English
Related papers

Related papers: Born-Jordan Quantization and the Uncertainty Princ…

200 papers

A theory of nonunitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for…

Quantum Physics · Physics 2016-09-08 T. Hakioglu

Bohr's complementarity principle has long been a fundamental concept in quantum mechanics, positing that, within a given experimental setup, a quantum system (or quanton) can exhibit either its wave-like character, denoted as $W$, or its…

Quantum Physics · Physics 2024-12-24 Diego S. Starke , Marcos L. W. Basso , Jonas Maziero

The possibility to recover the which-way information, for example in the two slit experiment, is based on a natural but implicit assumption about the position of a particle {\it before} a position measurement is performed on it. This…

Quantum Physics · Physics 2007-06-13 Bruno Galvan

We show how the quantum potential arises in various ways and trace its connection to quantum fluctuations and Fisher information along with its realization in terms of Weyl curvature. It is a quantization factor for certain classical…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Robert Carroll

Heisenberg's uncertainty principle, which imposes intrinsic restrictions on our ability to predict the outcomes of incompatible quantum measurements to arbitrary precision, demonstrates one of the key differences between classical and…

Quantum Physics · Physics 2021-05-05 Yunlong Xiao , Kuntal Sengupta , Siren Yang , Gilad Gour

Wave-particle duality is one of the fundamental properties of matter and at the same time, one of the mysteries of modern physics. In this paper, we propose and analyze a new interpretation of the wave-particle duality, and propose a new…

Quantum Physics · Physics 2015-06-15 S. A. Rashkovskiy

A longstanding issue in attempts to understand the Everett (Many-Worlds) approach to quantum mechanics is the origin of the Born rule: why is the probability given by the square of the amplitude? Following Vaidman, we note that observers…

Quantum Physics · Physics 2018-10-26 Charles T. Sebens , Sean M. Carroll

There are known obstructions to a full quantization in the spirit of Dirac's approach, the most known being the Groenewold-van Hove no-go result. We show, following a suggestion of S. K. Kauffmann, that it is possible to construct a…

Mathematical Physics · Physics 2016-09-21 Maurice de Gosson

We have shown in previous work that the equivalence of the Heisenberg and Schr\"odinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work, we give further evidence that the…

Quantum Physics · Physics 2017-09-06 Maurice A. de Gosson

In this article we present the quantization process for Schwarzschild space-time in the context of Teleparallel gravity. In order to achieve such a goal we use the Weyl formalism that establishes a well defined correspondence between…

General Relativity and Quantum Cosmology · Physics 2014-07-18 S. C. Ulhoa , R. G. G. Amorim

A generalized Weyl quantization formalism for a particle on the circle investigated in \cite{1} is developed. A Wigner function for the state $\hat{\varrho}$ and the kernel $\mathcal{K}$ for a particle on the circle is defined and its…

Mathematical Physics · Physics 2015-06-18 Maciej Przanowski , Przemyslaw Brzykcy , Jaromir Tosiek

We revisit the uncertainty principle from the point of view suggested by A. Wigderson and Y. Wigderson. This approach is based on a primary uncertainty principle from which one can derive several inequalities expressing the impossibility of…

Functional Analysis · Mathematics 2025-04-30 Nuno Costa Dias , Franz Luef , João Nuno Prata

While the Born rule is traditionally introduced as a separate postulate of quantum mechanics, we show it emerges naturally from a modified Schr\"odinger equation that includes "small-signal truncation". This parallels the way quantum…

Quantum Physics · Physics 2025-05-19 Martin Weidner

We show that Weyl's abandoned idea of local scale invariance has a natural realization at the quantum level in pilot-wave (de Broglie-Bohm) theory. We obtain the Weyl covariant derivative by complexifying the electromagnetic gauge coupling…

Quantum Physics · Physics 2026-02-11 Indrajit Sen , Matthew Leifer

The peculiar uncertainty or randomness of quantum measurements stems from coherence, whose information-theoretic characterization is currently under investigation. Under the resource theory of coherence, it is interesting to investigate…

Quantum Physics · Physics 2019-10-25 Xiao Yuan , Qi Zhao , Davide Girolami , Xiongfeng Ma

An extension of the Weyl-Wigner-Moyal formulation of quantum mechanics suitable for a Dirac quantized constrained system is proposed. In this formulation, quantum observables are described by equivalent classes of Weyl symbols. The Weyl…

Quantum Physics · Physics 2009-11-06 Domingo J. Louis-Martinez

The theory of Non-Relativistic Quantum Mechanics was created (or discovered) back in the 1920's mainly by Schr\"odinger and Heisenberg, but it is fair enough to say that a more modern and unified approach to the subject was introduced by…

Quantum Physics · Physics 2013-01-01 Augusto Cesar Lobo , Clyffe de Assis Ribeiro

Attempts for a geometrical interpretation of Quantum Theory were made, notably the deBroglie-Bohm formulation. This was further refined by Santamato who invoked Weyl's geometry. However these attempts left a number of unanswered questions.…

General Physics · Physics 2007-05-23 B. G. Sidharth

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary…

funct-an · Mathematics 2009-10-28 R. Aldrovandi , L. A. Saeger

The Born rule, a foundational axiom used to deduce probabilities of events from wavefunctions, is indispensable in the everyday practice of quantum physics. It is also key in the quest to reconcile the ostensibly inconsistent laws of the…