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In this article, we describe various aspects of categorification of the structures appearing in information theory. These aspects include probabilistic models both of classical and quantum physics, emergence of F-manifolds, and motivic enrichments., LaTeX, 40 pages

A common assumption in non-relativistic quantum mechanics is that self-adjoint operators mathematically represent properties of quantum systems. Focusing on spin, we argue that a natural view considers observables as determinable properties and their eigenvalues as their corresponding determinates. We provide a taxonomy of the different views that one can hold, once it is accepted that spin can be modelled with the determinable-determinate relation. In particular, we present the two main families of views, dubbed Spin Monism and Pluralism, and we show that the current literature does not take a stance between the two. Then we put forward two arguments in favour of the former. Finally, we present a new account of Spin Monism, that is absent in current literature; such a view is worth discussing, or so we contend, because several compelling considerations support it, and it opens new ways of thinking about the ontology of quantum mechanics.

A large and mostly unexplored part of the phase diagram lies above the critical point. The supercritical matter was traditionally believed to be physically homogeneous with no discernible differences between liquidlike and gaslike states. More recently, several proposals have been put forward challenging this view, and here we review the history of this research. About a decade ago, it was proposed that the Frenkel line (FL), corresponding to the dynamical transition of particle motion and related thermodynamic and structural transitions, gives a unique and path-independent way to separate the supercritical states into two qualitatively different states and extends to arbitrarily high pressure and temperature on the phase diagram. Here, we review several lines of enquiry that followed. We focus on the experimental evidence of transitions in deeply supercritical Ne, N 2 , CH 4 , C 2 H 6 , CO 2 and H 2 O at the FL detected by a number of techniques including X-ray, neutron and Raman scattering experiments. We subsequently summarise other developments in the field: recent extensions of analysis of dynamics at the FL, quantum simulations, topological and geometrical approaches, the universality of properties at the FL including transport properties, their fundamental bounds and the implications of the supercritical crossover for astrophysics and planetary science. Finally, we review current theoretical understanding of the supercritical state including its thermodynamic theory and list open problems in the field.

This piece highlights the rich scientific legacy of Richard Ernst in the field of magnetic resonance, which encompasses studies of chemical exchange, Overhauser effects, cross-correlated relaxation, quantum computing, and phase encoding in magnetic resonance imaging.

Physicists can't stop discovering bizarre new states of matter. Are we closing in on a complete collection? Jon Cartwright investigates

In order to highlight time-varying constants such as the universal gravitation constant and to elucidate the effects of higher dimensions on cosmological parameters in the universe, we developed a toy cosmological model based upon an anisotropic n-dimensional spatial universe within an (n + 1)-dimensional spacetime. A dynamical power law model for dark energy is considered. The observational parameters of this cosmology are predicted and discussed. Considerable attention is devoted to the application of the extra-dimensional n-dimensional anisotropic cosmology model resulting in a universe consistent with current observations.

We argue against claims that the classical ℏ → 0 limit is “singular” in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ℏ → 0 limit. We then use the tools of category theory to demonstrate one way that this reduction is explanatory: it illustrates a sense in which the structure of quantum mechanics determines that of classical mechanics.

Dasgupta (2015) has recently put forward a novel argument, which he calls the ‘curvature argument’, that aims to show that Galilean spacetime is not an ideal setting for our classical theory of motion. This paper examines the curvature argument and argues that it is not sound. The discussion yields a remark about the conditions under which a ‘symmetry argument’ demonstrates that a particular spacetime is a non-ideal setting for our theory of motion.

In this article we will develop some techniques aimed at the strong couplings in two-dimensional wave-Klein-Gordon system. We distinguish the roles of different type of decay factors and develop a method which permits us to "exchange" one type of decay into the other. Then a global existence result of a model problem is established. We also give a sketch of the Klein-Gordon-Zakharov system and establish the associate global existence result., Some typos on references are corrected

In the present work we show application of Brans-Dicke theory of gravitation, as an alternative to Einstein’s general relativity, in modeling anisotropic compact stellar objects. To make the field equations solvable we consider the space-time under Class 1 embedding condition. The numerical solution of wave equation for Brans-Dicke scalar field Φ has been well fitted with well known function proposed by Bruckman and Kazes (Phys.Rev.D 16:261,1977). The solutions set seems viable as far as observational data are concerned.

