Operators of quantum theory of Dirac's free field

• URL: http://arxiv.org/abs/2304.12182v9
• Date: Fri, 01 Nov 2024 09:25:20 GMT
• Title: Operators of quantum theory of Dirac's free field
• Authors: Ion I. Cotaescu,
• Abstract summary: The Pryce (e) spin and position operators of the quantum theory of Dirac's free field were re-defined and studied recently. A new spin symmetry and suitable spectral representations are presented. It is shown that an apparatus measuring these new observables may prepare and detect one-particle wave-packets moving uniformly without Zitterbewegung or spin dynamics.
• Score: 0.0
• License:
• Abstract: The Pryce (e) spin and position operators of the quantum theory of Dirac's free field were re-defined and studied recently with the help of a new spin symmetry and suitable spectral representations [I. I. Cot\u aescu, Eur. Phys. J. C (2022) 82:1073]. This approach is generalized here associating a pair of integral operators acting directly on particle and antiparticle wave spinors in momentum representation to any integral operator in configuration representation, acting on mode spinors. This framework allows an effective quantization procedure giving a large set of one-particle operators with physical meaning as the spin and orbital parts of the isometry generators, the Pauli-Lubanski and position operators or other spin-type operators proposed so far. A special attention is paid to the operators which mix the particle and antiparticle sectors whose off-diagonal associated operators have oscillating terms producing Zitterbevegung. The principal operators of this type including the usual coordinate operator are derived here for the first time. As an application, it is shown that an apparatus measuring these new observables may prepare and detect one-particle wave-packets moving uniformly without Zitterbewegung or spin dynamics, spreading in time normally as any other relativistic even non-relativistic wave-packet.

Related papers

• Lorentz-covariance of Position Operator and its Eigenstates for a massive spin $1/2$ field [0.0]
  We present a derivation of a position operator for a massive field with spin $1/2$. The eigenvalues of the field position operator correspond to the spatial components of the Lorentz-covariant space-time coordinate $4$-vector. We show that the field position operator can serve as a one-particle position operator for both particles and antiparticles.
  arXiv  Detail & Related papers  (2024-08-20T04:44:42Z)
• Conserved spin operator of Dirac's theory in spatially flat FLRW spacetimes [0.0]
  New conserved spin and angular momentum operators of Dirac's theory on spatially flat FLRW spacetimes are proposed. The one-particle spin and orbital angular momentum operators have the same form in any FLRW spacetime regardless their concrete geometries.
  arXiv  Detail & Related papers  (2023-08-10T15:02:52Z)
• Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
  Indistinguishability of particles is a fundamental principle of quantum mechanics. braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions. We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
  arXiv  Detail & Related papers  (2022-10-19T02:28:44Z)
• The role of Pryce's spin and coordinate operators in the theory of massive Dirac fermions [0.0]
  It is shown that the components of Pryce's spin operator of Dirac's theory are $SU(2)$ generators of a representation carried by the space of Pauli's spinors. The corresponding one-particle operators of quantum theory are derived showing how these are related to the isometry generators of the massive Dirac fermions of any polarization.
  arXiv  Detail & Related papers  (2022-06-22T12:21:14Z)
• Spin and Contextuality in Extended de Broglie-Bohm-Bell Quantum Mechanics [0.0]
  This paper introduces an extension of the de Broglie-Bohm-Bell-Bell formulation of quantum mechanics. It includes intrinsic particle degrees of freedom, such as spin, as elements of reality.
  arXiv  Detail & Related papers  (2022-03-26T09:29:57Z)
• From Quantum Field Theory to Quantum Mechanics [0.0]
  We construct the algebra of operators acting on the Hilbert spaces of Quantum Mechanics for systems of $N$ identical particles. We provide the explicit relation between the position and momentum operators acting in the former spaces and the field operators acting on the latter. It may not be possible to extend the procedure to interacting field theories since it relies crucially on particle number conservation.
  arXiv  Detail & Related papers  (2021-07-25T04:49:54Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)
• Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
  Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
  arXiv  Detail & Related papers  (2020-10-13T15:50:49Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Position and spin in relativistic quantum mechanics [68.8204255655161]
  The position and spin operators in the Foldy-Wouthuysen representation are quantum-mechanical counterparts of the classical position and spin variables. The spin-orbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the rest-frame spin are used.
  arXiv  Detail & Related papers  (2020-03-14T07:49:40Z)

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.