arXiv subjects

Jens Köplinger

Publications and source records attributed to Jens Köplinger.

5 recordsLinked to original sources

arXiv2026

Operational reconstruction of Feynman rules for quantum amplitudes via composition algebras

This article explores an operational model for transition amplitudes between measurements proposed by Goyal et al. within the quantum reconstruction program. To classify suitable amplitude algebras, we distinguish mathematical axioms, physical choices, and their consequences. This leads to several improvements on the published work: Our coordinate-independent approach requires no two-dimensional amplitudes a priori. All scalar field and vector space axioms are traced from model axioms and observer choices, including additive and multiplicative units and inverses. Existing mathematical characterizations identify allowable amplitude algebras as the real associative composition algebras, namely the complex numbers and the quaternions, as well as their split forms. Observed probabilities are quadratic in amplitudes, akin to the Born rule. We examine selected implications of the proposed axioms, reformulate observer questions, and highlight the broad applicability of our framework to subsequent discovery.

quant-ph↗

arXiv2023

Remarks on four dimensional Euclidean gravity without Wick rotation

In reference to S. W. Hawking's article "Information Loss in Black Holes" [S. W. Hawking, Phys. Rev. D 72 (2005) 084013], where a four dimensional Euclidean spacetime without Wick rotation is adopted for quantum gravity, an arithmetic with multiplicative modulus is mentioned here which incorporates both a hyperbolic (Minkowski) and circular (Euclidean) metric: The 16 dimensional conic sedenion number system is built on nonreal square roots of +1 and -1, and describes the Dirac equation through its 8 dimensional hyperbolic octonion subalgebra [J. Köplinger, Appl. Math. Comput. (2006), in print, doi: 10.1016/j.amc.2006.04.005]. The corresponding circular octonion subalgebra exhibits Euclidean metric, and its applicability in physics is being proposed for validation. In addition to anti-de Sitter (AdS) spacetimes suggested by Hawking, these conic sedenions are offered as computational tool to potentially aid a description of quantum gravity on genuine four-dimensional Euclidean spacetime (without Wick rotation of the time element), while being consistent with canonical spacetime metrics.

hep-th↗

arXiv2023

Phenomenology from Dirac equation with Euclidean-Minkowskian "gravity phase"

Over the past decades, many authors advertised models on complexified spacetime algebras for use in describing gravity. This work aims at providing phenomenological support to such claims, by introducing a one-parameter real phase $α$ to the conventional Dirac equation with $\frac{1}{r}$-type potential. This phase allows to transition between Euclidean ($α=0,\pmπ,\pm2π,\ldots$) and Minkowskian ($α=\pm\fracπ{2},\pm\frac{3π}{2},\ldots$) geometry, as two distinct cases that one may expect from some complexified spacetime. The configuration space is modeled on $4\times4$ matrix algebra over the bicomplex numbers, $\mathbb{C}\oplus\mathbb{C}$. Spin-$\frac{1}{2}$ Coulomb scattering (Rutherford scattering) in Born approximation is then executed. All calculations are done ``from scratch'', as they could have been done some 85 years ago. By removing elegance from field theory that has since become customary, this paper aims at remaining as generally applicable as possible, for a wide range of candidate models that contain such a phase $α$ in one way or another. Results for backscattering and cross section at high energies are compared with results from General Relativity calculations. Effects on intergalactic gas distribution and momentum transfer from scattering high-energy leptons are sketched.

physics.gen-ph↗

arXiv2012

An analysis of Rick Lockyer's "octonion variance sieve"

In "Octonion Algebra and its Connection to Physics" [16] an algorithm on octonions is brought forward for description of physical law, the "octonion variance sieve process". This paper expresses the used algorithm in symbolic form, and highlights the structure between the "function", "distance", and "algebraic invariant" concepts therein. An alternative description in terms of derivation algebras is shown.

math-ph↗

arXiv2008

Quantum of area from gravitation on complex octonions

Using spin 1/2 particle elastic scattering on a fixed target, in a 1/|x| potential on Euclidean metric, a minimum scattering cross section appears from the spin contribution. Interpreted as semi-classical limit of an earlier proposed operator formulation of four dimensional Euclidean quantum gravity, using non-associative complex octonion algebra, this is understood as an area quantum for the observation: Existence of finite (quantized) charges yields a minimum area element of interaction. This suggests that models built on the fundamental assumption of a quantized area element (namely as in Loop Quantum Gravity) may in principle approximate General Relativity in the non-quantum limit.

physics.gen-ph↗