We discuss several results in electrostatics: Onsager's inequality, an extension of Earnshaw's theorem, and a result stemming from the celebrated conjecture of Maxwell on the number of points of electrostatic equilibrium. Whenever possible, we try to provide a brief historical context and references., Comment: 14 pages

We present an inspection of the statistics of particles including composite fermions on a torus starting from a braid group analysis. For this purpose we considered a system of electrons confined to the surface of a torus under the influence of a strong magnetic field and interacting through a general rotational invariant potential. An explanation of the appearance of the cyclotron braids as an effect of restriction imposed by magnetic field on braid trajectories which in analyzed case reduces the full braid group to one of its subgroups (i.e. cyclotron subgroups), is given. The modified Feynman path-integral method is also reproduced with some minor enhancements. We improve known results concerning on braid groups on a torus in two directions: we obtain new estimates in terms of cyclotron braid subgroups and cyclotron band generator, respectively; we demonstrate that only multi-loop generators are accessible in the fractional quantum regime well and we also formally explain the unique statistic of composite fermions by construct trial wave function for the system on a torus, based on this idea. The topological oddness of torus geometry can be driven by shifting of electrons between the two different group of generators allowed for an explanation in satisfactory accordance the both compact commensurability condition and some numerical calculations in toroidal geometry. Besides, our approach may shed some new light on few interesting aspects in better understanding the fractional quantum Hall effect.

A radical way of formulating laws of nature promises insights into everything from quantum gravity to what makes us tick, says physicist Chiara Marletto

It has been a longstanding question how stars are packed or distributed in the universe. Here we show that the spatial distribution of stars follows some geometric rules although there may be local inhomogeneities. The topological and metric properties of their Voronoi tessellations exhibit a lognormal distribution. Moreover, these distributions can be connected with those established for the packing of spheres, corresponding to the loosest packing state. The findings provide a new angle to understand the packing structure of stars in the universe.

Nothing truly exists – except in relation to other things. If we can get our heads around that one idea, we can begin to grasp the quantum realm, says Carlo Rovelli

Metal hydrides are known to mediate a number of critical chemical transformations including proton (H+), hydrogen-atom (H•), and hydride (H–) transfer. This preview discusses a recent contribution from Dempsey and co-workers outlining how spectroscopy and electrochemistry can be coupled to disentangle the mechanism of cobalt-hydride formation; loose parallels are drawn between such elementary reactions and the good old game of American football!

Recent advances in nuclear structure theory have significantly enlarged the accessible part of the nuclear landscape via ab initio many-body calculations. These developments open new ways for microscopic studies of light, medium-mass and heavy nuclei as well as nuclear matter and represent an important step toward a systematic and comprehensive understanding of atomic nuclei across the nuclear chart. While remarkable agreement has been found between different many-body methods for a given nuclear Hamiltonian, the comparison with experiment and the understanding of theoretical uncertainties are still important open questions. The observed discrepancies to experiment indicate deficiencies in presently used nuclear interactions and operators. Chiral effective field theory (EFT) allows to systematically derive contributions to nucleon-nucleon (NN), three-nucleon (3N) and higher-body interactions including estimates of theoretical uncertainties. While the treatment of NN interactions in many-body calculations is well established, the calculation of 3N interactions and their incorporation in ab initio frameworks is still a frontier. This work reviews in detail recent and current developments on the derivation and implementation of improved 3N interactions and provides a comprehensive introduction to fundamental methods for their practical calculation and representation. We further give an overview of novel and established methods that facilitate the inclusion and treatment of 3N interactions in ab initio nuclear structure frameworks and present a selection of the latest calculations of atomic nuclei as well as nuclear matter based on state-of-the-art nuclear NN and 3N interactions derived within chiral EFT. Finally, we discuss ongoing efforts, open questions and future directions., Comment: 148 pages, 77 figures, 9 tables, published version

Newton published his deduction of universal gravity in Principia (first ed., 1687). To establish the universality (the particle-to-particle nature) of gravity, Newton must establish the additivity of mass. I call 'additivity' the property a body's quantity of matter has just in case, if gravitational force is proportional to that quantity, the force can be taken to be the sum of forces proportional to each particle's quantity of matter. Newton's argument for additivity is obscure. I analyze and assess manuscript versions of Newton's initial argument within his initial deduction, dating from early 1685. Newton's strategy depends on distinguishing two quantities of matter, which I call 'active' and 'passive', by how they are measured. These measurement procedures frame conditions on the additivity of each quantity so measured. While Newton has direct evidence for the additivity of passive quantity of matter, he does not for that of the active quantity. Instead, he tries to infer the latter from the former via conceptual analyses of the third law of motion grounded largely on analogies to magnetic attractions. The conditions needed to establish passive additivity frustrate Newton's attempted inference to active additivity.

