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Frederik G. Scholtz

Publications and source records attributed to Frederik G. Scholtz.

11 recordsLinked to original sources
arXiv2026

Quantum-Gravitational Backreaction in the BTZ Background from Curved Momentum Space

We explore how quantum properties of spacetime, specifically the curvature of momentum space, can backreact on classical gravity within a tractable semiclassical (2+1)-dimensional framework with a negative cosmological constant. Motivated by quantum-gravity scenarios, we investigate how Planck-scale modifications of particle kinematics influence both dynamics and gravitational solutions. Starting from a first-order action, we derive an effective configuration-space description and show that particle trajectories remain geodesic, preserving the weak equivalence principle despite the underlying deformation. Coupling this modified matter sector to Einstein gravity, we obtain a deformed BTZ black hole solution. Remarkably, the local geometric structure and thermodynamic relations retain their standard form, while all quantum-gravity effects are encoded in a nonlinear mapping between the microscopic mass parameter and the ADM mass. This induces a renormalization of the horizon radius and thermodynamic quantities without altering their functional dependence. As a concrete observable consequence, we compute corrections to the return time of massless probes traveling along null geodesics between the horizon and the AdS3 boundary. Our results demonstrate that Planck-scale kinematic effects can leave controlled and potentially measurable imprints on classical geometry, providing a clear and consistent bridge between quantum-gravity ideas and semiclassical observables.

gr-qc↗
arXiv2025

Quantum Geometric Phases as a New Window on Gravitational Waves

We investigate how low-frequency gravitational waves (LFGWs), originating from distant astrophysical or cosmological sources, can induce purely quantum geometric phases in mesoscopic optomechanical systems. These phases represent subtle imprints with no classical counterpart, going beyond standard dynamical or Berry-type contributions that admit Hannay-angle analogues. Such ultra-weak waves couple to the motion of a mechanical mirror and generate distinctive phase shifts in the system's quantum state that cannot arise in any classical description. To access this effect, we propose a Ramsey-type interferometric protocol in which the photon-number states of a quantized optical mode become entangled with the mirror's center-of-mass motion, enabling a direct readout of the LFGW-induced geometric phase. This framework establishes a distinctly quantum approach for probing low-frequency gravitational wave modes, offering an alternative to conventional detection strategies based on spacetime strain.

hep-th↗
arXiv2023

The hidden Lorentz Covariance of Quantum Mechanics

This paper introduces a systematic algorithm for deriving a new unitary representation of the Lorentz algebra ($so(1,3)$) and an irreducible unitary representation of the extended (anti) de-Sitter algebra ($so(2,4)$) on $\mathcal{L}^{2}(\mathcal{R}^{3},\frac{1}{r})$. This representation is equivalent to a representation on $\mathcal{L}^{2}(\mathcal{R}^{3})$, and the corresponding similarity transformation is identified. An explicit representation in terms of differential operators is given, and it is shown that the inner product is Lorentz invariant. Ensuring Lorentz covariance demands a modification of the Heisenberg algebra, recognized as a phase space algebra at the interface of gravitational and quantum realms (IGQR), which we consider subordinate to Lorentz covariance. It is also demonstrated that time evolution can be cast in a manifestly covariant form. Each mass sector of the Hilbert space carries a representation of the Lorentz algebra, and the (anti) de-Sitter algebra on each mass sector contracts to the Poincare algebra in the flat configuration and momentum space limits. Finally, we show that three-dimensional fuzzy space also carries a unitary representation of these algebras, algebraically equivalent to the $\mathcal{L}^{2}(\mathcal{R}^{3},\frac{1}{r})$ representation but not necessarily equivalent as representations. Several outstanding issues are identified for future exploration.

