{O}(0,0)\rangle$ in chaotic quantum many-body systems. These correlators show universal structure at late times, determined by the dominant operator-space Feynman trajectories for the evolving operator $\mathcal{O}(\mathbf{x},t)$. The relevant trajectories involve the operator contracting to a point at both the initial and final time and so are structurally different from those dominating the out-of-time-order correlator. In the absence of conservation laws, correlations decay exponentially: $\langle\mathcal{O}(\math…

History operators in quantum mechanics

It is convenient to describe a quantum system at all times by means of a "history operator" $C$, encoding measurements and unitary time evolution between measurements. These operators naturally arise when computing the probability of measurement sequences, and generalize the "sum over position histories " of the Feynman path-integral. As we argue in the present note, this description has some computational advantages over the usual state vector description, and may help to clarify some issues regarding nonlocality of quantum correlations and collapse. A measurement on a system described by $C$…

由传播子和路径积分得到的星指数

Star exponentials from propagators and path integrals

本文建立了形变量子化中星指数与费曼路径积分的关系，通过将传播子表示为星指数的积分变换，构造了不依赖形式级数收敛性的星指数，并给出了有限维系统的星积分类似量子场论表示。

Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with Applications

We derive differential equations for the modified Feynman propagator and for the density operator describing time-dependent measurements or histories continuous in time. We obtain an exact series solution and discuss its applications. Suppose the system is initially in a state with density operator $ρ(0)$ and the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured continuously from $t = 0$ to $T$, where $E$ is a projector obeying $Eρ(0) E = ρ(0)$ and $U(t)$ a unitary operator obeying $U(0) = 1$ and some smoothness conditions in $t$. Then the probability of always finding $E(t) = 1$ fr…

Complex action suggests future-included theory

In quantum theory its action is usually taken to be real, but we can consider another theory whose action is complex. In addition, in the Feynman path integral, the time integration is usually performed over the period between the initial time $T_A$ and some specific time, say, the present time $t$. Besides such a future-not-included theory, we can consider the future-included theory, in which not only the past state $| A(T_A) \rangle$ at the initial time $T_A$ but also the future state $| B(T_B) \rangle$ at the final time $T_B$ is given at first, and the time integration is performed over the…

源自时空量子作用量的路径积分

Path Integrals from Spacetime Quantum Actions

本研究建立量子作用量算符与费曼路径积分的关联，提出将历史求和等同于量子迹的新形式体系，为路径积分的量子计算及协变时空对称处理提供新途径。