Relativistic Bohmian mechanics from scalar gravity
Benjamin Koch
在这篇文章中，我们表明，相对论性玻姆力学的基本方程的单粒子可以从弯曲时空的标量理论。
In this article we show that the fundamental equations of relativistic Bohmian mechanics for a single particle can be derived from a scalar theory of curved space-time.
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Bohmian mechanics in relativistic quantum mechanics, quantum field theory and string theory
我提出了一个简短的概述我最近的成就在相对论量子力学，量子场论和弦论的玻姆解释。这包括粒子轨迹的相对论协变玻姆方程，粒子的产生和毁灭问题，费米场的玻姆解释，以及基于De Donder-Weyl协变正则形式主义的场和弦的内在玻姆量子化。
Since Bohmian mechanics is explicitly nonlocal, it is widely believed that it is very hard, if not impossible, to make Bohmian mechanics compatible with relativistic quantum field theory (QFT). I explain, in simple terms, that it is not hard at all to construct a Bohmian theory that lacks Lorentz covariance, but makes the same measurable predictions as relativistic QFT. All one has to do is to construct a Bohmian theory that makes the same measurable predictions as QFT in one Lorentz frame, because then standard relativistic QFT itself guarantees that those predictions are Lorentz invariant. I…
It is shown how Fermionic material particles can emerge from a covariant formulation of the de Broglie-Bohm theory. Material particles are continuous fields, formed as the eigenvalue of the Schrodinger field operator, evaluated along a Bohmian trajectory. The motivation for this work is due to a theorem proved by Malament that states there cannot be a relativistic quantum mechanics of localizable particles.
Probability in relativistic Bohmian mechanics of particles and strings
尽管由守恒克莱因-戈登流的积分曲线给出的玻姆轨迹可能涉及时间上的反向运动，粒子位置的自然相对论概率密度是明确定义的。玻姆理论预测的结果与传统量子理论的统计预测结果有细微的偏差，但似乎目前还没有实验能排除这个理论。只要给出一个较好的时空叶理，对多粒子或弦的推广就很简单了。
Relativistic Bohmian interpretation of quantum mechanics
我提出了一个相对论协变版本的量子力学的玻姆解释，并讨论了相应的可测量的预测。协方差被编码在非定域量子势作为标量变换的事实中，这是非定域波函数作为标量变换的事实的结果。用决定论的玻姆解释所能得到的可测量的预言，用常规解释是得不到的，这仅仅是因为常规的概率解释在相对论性量子力学的情况下不起作用。
In non-relativistic Bohmian mechanics the universe is represented by a probability space whose sample space is composed of the Bohmian trajectories. In relativistic Bohmian mechanics an entire class of empirically equivalent probability spaces can be defined, one for every foliation of spacetime. In the literature the hypothesis has been advanced that a single preferred foliation is allowed, and that this foliation derives from the universal wave function by means of a covariant law. In the present paper the opposite hypothesis is advanced, i.e., no law exists for the foliations and therefore …
Overcoming a challenge for Bohmian mechanics
针对玻姆力学因粒子运动不限于波函数相位梯度而受到的挑战，本文指出玻姆速度由连续性方程定义，并通过显式构造合适速度克服了该挑战。
Bohmian particle trajectories in relativistic fermionic quantum field theory
德布罗意-玻姆对量子力学和量子场论的解释被推广到描述相对论性费米子粒子和反粒子的轨迹，并提供了它们产生和毁灭过程的因果描述。本文发展了量子系统因果解释的一般方法，并将其应用于由c-数值波泛函表示的费米子量子场论的因果解释。
Strings, world-sheet covariant quantization and Bohmian mechanics
基于De Donder-Weyl协变正则形式的量子化的协变正则方法被用来描述玻色弦的世界片协变量子化。为了与标准的非协变正则量子化保持一致，必须采用一个玻姆确定性隐变量运动方程。这样，弦论就为量子力学的测量问题提供了一个解决方案。
Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an objective definition of particles makes the Bohmi…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating the squared norm of the wave function as a space-time probability density. The particle's configurations evolve in space-time in terms of a parameter σ, with dimensions of time. In this work this model is further analyzed and extended to the case of an interaction with an external electromagnetic field. The physical meaning of σ is explored. Two special situat…
In classical relativistic mechanics, a "preferred" proper direction in spacetime for each particle is determined by the direction of its 4-momentum. Analogously, for each quantum particle we find a local direction uniquely determined by the many-particle wave function, which for each particle defines the proper foliation of spacetime. This can be used to formulate a relativistic-covariant version of Bohmian mechanics, with equivariant probability density on proper hypersurfaces.