In this paper I examine the extent to which recent work in information-theoretic foundations of quantum mechanics can be thought to facilitate understanding, either of quantum phenomena or quantum theory. To do so I utilize the modal view of understanding phenomena. I extend this view to develop an analysis of understanding of theories. The extended modal view of understanding provides a unified view of recent work in information-theoretic foundations of quantum mechanics and explains how it facilitates understanding.

The universe is expanding faster than our models can explain. It might be time for a radical rethink of how the cosmos works, says Stuart Clark

This paper engages with the following closely related questions that have recently received some attention in the literature: (a) what is the status of the equivalence principle in general relativity (GR)?; (b) how does the metric field obtain its property of being able to act as a metric?; and (c) is the metric of GR derivative on the dynamics of the matter fields? The paper attempts to complement these debates by studying the spin-2 approach to (quantum) gravity. In particular, the paper argues that three lessons can be drawn from the spin-2 approach: (1) different from what is sometimes claimed in the literature, central aspects of the non-linear theory of GR are already derivable in classical spin-2 theory; in particular, ‘universal coupling’ can be considered a derived ‘theorem’ in both the classical and the quantum spin-2 approach; this provides new insights for the investigation of the equivalence principle; (2) the ‘second miracle’ that Read et al. argue characterises GR is explained in the classical as well as in the quantum version of the spin-2 approach; (3) the spin-2 approach allows for an ontological reduction of the metrical part of spacetime to the dynamics of matter fields.

Space-time symmetries and the principle of relativity alone suffice to obtain Lorentz-like coordinate transformations, in which a free parameter, k, plays the part of c − 2 in special relativity. Several authors have concluded that special relativity does not need the postulate of the constancy of the speed of light (the “second postulate”). I oppose this claim and argue that the transformations have no physical content unless different observers can ensure that they use the same units. The relativity of lengths and durations makes this non-trivial. One usually assumes boostability to solve this problem. I analyze this concept and show it is also non-trivial and cannot be assumed in general. The second postulate offers a way around this, as well as an economical method to match both time and length units. Without it, additional postulates are necessary to ground the physical meaning of the transformations.

This paper scrutinises the tenability of a strict conceptual distinction between space(time) and matter via the lens of the debate between modified gravity and dark matter. In particular, we consider Berezhiani and Khoury's novel ‘superfluid dark matter theory’ (SFDM) as a case study. Two families of criteria for being matter and being spacetime, respectively, are extracted from the literature. Evaluation of the new scalar field postulated by SFDM according to these criteria reveals that it is as much (dark) matter as anything could possibly be, but also—below the critical temperature for superfluidity—as much (of a modification of) spacetime as anything could possibly be. A sequel paper examines possible interpretations of SFDM in light of this result, as well as the consequences for our understanding of (the importance of) the modified gravity/dark matter distinction and the broader spacetime–matter distinction.

We review briefly the origin of gauge physics as well as their modern manifestations e.g. in Yang–Mills, Aharonov–Bohm, Aharonov–Casher, and the Berry–Pancharatnam effects. Yang–Mills has its origin in the high energy physics, and has since been widely studied in condensed matter and atomic physics. Recently research in spin–orbit coupling is increasingly being cast in the light of Yang–Mills, leading to new approaches in the study of quantum transport in nanoscale settings like the 2D-graphene and semiconductor nanostructures. It is important to note that this paper will not review non-Abelian physics in condensed matter systems like superfluid, Mott insulators, and atomic quantum gases. The main coverage of this paper would be the non-Abelian, Yang–Mills-inspired gauge physics in fields that straddle condensed matter and quantum spin transport – a technologically relevant field of research also known as the spintronics. Our perspectives are the force and phase physics and their connection with well-known spintronic and magnetic phenomena. The force physics of the spintronic gauge, e.g. the spin Hall, spin jitter motion, quantum spin Hall, and spin torque is discussed. The other important aspect of the gauge field, i.e. its phase physics would be discussed in the context of spin interference and the persistent spin helix.

