Tensorial Quantum Mechanics: Back to Heisenberg and Beyond

• URL: http://arxiv.org/abs/2410.09535v1
• Date: Sat, 12 Oct 2024 13:52:26 GMT
• Title: Tensorial Quantum Mechanics: Back to Heisenberg and Beyond
• Authors: Christian de Ronde, Raimundo Fernández Mouján, César Massri,
• Abstract summary: We will argue that while Heisenberg's approach was consistently developed, Dirac's axiomatic re-formulation was, instead, developed. We will present a new tensorial proposal which -- taking as a standpoint Heisenberg's original approach -- will prove capable.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work we discuss the establishment of Standard Quantum Mechanics (SQM) developed through Schr\"odinger's and Dirac's wave-vectorial reformulations of Heisenberg's original matrix mechanics. We will argue that while Heisenberg's approach was consistently developed -- taking as a standpoint the intensive patterns that were observed in the lab -- as an invariant-operational formalism, Dirac's axiomatic re-formulation was, instead, developed -- taking as a standpoint Schr\"odinger's wave mechanics and the methodological guide of Bohr and logical positivists -- as an essentially inconsistent "recipe" intended (but unable) to predict (binary) measurement outcomes. Leaving SQM behind and attempting to restore the consistent and coherent account of a real state of affairs, we will present a new tensorial proposal which -- taking as a standpoint Heisenberg's original approach -- will prove capable not only to extend the matrix formalism to a tensorial representation but also to account for new experimental phenomena.

Related papers

• Phenomenological quantum mechanics: deducing the formalism from experimental observations [0.0]
  We show that it is possible to derive in such a way a complete and fully functional formalism based on the structures of Hilbert spaces. The obtained formal description -- the bi-trajectory formalism -- turns out to be quite different from the standard state-focused formalism.
  arXiv  Detail & Related papers  (2024-10-18T12:17:30Z)
• The Dual Dynamical Foundation of Orthodox Quantum Mechanics [0.0]
  A deduction of the canonical commutation relations ( CCR) from the tenets of Matrix Mechanics. A discussion of the meaning of Schr"odinger's first derivation of the wave equation. A critical assessment of von Neumann's construction of unified quantum mechanics over Hilbert space.
  arXiv  Detail & Related papers  (2024-02-23T00:10:53Z)
• Relaxation of first-class constraints and the quantization of gauge theories: from "matter without matter" to the reappearance of time in quantum gravity [72.27323884094953]
  We make a conceptual overview of an approach to the initial-value problem in canonical gauge theories. We stress how the first-class phase-space constraints may be relaxed if we interpret them as fixing the values of new degrees of freedom.
  arXiv  Detail & Related papers  (2024-02-19T19:00:02Z)
• Beyond semiclassical time: dynamics in quantum cosmology [0.0]
  We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance. We discuss in which sense both approaches exhibit an inner product that is gauge-fixed via an operator version of the usual Faddeev-Popov procedure. We note that a conditional probability interpretation of the physical states is possible, so that both formalisms are examples of quantum mechanics with a relational dynamics.
  arXiv  Detail & Related papers  (2023-02-15T19:00:09Z)
• Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model [0.0]
  We modify the Heisenberg Uncertainty Principle into the Generalized Uncertainty Principle. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. We construct a quantum field theoretic toy model based on the Generalized Uncertainty Principle.
  arXiv  Detail & Related papers  (2021-09-30T16:55:48Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Quantum Mechanical description of Bell's experiment assumes Locality [91.3755431537592]
  Bell's experiment description assumes the (Quantum Mechanics-language equivalent of the classical) condition of Locality. This result is complementary to a recently published one demonstrating that non-Locality is necessary to describe said experiment. It is concluded that, within the framework of Quantum Mechanics, there is absolutely no reason to believe in the existence of non-Local effects.
  arXiv  Detail & Related papers  (2020-02-27T15:04:08Z)
• The (Quantum) Measurement Problem in Classical Mechanics [0.0]
  We show why this is not an "obvious" nor "self evident" problem for the theory of quanta. We discuss a representational realist account of both physical 'theories' and'measurement' We show how through these same set of presuppositions it is easy to derive a completely analogous paradox for the case of classical mechanics.
  arXiv  Detail & Related papers  (2020-01-01T17:07:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.