Klein-Gordon equation within the real Hilbert space formalism

• URL: http://arxiv.org/abs/2510.16602v1
• Date: Sat, 18 Oct 2025 17:58:13 GMT
• Title: Klein-Gordon equation within the real Hilbert space formalism
• Authors: Cristiano Rosa, Sergio Giardino,
• Abstract summary: The complex formulation comprises hermitian and non-hermitian cases, while the quaternionic solutions additionally set in motion self-interacting particles.<n>The obtained autonomous particle solutions, as well as the Klein problem agree to the previously discovered self-interacting non-relativistic particle.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Within this article one finds the statement of the Klein-Gordon problem within the real Hilbert space formalism ($\mathbbm R$HS) in terms of complex wave functions, and in terms of quaternionic wave functions as well. The complex formulation comprises hermitian and non-hermitian cases, while the quaternionic solutions additionally set in motion self-interacting particles. The non-hermitian cases comprise non-conservative processes, while the self-interaction physically implies the increase of the effective mass of the particle, an effect that cannot be reproduced using a complex wave function. The obtained autonomous particle solutions, as well as the Klein problem agree to the previously discovered self-interacting non-relativistic particle, and thus reinforce $\mathbbm R$HS as viable and consistent way to explore open problems in quantum mechanics. Also important, the negative energy problem that plagues the usual formalism is eliminated within this approach.

Related papers

• Quantum self-interaction within an infinitely deep cavity [0.0]
  The solutions are considered in terms of complex wave functions, and also in terms of quaternionic wave functions.<n>The complex results reproduce the usual achievements established in the complex Hilbert space.<n>The quaternionic cases further admit the incidence of self-interaction, something that cannot be observed in complex solutions.
  arXiv  Detail & Related papers  (2026-02-08T13:01:06Z)
• Self-interacting quantum particles and the Dirac delta potential [0.0]
  Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions.<n>As has been previously determined, the real Hilbert space approach enables the possibility of self-interacting physical systems.
  arXiv  Detail & Related papers  (2025-11-18T12:28:11Z)
• Analogue black string in a quantum harmonic oscillator [49.1574468325115]
  We write the exact solution of the Klein-Gordon equation in the background of a chargeless, static black string.<n>The eigenvalue problem provides complex energy values for the particle, which may indicate the presence of quasinormal modes.<n>We show a simple quantum system that can imitate the particle in the black string background, whose solutions are also applications of the biconfluent Heun function.
  arXiv  Detail & Related papers  (2024-12-31T15:03:57Z)
• Non-Bloch self-energy of dissipative interacting fermions [4.41737598556146]
  The non-Hermitian skin effect describes the phenomenon of exponential localization of single-particle eigenstates near the boundary of the system. We explore its generalization to the many-body regime by investigating interacting fermions in open quantum systems. Our formulation provides a quantitative tool for investigating dissipative interacting fermions with non-Hermitian skin effect.
  arXiv  Detail & Related papers  (2024-11-20T19:08:24Z)
• Reproducing Kernel Hilbert Space Approach to Non-Markovian Quantum Stochastic Models [0.0]
  We give a derivation of the non-Markovian quantum state diffusion equation of Di'osi and Strunz. We show that the complex trajectories arises as a consequence of using the Bargmann-Segal representation of the bath.
  arXiv  Detail & Related papers  (2024-07-09T21:10:54Z)
• Closed-form solutions for the Salpeter equation [41.94295877935867]
  We study the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. The analytical extension of the Hamiltonian in the complex plane allows us to formulate the equivalent problem, namely the B"aumer equation. This B"aumera corresponds to the Green function of a relativistic diffusion process that interpolates between Cauchy for small times and Gaussian diffusion for large times.
  arXiv  Detail & Related papers  (2024-06-26T15:52:39Z)
• Klein-Gordon oscillators and Bergman spaces [55.2480439325792]
  We consider classical and quantum dynamics of relativistic oscillator in Minkowski space $mathbbR3,1$. The general solution of this model is given by functions from the weighted Bergman space of square-integrable holomorphic (for particles) and antiholomorphic functions on the K"ahler-Einstein manifold $Z_6$.
  arXiv  Detail & Related papers  (2024-05-23T09:20:56Z)
• Quantum electrodynamics of lossy magnetodielectric samples in vacuum: modified Langevin noise formalism [55.2480439325792]
  We analytically derive the modified Langevin noise formalism from the established canonical quantization of the electromagnetic field in macroscopic media. We prove that each of the two field parts can be expressed in term of particular bosonic operators, which in turn diagonalize the electromagnetic Hamiltonian.
  arXiv  Detail & Related papers  (2024-04-07T14:37:04Z)
• Ultracold Neutrons in the Low Curvature Limit: Remarks on the post-Newtonian effects [49.1574468325115]
  We apply a perturbative scheme to derive the non-relativistic Schr"odinger equation in curved spacetime. We calculate the next-to-leading order corrections to the neutron's energy spectrum. While the current precision for observations of ultracold neutrons may not yet enable to probe them, they could still be relevant in the future or in alternative circumstances.
  arXiv  Detail & Related papers  (2023-12-30T16:45:56Z)
• Denoising and Extension of Response Functions in the Time Domain [48.52478746418526]
  Response functions of quantum systems describe the response of a system to an external perturbation. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain.
  arXiv  Detail & Related papers  (2023-09-05T20:26:03Z)
• Wigner function dynamics with boundaries expressed as convolution [0.0]
  A method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. The solution is brought to a form of convolution of the free particle solution with some function, defined by the shape of the well.
  arXiv  Detail & Related papers  (2023-04-28T15:39:44Z)
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains [62.997667081978825]
  Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
  arXiv  Detail & Related papers  (2022-02-15T19:00:09Z)
• 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)

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.