How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem

• URL: http://arxiv.org/abs/2409.00677v1
• Date: Sun, 1 Sep 2024 09:41:02 GMT
• Title: How a Space-Time Singularity Helps Remove the Ultraviolet Divergence Problem
• Authors: Joscha Henheik, Bipul Poudyal, Roderich Tumulka,
• Abstract summary: Particle creation terms in quantum Hamiltonians are usually ultraviolet divergent and thus mathematically ill defined. Previous papers showed that this approach works in the non-relativistic regime, but particle creation is mostly relevant in the relativistic case after all. We prove rigorously the existence of well-defined, self-adjoint Hamiltonians with particle creation at the singularity, based on interior-boundary conditions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Particle creation terms in quantum Hamiltonians are usually ultraviolet divergent and thus mathematically ill defined. A rather novel way of solving this problem is based on imposing so-called interior-boundary conditions on the wave function. Previous papers showed that this approach works in the non-relativistic regime, but particle creation is mostly relevant in the relativistic case after all. In flat relativistic space-time (that is, neglecting gravity), the approach was previously found to work only for certain somewhat artificial cases. Here, as a way of taking gravity into account, we consider curved space-time, specifically the super-critical Reissner-Nordstr\"om space-time, which features a naked timelike singularity. We find that the interior-boundary approach works fully in this setting; in particular, we prove rigorously the existence of well-defined, self-adjoint Hamiltonians with particle creation at the singularity, based on interior-boundary conditions. We also non-rigorously analyze the asymptotic behavior of the Bohmian trajectories and construct the corresponding Bohm-Bell process of particle creation, motion, and annihilation. The upshot is that in quantum physics, a naked space-time singularity need not lead to a breakdown of physical laws, but on the contrary allows for boundary conditions governing what comes out of the singularity and thereby removing the ultraviolet divergence.

Related papers

• Quantum Isotropic Universe in RQM Analogy: the Cosmological Horizon [0.0]
  We investigate the quantum dynamics of the isotropic Universe in the presence of a free massless scalar field. We show how the introduction of a "turning point" in the Universe evolution allows to overcome an intrinsic ambiguity in representing the expanding and collapsing Universe.
  arXiv  Detail & Related papers  (2024-04-10T14:45:56Z)
• A non-hermitean momentum operator for the particle in a box [49.1574468325115]
  We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example. The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
  arXiv  Detail & Related papers  (2024-03-20T12:51:58Z)
• 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)
• Parametrically driving a quantum oscillator into exceptionality [0.0]
  We consider the nature of exceptional points arising in quantum systems described within an open quantum systems approach. In particular, we discuss how the populations, correlations, squeezed quadratures and optical spectra crucially depend on being above or below the exceptional point. Our results invite the experimental probing of quantum resonators under two-photon driving.
  arXiv  Detail & Related papers  (2023-07-07T13:27:20Z)
• A quantum trajectory analysis of singular wave functions [0.0]
  The Schr"odinger equation admits smooth and finite solutions that spontaneously evolve into a singularity, even for a free particle. We resort to the notion of quantum trajectories to reinterpret this singular behavior.
  arXiv  Detail & Related papers  (2023-01-30T19:00:01Z)
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue [68.8204255655161]
  We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime. We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
  arXiv  Detail & Related papers  (2022-12-02T18:28:23Z)
• Extended Uncertainty Principle via Dirac Quantization [0.0]
  We show that generic infrared (IR) modifications arise when we describe quantum theory in curved spacetime. We study particle dynamics in an arbitrary curved spacetime by embedding them in a higher-dimensional flat geometry.
  arXiv  Detail & Related papers  (2022-04-04T18:23:30Z)
• The Time-Evolution of States in Quantum Mechanics [77.34726150561087]
  It is argued that the Schr"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states replacing the Schr"odinger equation is formulated within the so-called ETH-Approach to Quantum Mechanics.
  arXiv  Detail & Related papers  (2021-01-04T16:09:10Z)
• Towards a Probabilistic Foundation of Relativistic Quantum Theory: The One-Body Born Rule in Curved Spacetime [0.0]
  This work is based on generalizing the quantum-mechanical Born rule for determining particle position probabilities to curved spacetime. A principal motivator for this research has been to overcome internal mathematical problems of quantum field theory. The main contribution of this work to the mathematical physics literature is the development of the Lagrangian picture.
  arXiv  Detail & Related papers  (2020-12-09T18:22:18Z)
• Bell's theorem for trajectories [62.997667081978825]
  A trajectory is not an outcome of a quantum measurement, in the sense that there is no observable associated with it. We show how to overcome this problem by considering a special case of our generic inequality that can be experimentally tested point-by-point in time.
  arXiv  Detail & Related papers  (2020-01-03T01:40:44Z)
• Projection evolution and quantum spacetime [68.8204255655161]
  We discuss the problem of time in quantum mechanics. An idea of construction of a quantum spacetime as a special set of the allowed states is presented. An example of a structureless quantum Minkowski-like spacetime is also considered.
  arXiv  Detail & Related papers  (2019-10-24T14:54:11Z)

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.