Positive Energy Unitary Irreducible Representations of the Superalgebra osp(1|8,R)

We continue the study of positive energy (lowest weight) unitary irreducible representations of the superalgebras osp(1|2n,R). We present the full list of these UIRs. We give the Proof of the case osp(1|8,R).Comment: 17 pages, v2: changed format to include figur

Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary

In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model.info:eu-repo/semantics/publishedVersio

The hard problem and the measurement problem: a no-go theorem and potential consequences

The "measurement problem" of quantum mechanics, and the "hard problem" of cognitive science are the most profound open problems of the two research fields, and certainly among the deepest of all unsettled conundrums in contemporary science in general. Occasionally, scientists from both fields have suggested some sort of interconnectedness of the two problems. Here we revisit the main motives behind such expectations and try to put them on more formal grounds. We argue not only that such a relation exists, but that it also bears strong implications both for the interpretations of quantum mechanics and for our understanding of consciousness. The paper consists of three parts. In the first part, we formulate a "no-go-theorem" stating that a brain, functioning solely on the principles of classical physics, cannot have any greater ability to induce subjective experience than a process of writing (printing) a certain sequence of digits. The goal is to show, with an attempt to mathematical rigor, why the physicalist standpoint based on classical physics is not likely to ever explain the phenomenon of consciousness - justifying the tendency to look beyond the physics of the 19th century. In the second part, we aim to establish a clear relation, with a sort of correspondence mapping, between attitudes towards the hard problem and interpretations of quantum mechanics. Then we discuss these connections in the light of the no-go theorem, pointing out that the existence of subjective experience might differentiate between otherwise experimentally indistinguishable interpretations. Finally, the third part is an attempt to illustrate how quantum mechanics could take us closer to the solution of the hard problem and break the constraints set by the no-go theorem

2022 Nobel Prize in Physics and the End of Mechanistic Materialism

The ideas and results that are in the background of the 2022 Nobel Prize in physics had an immense impact on our understanding of reality. Therefore, it is crucial that these implications reach also the general public, not only the scientists in the related fields of quantum mechanics. The purpose of this review is to attempt to elucidate these revolutionary changes in our worldview that were eventually acknowledged also by the Nobel's committee, and to do it with very few references to mathematical details (which could be even ignored without undermining the take-away essence of the text). We first look into the foundational disputes between Einstein and Bohr about the nature of quantum mechanics, which culminated in the so-called EPR paradox -- the main impetus for all the research that would ensue in this context. Next, we try to explain the statement of the famous Bell's theorem -- the theorem that relocated the Einstain-Bohr discussions from the realm of philosophy and metaphysics to hard-core physics verifiable by experiments (we also give a brief derivation of the theorem's proof). Then we overview the experimental work of the last year's laureates, that had the final say about who was right in the debate. The outcome of these experiments forced us to profoundly revise our understanding of the universe. Finally, we discuss in more detail the implications of such outcomes, and what are the possible ways that our worldviews can be modified to account for the experimental facts. As we will see, the standard mechanist picture of the universe is no longer a viable option, and can be never again. Nowadays, we know this with certainty unusual for physics, that only a strict mathematical theorem could provide