hep-th↗
arXiv2022

Pinhole interference in three-dimensional fuzzy space

We investigate a quantum-to-classical transition which arises naturally within the fuzzy sphere formalism for three-dimensional non-commutative quantum mechanics. This transition may be understood as the mechanism of decoherence, but without requiring an additional external heat bath. We focus on treating a two-pinhole interference configuration within this formalism, as it provides an illustrative toy model for which this transition is readily observed and quantified. Specifically, we demonstrate a suppression of the quantum interference effects for objects passing through the pinholes with sufficiently-high energies or numbers of constituent particles. Our work extends a similar treatment of the double slit experiment by Pittaway and Scholtz (2021) within the two-dimensional Moyal plane, only it addresses two key shortcomings that arise in that context. These are, firstly that the interference pattern in the Moyal plane lacks the expected reflection symmetry present in the pinhole setup, and secondly that the quantum-to-classical transition manifested in the Moyal plane occurs only at unrealistically high velocities and/or particle numbers. Both of these issues are solved in the fuzzy sphere framework.

quant-ph↗
arXiv2015

Grand canonical potential of a magnetized neutron gas

We compute the effective action for stationary and spatially constant magnetic fields, when coupled anomalously to charge neutral fermions, by integrating out the fermions. From this the grand canonical partition function and potential of the fermions and fields are computed. This also takes care of magnetic field dependent vacuum corrections to the grand canonical potential. Possible applications to neutron stars are indicated.

nucl-th↗
arXiv2011

The entropy of dense non-commutative fermion gases

We investigate the properties of two- and three-dimensional non-commutative fermion gases with fixed total z-component of angular momentum, J_z, and at high density for the simplest form of non-commutativity involving constant spatial commutators. Analytic expressions for the entropy and pressure are found. The entropy exhibits non-extensive behaviour while the pressure reveals the presence of incompressibility in two, but not in three dimensions. Remarkably, for two-dimensional systems close to the incompressible density, the entropy is proportional to the square root of the system size, i.e., for such systems the number of microscopic degrees of freedom is determined by the circumference, rather than the area (size) of the system. The absence of incompressibility in three dimensions, and subsequently also the absence of a scaling law for the entropy analogous to the one found in two dimensions, is attributed to the form of the non-commutativity used here, the breaking of the rotational symmetry it implies and the subsequent constraint on J_z, rather than the angular momentum J. Restoring the rotational symmetry while constraining the total angular momentum J seems to be crucial for incompressibility in three dimensions. We briefly discuss ways in which this may be done and point out possible obstacles.

math-ph↗
arXiv2010

Strings from position-dependent noncommutativity

We introduce a new set of noncommutative space-time commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative space-time relations taken here to have position dependent structure constants. Some of the new variables are non-Hermitian in the most natural choice. We construct their Hermitian counterparts by means of a Dyson map, which also serves to introduce a new metric operator. We propose PTlike symmetries, i.e.antilinear involutory maps, respected by these deformations. We compute minimal lengths and momenta arising in this space from generalized versions of Heisenberg's uncertainty relations and find that any object in this two dimensional space is string like, i.e.having a fundamental length in one direction beyond which a resolution is impossible. Subsequently we formulate and partly solve some simple models in these new variables, the free particle, its PT-symmetric deformations and the harmonic oscillator.

hep-th↗
arXiv2007

The Weyl-Heisenberg Group on the Noncommutative Two-Torus: A Zoo of Representations

In order to assess possible observable effects of noncommutativity in deformations of quantum mechanics, all irreducible representations of the noncommutative Heisenberg algebra and Weyl-Heisenberg group on the two-torus are constructed. This analysis extends the well known situation for the noncommutative torus based on the algebra of the noncommuting position operators only. When considering the dynamics of a free particle for any of the identified representations, no observable effect of noncommutativity is implied.

hep-th↗
arXiv2005

Non(anti) commutativity for open superstrings

Non(anti)commutativity in an open free superstring and also one moving in a background anti-symmetric tensor field is investigated. In both cases, the non(anti)commutativity is shown to be a direct consequence of the non-trivial boundary conditions which, contrary to several approaches, are not treated as constraints. The above non(anti)commutative structures lead to new results in the algebra of super constraints which still remain involutive, indicating the internal consistency of our analysis.

hep-th↗