Generalized uncertainty principle or curved momentum space?

• URL: http://arxiv.org/abs/2110.11067v3
• Date: Thu, 9 Dec 2021 07:49:40 GMT
• Title: Generalized uncertainty principle or curved momentum space?
• Authors: Fabian Wagner
• Abstract summary: Curved momentum space is at the heart of similar applications such as doubly special relativity. We introduce a duality between theories yielding generalized uncertainty principles and quantum mechanics on nontrivial momentum space. We explicitly derive the vielbein corresponding to a generic generalized uncertainty principle in $d$ dimensions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The concept of minimum length, widely accepted as a low-energy effect of quantum gravity, manifests itself in quantum mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at the heart of similar applications such as doubly special relativity. We introduce a duality between theories yielding generalized uncertainty principles and quantum mechanics on nontrivial momentum space. In particular, we find canonically conjugate variables which map the former into the latter. In that vein, we explicitly derive the vielbein corresponding to a generic generalized uncertainty principle in $d$ dimensions. Assuming the predominantly used quadratic form of the modification, the curvature tensor in momentum space is proportional to the noncommutativity of the coordinates in the modified Heisenberg algebra. Yet, the metric is non-Euclidean even in the flat case corresponding to commutative space, because the resulting momentum basis is noncanonical. These insides are used to constrain the curvature and the deviation from the canonical basis.

Related papers

• Second-Order Moment Quantum Fluctuations and Quantum Equivalence Principle [0.0]
  We find that the second-order moment quantum fluctuations are actually distinguished into two parts: a dynamic part and a geometric part. The dynamic part is indeed mass-dependent and governed by a non-zero Hamiltonian in a non-general sigma-covariant inertial frame. The geometric part is mass-independent and universal, so it is only this part measures the universal second-order moment quantum fluctuation of the spacetime.
  arXiv  Detail & Related papers  (2024-08-19T01:26:01Z)
• 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)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Does the Universe have its own mass? [62.997667081978825]
  The mass of the universe is a distribution of non-zero values of gravitational constraints. A formulation of the Euclidean quantum theory of gravity is also proposed to determine the initial state. Being unrelated to ordinary matter, the distribution of its own mass affects the geometry of space.
  arXiv  Detail & Related papers  (2022-12-23T22:01:32Z)
• Equivalence principle violation from large scale structure [0.0]
  We explore the interplay between the equivalence principle and a generalization of the Heisenberg uncertainty relations known as extended uncertainty principle. We observe that, when the modified uncertainty relations hold, the weak formulation of the equivalence principle is violated, since the inertial mass of quantum systems becomes position-dependent whilst the gravitational mass is left untouched.
  arXiv  Detail & Related papers  (2022-05-21T11:17:15Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Relativistic Extended Uncertainty Principle from Spacetime Curvature [0.0]
  Investigation directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. Applying the 3+1-splitting in accordance with the ADM-formalism, we find the relativistic physical momentum operator and compute its standard deviation for wave functions confined to a geodesic ball on a spacelike hypersurface.
  arXiv  Detail & Related papers  (2021-11-30T17:21:49Z)
• Quantum superposition of spacetimes obeys Einstein's Equivalence Principle [0.0]
  We argue that the Equivalence Principle can be generalised so that it holds for reference frames associated to quantum systems in a superposition of spacetimes. This procedure reconciles the principle of linear superposition in Quantum Theory with the principle of general covariance and the Equivalence Principle of General Relativity.
  arXiv  Detail & Related papers  (2021-09-03T09:51:18Z)
• Gentle Measurement as a Principle of Quantum Theory [9.137554315375919]
  We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics. We show, within the framework of general probabilistic theories, that GMP imposes strong restrictions on the law of physics.
  arXiv  Detail & Related papers  (2021-03-28T11:59:49Z)
• Gravitationally induced uncertainty relations in curved backgrounds [0.0]
  In particular, we assume the quantum wave function to be confined to a geodesic ball on a given space-like hypersurface whose radius is a measure of the position uncertainty. We concurrently work out a viable physical definition of the momentum operator and its standard deviation in the non-relativistic limit of the 3+1 formalism. For the sake of illustration, we apply our general result to a number of examples arising in the context of both general relativity and extended theories of gravity.
  arXiv  Detail & Related papers  (2021-01-14T11:19:17Z)
• 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)

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.