New symmetries, conserved quantities and gauge nature of a free Dirac field

• URL: http://arxiv.org/abs/2209.00460v1
• Date: Wed, 31 Aug 2022 13:49:49 GMT
• Title: New symmetries, conserved quantities and gauge nature of a free Dirac field
• Authors: Vladimir V. Kassandrov and Nina V. Markova
• Abstract summary: We present and amplify some of our previous statements on non-canonical interrelations between the solutions to free Dirac equation (DE) and Klein-Gordon equation (KGE) We demonstrate that all the solutions to the DE can be obtained via differentiation of a corresponding pair of the KGE solutions for a doublet of scalar fields.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present and amplify some of our previous statements on non-canonical interrelations between the solutions to free Dirac equation (DE) and Klein-Gordon equation (KGE). We demonstrate that all the solutions to the DE (possessing point- or string-like singularities) can be obtained via differentiation of a corresponding pair of the KGE solutions for a doublet of scalar fields. On this way we obtain a "spinor analogue" of the mesonic Yukawa potential and previously unknown chains of solutions to DE and KGE, as well as an exceptional solution to the KGE and DE with a finite value of the field charge ("localized" de Broglie wave). The pair of scalar "potentials" is defined up to a gauge transformation under which corresponding solution of the DE remains invariant. Under transformations of Lorentz group, canonical spinor transformations form only a subclass of a more general class of transformations of the solutions to DE upon which the generating scalar potentials undergo transformations of internal symmetry intermixing their components. Under continious turn by one complete revolution the transforming solutions, as a rule, return back to their initial values ("spinor two-valuedness" is absent). With arbitrary solution of the DE one can associate, apart of the standard one, a non-canonical set of conserved quantities, positive definite "energy" density among them, and with any KGE solution -- positive definite "probability density", etc. Finally, we discuss a generalization of the proposed procedure to the case when the external electromagnetic field is present

Related papers

• Entanglement resolution of free Dirac fermions on a torus [68.8204255655161]
  We first evaluate the SRE for massless Dirac fermions in a system at finite temperature and size. The charge-dependent entropies turn out to be equally distributed among all the symmetry sectors at leading order.
  arXiv  Detail & Related papers  (2022-12-14T14:54:35Z)
• $O(N^2)$ Universal Antisymmetry in Fermionic Neural Networks [107.86545461433616]
  We propose permutation-equivariant architectures, on which a determinant Slater is applied to induce antisymmetry. FermiNet is proved to have universal approximation capability with a single determinant, namely, it suffices to represent any antisymmetric function. We substitute the Slater with a pairwise antisymmetry construction, which is easy to implement and can reduce the computational cost to $O(N2)$.
  arXiv  Detail & Related papers  (2022-05-26T07:44:54Z)
• Relativistic dynamical inversion in manifestly covariant form [0.0]
  The Relativistic Dynamical Inversion technique is a novel tool for finding analytical solutions to the Dirac equation. The most remarkable feature of the new method is the ease of performing non-trivial change of reference frames. A whole family of normalizable analytic solutions to the Dirac equation is constructed.
  arXiv  Detail & Related papers  (2022-05-24T10:19:28Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• General solution vs spin invariant eigenstates of the Dirac equation with the Coulomb potential [0.0]
  Solutions of the Dirac equation for an electron in the Coulomb potential are obtained using operator invariants of the equation. It is shown for the first time that these invariants determine electron spatial probability amplitude and spin polarization in each quantum state.
  arXiv  Detail & Related papers  (2021-11-16T15:27:56Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach [51.819912248960804]
  We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
  arXiv  Detail & Related papers  (2021-03-12T13:16:18Z)
• 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)
• Unification of massless field equations solutions for any spin [0.0]
  A unification of Klein--Gordon, Dirac, Maxwell, Rarita--Schwinger and Einstein equations exact solutions is presented. The method is based on writing all of the relevant dynamical fields in terms of products and derivatives of pre--potential functions.
  arXiv  Detail & Related papers  (2021-02-02T13:38:28Z)
• The hydrogen atom: consideration of the electron self-field [0.0]
  We substantiate the need for account of the proper electromagnetic field of the electron in the canonical problem of hydrogen. We demonstrate that only particular classes of solutions, "nonlinear" analogues of s- and p-states, can be obtained through decomposition of a solution in a series.
  arXiv  Detail & Related papers  (2021-01-05T21:52:41Z)
• General solution of the Dirac equation with the Coulomb potential [0.0]
  The general solution of the Dirac equation with the Coulomb potential is shown to contain free parameters. The spatial distributions of these characteristics are shown to depend essentially on the invariant set.
  arXiv  Detail & Related papers  (2020-09-17T10:39:03Z)

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.