Yang–Mills theories are an important building block of the standard model and in particular of quantum chromodynamics. Its correlation functions describe the behavior of its elementary particles, the gauge bosons. In quantum chromodynamics, the correlation functions of the gluons are basic ingredients for calculations of hadrons from bound state equations or properties of its phase diagram with functional methods. Correlation functions of gluons are defined only in a gauge fixed setting. The focus of many studies is the Landau gauge which has some features that alleviate calculations. I discuss recent results of correlation functions in this gauge obtained from their equations of motions. Besides the four-dimensional case also two and three dimensions are treated, since the effects of truncations, viz., the procedure to render the infinitely large system of equations finite, can be studied more directly in these cases. In four dimensions, the anomalous running of dressing functions plays a special role and it is explained how resummation is realized in the case of Dyson–Schwinger equations. Beyond the Landau gauge other gauges can provide additional insights or can alleviate the development of new methods. Some aspects or ideas are more easily accessible in alternative gauges and the results presented here for linear covariant gauges, the Coulomb gauge and the maximally Abelian gauge help to refine our understanding of Yang–Mills theories.

Flames unfettered by gravity are more than just beautiful. Studying them is a powerful way to help us control combustion on solid ground, reports Philip Ball

In this paper, we investigate the existence of anisotropic compact stellar structures in the framework of f ( G , T ) gravity. We assume static spherically symmetric spacetime and utilize the embedding class-I approach to evaluate the unknown metric functions corresponding to a particular f ( G , T ) model. We determine the unknown constants by matching the interior and exterior geometries. The viability of the model is checked for different compact stars through energy bounds, compactness, gravitational redshift, Heintzmann condition for adiabatic index and Herrera stability condition but the graphical analysis is given only for SAX J1808.4-3658 compact star candidate. The behavior of physical parameters indicates viable and stable structure of the stellar model.

It is standardly claimed in loop quantum gravity (LQG) that spacetime both disappears, fundamentally, and emerges from spin-networks in the low energy regime. In this paper, I critically explore these claims and develop a variety of substantival and relational interpretations of LQG for which these claims are false. According to most of the interpretations I consider, including the “received interpretation", it is in fact false that spacetime emerges from spin-networks. In the process of supporting these claims, I also explain why spacetime is thought to be missing from the theory’s fundamental ontology and demonstrate how this conclusion depends on our interpretation of the theory. In fact, I will argue that for a variety of interpretations spacetime survives quantization just as the electromagnetic field survives quantization. The upshot of the following analysis is a much needed clarification of the ontology of LQG and how it relates, or fails to relate, to the spacetime of general relativity.

This essay considers an interpretation of the AdS/CFT correspondence under which the bulk and the boundary emerge from a more fundamental discrete system that realizes the structure of an erasure-protection quantum error-correcting code (QECC). I consider the extent to which this view underwrites the claim that spacetime is a QECC (as some authors have suggested), and how it fits into recent schemes of realist interpretations of dualities.

Stein has characterized one of the central problems in accounting for our knowledge in physics as that of getting the laboratory, or observatory, inside the theory — that is, of understanding how the mathematical structures of fundamental physical theories have empirical content. He has argued that physicists respond to this problem by giving schematic representations of observers and experiments. In addition, Stein emphasizes the importance of regarding knowledge as an enterprise, with current theories providing guidance for future inquiry. I will explore some ramifications of this way of thinking about the structure of scientific theories for contemporary cosmology. One goal of observational cosmology is to measure the six basic parameters appearing in the standard model of cosmology. These parameters are well-defined if the universe is suitably approximated at some scale by a perturbed FLRW model. The enormous extrapolations involved in the standard model are often justified by the consistent determination of these parameters via a variety of methods. Here I will consider two recent debates regarding this approach to cosmology, inspired by Stein's work. The first debate regards the impact of different ways of characterizing the propagation of light through a cosmological spacetime on the determination of cosmological parameters (such as H 0 ). The second regards how the highly symmetric FLRW models relate to describing the real universe, at small scales where it is very lumpy.

In this paper we study both analytical and combinatorial properties of solutions of the eigenproblem for the Heisenberg s-1/2 model for two deviations. Our analysis uses Chebyshev polynomials, inverse Bethe Ansatz, winding numbers and rigged string configurations. We show some combinatorial aspects of strings in a geometric way. We discuss some exceptions from the connection between the combinatorial nature of an eigenstate and the analytical type of a solution of the eigenproblem. In particular, as an illustration of the aforementioned exceptions, we analyze the singularities of Bethe parameters for bound states at the border of the Brillouin zone.

