On a Quantum Action Principle
Natalya Gorobey, Alexander Lukyanenko
一个量子版本的作用原理制定的波泛函的实参数。得到了谐振子量子作用量的经典极限。
A quantum version of the action principle is formulated in terms of real parameters of a wave functional. The classical limit of the quantum action of a harmonic oscillator is obtained.
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Quantum Action Principle in Relativistic Mechanics
一个量子版本的作用原理被认为是在一个自由的相对论粒子的情况下。得到了量子作用量的经典极限。
We use the Schwinger action principle to obtain the equations of motion in the Koopman-von Neumann operational version of classical mechanics. We restrict our analysis to non-dissipative systems. We show that the Schwinger action principle can be interpreted as a variational principle for velocity-independent forces.
Lagrangian Densities and Principle of Least Action in Nonrelativistic Quantum Mechanics
最小作用量原理与简单的拉格朗日密度一起使用，涉及波函数的二阶导数，以获得薛定谔方程。从这个简单的拉格朗日密度得到的哈密尔顿密度表明，哈密尔顿方程也给出了薛定谔方程。这个简单的拉格朗日密度等价于具有一阶导数的标准拉格朗日密度。对于一个与时间无关的系统，最小作用量原理归结为能量变分原理。对于时变系统，最小作用量原理给出时变近似。利用含时多玻色子系统的Hartree乘积试探波函数，应用最小作用量原理，得到描述玻色-爱因斯坦凝聚体的Gross-Pitaevskii方程.
An analysis of the path-integral approach to quantum theory motivates the hypothesis that two experiments with the same classical action should have dual ontological descriptions. If correct, this hypothesis would not only constrain realistic interpretations of quantum theory, but would also act as a constructive principle, allowing any realistic model of one experiment to generate a corresponding model for its action-dual. Two pairs of action-dual experiments are presented, including one experiment that violates the Bell inequality and yet is action-dual to a single particle. The implications…
The action reaction principle is violated in the standard formulation of Quantum Mechanics, so that its phase space is incomplete. Moreover, projection of state of a quantum system under indirect measurement, when there are alternative virtual paths and one of them is discarded by negative detection implies, according to the action reaction principle, a reaction on the detector, although its macroscopic state does not change. If all interactions are local, mediated by fields with relativistically causal evolution, some system, different from the particle which follows another path, must locall…
A discrete action principle for general quantum automata is proposed. This action principle is particularized to Discrete Time Quantum Walks (DTQWs) and then extended into an energy and momentum preserving, manifestly covariant formulation. Space-time coordinates are introduced as new variables of the action and their equations of motion enforce energy and momentum conservation. This guarantees that the proposed action can be used to build future, DTQW-based self-consistent models of spinors interacting with gauge fields. A discrete stress-energy tensor for the DTQW is also obtained by functio…
Born's principle and Action-Reaction problem
在最近的一篇论文中，A.Valentini试图在玻姆理论的框架下，利用经典H-定理和一个适当的量子H-定理的定义，得到玻恩原理作为亚量子热寂的结果。在本文中，我们将显示的可能性，解决问题的作用-反应的不对称性存在于玻姆的理论，通过修改Valentini的程序。我们也得到了他的主要成果。
From Fermat Principle to Wave equation
费马原理表明，光选择时间上最短的路径，这种“运动”的作用量是观测到的时间，它没有洛伦兹不变性。在本文中，我们展示了如何从相对论作用量得到这种作用量，以及如何从这种作用量得到光的经典波动方程。
The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a $|Ψ|^2$-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton's principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.
Born's Principle, Action-Reaction Problem and Arrow of Time
在玻姆理论的框架下，利用经典的${\cal H}$ -定理和一个真量子${\cal H}$ -定理的定义，得到了作为亚量子热寂结果的玻恩原理.我们将展示解决玻姆理论中存在的作用-反应不对称问题和我们程序中的时间箭头问题的可能性。
Recently in [Phys. Rev. D $99$ $(2019)$ 104010] the non-relativistic Feynman propagator for harmonic oscillator system is presented when the generalized uncertainty principle is employed. In this short comment it is shown that the expression is incorrect. We also derive the correct expression of it.
Quantum Mechanics Based on an Extended Least Action Principle and Information Metrics of Vacuum Fluctuations
本文基于扩展最小作用原理和真空涨落信息度量，推导出量子力学的基本框架，并揭示了Bohm势的起源及广义薛定谔方程的数学基础。
Demonstration of the quantum principle of least action with single photons
该研究通过直接测量单光子波函数实验观测费曼路径积分传播子，并据其极值得到经典轨迹，首次在量子层面验证了最小作用量原理。
A new form of covariant quantum theory based on a quantum version of the action principle is considered for the case of a free bosonic string. The central idea of the new approach is to delay conditions of stationarity of the classical action with respect to Lagrangian multipliers up to the quantum level where delayed conditions of stationarity are imposed on a quantum action. Physical states of the ordinary covariant quantum theory are replaced by well defined stationary states as those which obey quantum action principle. The stationary states have well defined energies.