Bohmian mechanics can be generalized to a relativistic theory without preferred foliation, with a price of introducing a puzzling concept of spacetime probability conserved in a scalar time. We explain how analogous concept appears naturally in classical statistical mechanics of relativistic particles, with scalar time being identified with the proper time along particle trajectories. The conceptual understanding of relativistic Bohmian mechanics is significantly enriched by this classical insight. In particular, the analogy between classical and Bohmian mechanics suggests the interpretation o…
Many-fingered time Bohmian mechanics
多粒子量子力学和量子场论的多指时间（MFT）表述是一个自然的框架，它克服了表现出非定域性的纠缠系统中的“瞬时坍缩”问题。相应的Bohmian解释也可以用MFT beables来表述，它通过使用与标准Bohmian解释不同的本体来解释在一定距离处的瞬时超距作用的问题。通过量子测量恢复了通常的单时间粒子位置和场的出现。
We study the de Broglie-Bohm interpretation of bosonic relativistic quantum mechanics and argue that the negative densities and superluminal velocities that appear in this interpretation do not lead to inconsistencies. After that, we study particle trajectories in bosonic quantum field theory. A new continuously changing hidden variable - the effectivity of a particle (a number between 0 and 1) - is postulated. This variable leads to a causal description of processes of particle creation and destruction. When the field enters one of nonoverlapping wave-functional packets with a definite number…
Bohmian Zitterbewegung
本研究提出一种新型玻姆量子相对论模型，通过引入不可直接观测的独立时间参数推导推广的Zitterbewegung效应，修正了量子势的作用方式并给出相对论版不确定性原理。
Quantum statistical mechanics from a Bohmian perspective
本研究基于多粒子位置空间的概率流构建量子统计力学一般表述，提出对应的玻姆轨迹诠释，在与标准量子理论预测一致的前提下，为宏观量子统计现象提供直观微观解释，并探讨了熵、混态及热力学的玻姆视角理解。
It is generally believed that the de Broglie-Bohm model does not admit a particle interpretation for massive relativistic spin-0 particles, on the basis that particle trajectories cannot be defined. We show this situation is due to the fact that in the standard (canonical) representation of the Klein-Gordon equation the wavefunction systematically contains superpositions of particle and anti-particle contributions.\ We argue that by working in a Foldy-Wouthuysen type representation uncoupling the particle from the anti-particle evolutions, a positive conserved density for a particle and associ…
Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which evolves according to some Schrödinger equation with a Hamiltonian that depends on the classical degrees of freedom. The classical degrees of freedom satisfy classical equations that depend on the expectation values of quantum operators. In this paper, we study an alternative approach based on Bohmian mechanics. In Bohmian mechanics the quantum system is not only d…
Attaching Theories of Consciousness to Bohmian Quantum Mechanics
量子力学的德布罗意-玻姆理论（这里简称为玻姆力学或BM）[1-10]是“裸”量子力学的扩充（裸理论由算符代数和设定这些算符期望值的量子态给出），包括一个确定的历史或玻姆轨迹。这种确定的轨迹使BM比大多数其他形式的量子力学（QM）更具有经典的味道（尽管轨迹在其演化过程中肯定具有高度非定域性和其他非经典的方面），但要看这是否对有意识的存在的观察产生了影响，我们需要将有意识知觉的理论与BM和其他形式的QM联系起来。在这里，我将为BM提出各种形式的意识理论，我将称之为{ \it Sensible Bohmian Mechanics}（SBM），并将它们与我提出的一种与纯粹QM相关的意识理论进行比较，我称之为{ \it Sensible量子力学}（SQM）[11-15]。我发现，只有某些特殊形式的SBM会给出本质上类似的预测SQM，虽然更广泛的类可能在实践中无法区分任何单一的观察者。我也仍然怀疑，一个可行的完整形式的SBM会像一个可行的完整形式的SQM一样简单地描述宇宙，但是当然，现在知道我们宇宙的最简单的完整理论的形式是什么还为时过早。
Covariant canonical quantization of fields and Bohmian mechanics
基于经典的场论的De Donder-Weyl协变正则公式，提出了一种显协变正则场量子化方法.由于协变性，场的空间和时间变元被同等对待。为了同时达到协变性和与闵可夫斯基时空中场的标准非协变正则量子化的一致性，有必要采用协变的量子场论的玻姆公式。由于纯粹的量子效应，时空的优先叶理动态地出现。讨论了该方法在一个简单的时间重参数化不变系统和量子引力中的应用，并与传统的非协变Wheeler-DeWitt方法进行了比较。
The Lorentz-invariant S-matrix elements in interacting quantum field theory (QFT) are used to represent the QFT state by a Lorentz-invariant many-time wave function. Such a wave function can be used to describe inelastic scattering processes (involving particle creation and destruction) by Bohmian particle trajectories satisfying relativistic-covariant equations of motion.
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