Important properties of a particle, wave or a statistical system depend on the form of a dispersion relation (DR). Two commonly-discussed dispersion relations are the gapless phonon-like DR and the DR with the energy or frequency gap. More recently, the third and intriguing type of DR has been emerging in different areas of physics: the DR with the gap in momentum, or $k$-space. It has been increasingly appreciated that gapped momentum states (GMS) have important implications for dynamical and thermodynamic properties of the system. Here, we review the origin of this phenomenon in a range of physical systems, starting from ordinary liquids to holographic models. We observe how GMS emerge in the Maxwell-Frenkel approach to liquid viscoelasticity, relate the $k$-gap to dissipation and observe how the gaps in DR can continuously change from the energy to momentum space and vice versa. We subsequently discuss how GMS emerge in the two-field description which is analogous to the quantum formulation of dissipation in the Keldysh-Schwinger approach. We discuss experimental evidence for GMS, including the direct evidence of gapped DR coming from strongly-coupled plasma. We also discuss GMS in electromagnetic waves and non-linear Sine-Gordon model. We then move on to discuss the recently developed quasihydrodynamic framework which relates the $k$-gap with the presence of a softly broken global symmetry and its applications. Finally, we review recent discussions of GMS in relativistic hydrodynamics and holographic models. Throughout the review, we point out essential physical ingredients required by GMS to emerge and make links between different areas of physics, with the view that new and deeper understanding will benefit from studying the GMS in seemingly disparate fields and from clarifying the origin of potentially similar underlying physical ideas and equations., Comment: v2: published version. In press in Physics Reports

The Principles of Quantum Mechanics and of Classical General Relativity indicate that Spacetime in the small (Planck scale) ought to be described by a noncommutative C* Algebra, implementing spacetime uncertainty relations. A model C* algebra of Quantum Spacetime and its Quantum Geometry is described. Interacting Quantum Field Theory on such a background is discussed, with open problems and recent progress. Applications to cosmology suggest that the Planck scale ought to depend upon dynamics, and possible consequences in the large of the quantum structure in the small are outlined.

Wormholes are considered as one of the most interesting hypothetical objects whose existence is also predicted by Einstein’s relativity. It is generally argued that the theoretical construction of such objects demands an exotic kind of anisotropic matter (a matter which is not compatible with the energy constraints). The existence of such matter is regarded as a primary condition for the existence of such geometries. The present manuscript examines the existence of wormhole structures in f(R, ϕ) gravity by taking hyperbolic shape function with constant and logarithmic redshift functions into account. For this purpose, we check the validity of energy condition bounds in both cases graphically. It is found that the wormhole geometries can be constructed for both constant and logarithmic redshift functions when anisotropic phantom fluid characterized by the EoS ω r = p r / ρ − 1 is taken. Further, we discuss the background features of such objects.

The magnetosphere structure of compact objects is considered in the context of a theory of gravity with dynamical torsion field beyond standard General Relativity (GR) introduced previously in Cirilo-Lombardo and Minotti (2019) . To this end, a new spherically symmetric solution is obtained. A particular case physically representing a compact object of pseudoscalar fields (for example, axion field) is analyzed from the magnetosphere dynamics viewpoint using the axially symmetric version of the Grad-Shafranov equation (GSE) previously derived. We explicitly show that, in sharp contrast with the dipole case, the quadrupole case (where we have two well defined toroidal lobes) the energy stored in the magnetosphere increases more than in the pure dipole case, fact that is important to explain the problem of excess energy in mechanics of the pulsars and in the structure of magnetars. In this way we briefly discuss with the same argument as the one presented in Wang et al. (2019) , how in our theoretical frame our model can help reinterpret phenomenological and observational results in the case of the X-ray emission of XTE J1810-197.

Nobel prizewinner Jim Peebles contributed more than most to our standard model of cosmology - but it´s unlikely to be the final answer, he says

We give a transparent algebraic formulation of our pictorial approach to the reflection positivity (RP), that we introduced in a previous paper. We apply this quantization to the 2 + 1 Levin–Wen model to obtain 1 + 1 anyonic/quantum spin chain theory on the boundary, possibly entangled in the bulk. The reflection positivity property has played a central role in both mathematics and physics, as well as providing a crucial link between the two subjects. In a previous paper we gave a new geometric approach to understanding reflection positivity in terms of pictures. Here we give a transparent algebraic formulation of our pictorial approach. We use insights from this translation to establish the reflection positivity property for the fashionable Levin–Wen models with respect both to vacuum and to bulk excitations. We believe these methods will be useful for understanding a variety of other problems.