Quantum Action Principle formulated earlier is used as a ground for a probabilistic interpretation of one-particle relativistic quantum mechanics. In this new approach the probability "flows" in the Minkowsky space being dependent on an inner time parameter which we interpret as a particle life time. The life time is determined as a function of observable parameters of the real experiment by means of an additional condition of stationarity for the quantum action.
Starting from the earlier notions of stationary action principles, we show how Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements is described. Part II will discuss the variational formulation of quantum electrodynamics and the development of source theory.
Despite the importance of the variational principles of physics, there have been relatively few attempts to consider them for a realistic framework. In addition to the old teleological question, this paper continues the recent discussion regarding the modal involvement of the principle of least action and its relations with the Humean view of the laws of nature. The reality of possible paths in the principle of least action is examined from the perspectives of the contemporary metaphysics of modality and Leibniz's concept of essences or possibles striving for existence. I elaborate a modal int…
A weak invariant associated with a master equation is characterized in such a way that its spectrum is not constant in time but its expectation value is conserved under time evolution generated by the master equation. Here, an intriguing relationship between the concept of weak invariants and the action principle for master equations based on the auxiliary operator formalism is revealed. It is shown that the auxiliary operator can be thought of as a weak invariant.
We present a new derivation of the proof for the TCP/CPT Theorem using the Dynamical Principle and Variation of Action methods first defined by Schwinger in 1951. This new proof will significantly extend the TCP Theorem beyond the original proofs by Pauli-Luders and Jost, which were significantly constrained by limits of free quantum fields and the asymptotic condition. This paper gives a more fundamental proof based on invariance of the Variation of Action with interactions included and no free field or asymptotic condition on the quantum fields. This new proof for TCP/CPT can now be applied …
In this paper, we show that the difficulties of interpretation of the principle of least action concerning "final causes" or "efficient causes" are due to the existence of two different actions, the "Euler-Lagrange action" (or classical action) and the "Hamilton-Jacobi action". These two actions, which are not clearly differentiated in the texbooks, are solutions to the same Hamilton-Jacobi equation, but with very different initial conditions: smooth conditions for the Hamilton-Jacobi action, singular conditions for the Euler-Lagrange action. There are related by the Minplus Path Integral whic…
Starting from the earlier notions of stationary action principles, we show how Julian Schwinger's Quantum Action Principle descended from Dirac's formulation, which independently led Feynman to his path-integral formulation of quantum mechanics. The connection between the two is brought out, and applications are discussed. The Keldysh-Schwinger time-cycle method of extracting matrix elements in nonequilibrium situations is described. The variational formulation of quantum field theory and the development of source theory constitute the latter part of this work. In this document, derived from S…
Violation of the action-reaction principle is shown to occur in the van der Waals interaction between two atoms, one of which is excited. It is accompanied by the transfer of linear momentum to the electromagnetic vacuum. The vacuum momentum results from the asymmetric interference of the virtual photons scattered off each atom along the interatomic direction, which is in itself a manifestation of the optical theorem. This momentum, of equal strength and opposite direction to the momentum gained by the two-atom system, is ultimately released through directional spontaneous emission. A quantita…
Quantum Scalar Field Theory Based on the Extended Least Action Principle
本文基于扩展最小作用原理，推导出非相对论量子力学和相对论量子标量场理论的薛定谔方程，通过引入信息度量和随机场波动，建立了新的理论框架。
We introduce an action principle for a class of integer valued cellular automata and obtain Hamiltonian equations of motion. Employing sampling theory, these discrete deterministic equations are invertibly mapped on continuum equations for a set of bandwidth limited harmonic oscillators, which encode the Schrödinger equation. Thus, the linearity of quantum mechanics is related to the action principle of such cellular automata and its conservation laws to discrete ones.
Action principle formulation for motion of extended bodies in General Relativity
本文给出了在弱引力场极限下研究广义相对论中扩展体运动的作用量原理公式。这就给出了耦合到引力场的任意阶多极矩的经典运动方程。特别地，由于八极矩的一个新的力被获得。在量子干涉实验中，由于所有多极矩的耦合，这种作用也产生引力诱导的相移。
This paper explores the issue of the unification of three languages of physics, the geometric language of forces, geometric language of fields or 4-dimensional space-time, and probabilistic language of quantum mechanics. On the one hand, equations in each language may be derived from the Principle of Least Action (PLA). On the other hand, Feynman's path integral method could explain the physical meaning of PLA. The axioms of classical and relativistic mechanics can be considered as consequences of Feynman's formulation of quantum mechanics.
Various gedanken experiments of quantum gravity phenomenology in search of a complete theory of gravity near the Planck scale indicate a modification of the Heisenberg uncertainty principle to the generalized uncertainty principle (GUP). This modification leads to nontrivial contributions on the Hamiltonian of a nonrelativistic particle moving in an arbitrary potential. In this paper we study the path integral representation of a particle moving in an arbitrary potential using the most general form of the GUP containing both the linear and quadratic contributions in momentum. First we work out…
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