The original and most common method to transpose horizontal to tilted diffuse irradiance is based on the Isotropic Sky Model (ISM). Various aspects of the ISM are explored here, including the connection between the ideal isotropic sky radiance distribution and the corresponding diffuse irradiance on a tilted collector. By completing an extensive literature review of the ISM, its origin and history are clearly established, and the methods of derivation are discussed. The oldest known derivations of the ISM are identified. In particular, the landmark contribution of Liu and Jordan (1960) is found not to be the original source of the ISM transposition formula, even though it is usually credited for it. The ISM significance is discussed in the present context of solar energy applications, where the accuracy of irradiance calculations is critical. A detailed review of the methods of derivation, including boundary conditions, is proposed to explain differing results and remove all sources of confusion that have permeated the literature. Lastly, the use of anisotropic models is advocated to avoid unnecessary systematic errors.

Introduced by Saari and Asay (2010), the “finesse point” extends the notion of core. Its definition is similar to the finagle point. Unlike the finagle point, there is a relatively simple geometrical construction of finesse point. In this note, we show that the aforementioned points do not agree. This questions the original definition of finesse point.

The following notes derive from review lectures on closed string field theory given at the Galileo Galilei Institute for Theoretical Physics in March 2019., Comment: v3: 54 pages, 19 figures. Redrawn figures with increased resolution; new appendix; other improvements as requested by referee

This paper develops an approach to the interpretation of quantum mechanics inspired by the philosophy of Howard Stein. Taking up Stein’s (1994) call to schematize the observer and the observation, I introduce a class of observables called ‘sensibles’ which provide a means to assign probabilities to an observer's experiences of experimental phenomena. In particular, sensibles provide an assignment of probabilities to an event space that, while satisfying the demands of probability theory, also allows for an interpretation of these events as occurring at definite space-time regions. On this understanding, the experimental events to which probabilities are ascribed are conditional occurrences—types of events which occur at a definite location in a specific experimental context. This proposal differs from dynamical collapse theories such as GRWf since these sensibles are genuine quantum observables arising from the unitary dynamics of the theory. I conclude with some remarks on the import of Stein's philosophy for the measurement problem.

According to the Standard Model of particle physics, some gauge transformations are physical symmetries. That is, they are mathematical transformations that relate representatives of distinct physical states of affairs. This is at odds with the standard philosophical position according to which gauge transformations are an eliminable redundancy in a gauge theory's representational framework. In this paper I defend the Standard Model's treatment of gauge from an objection due to Richard Healey. If we follow the Standard Model in taking some gauge transformations to be physical symmetries then we face the “strong CP problem”, but if we adopt the standard philosophical position on gauge then the strong CP problem dissolves. Healey offers this as a reason in favor of the standard philosophical view. However, as I argue here, following Healey's recommendation gives a theory that makes bad empirical predictions.

Physicists are limbering up for their greatest trick yet – explaining how decision-making beings like you and me fit into the cosmic order, says Richard Webb

The paper re-examines Nordstrom's scalar theory of gravity (NG) – arguably the most convincing relativistic theory of gravity before the advent of General Relativity. It exists in two different formulations. In Nordstrom's original one (1913), NG appears to describe a scalar gravitational field on Minkowski spacetime. In Einstein and Fokker’s (1914) version, NG seems to be a spacetime theory: It reconceptualises gravitational effects as manifestations of non-Minkowskian inertial structure. Both variants of NG give rise to three contradictory verdicts on the status and validity of fundamental principles: the Weak Equivalence Principle, the existence of gravitational energy, and energy conservation. Given the putative equivalence of both variants of NG, this ambiguity seems paradoxical to the spacetime realist. I'll proffer a resolution from the perspective of integrable Weyl geometry: The paradoxes rest on the failure to recognise a more apposite spacetime setting for NG.

We propose and investigate several complex versions of extensions and restrictions of the Skyrme model with a well-defined Bogomolny-Prasad-Sommerfield (BPS) limit. The models studied possess complex kink, anti-kink, semi-kink, massless and purely imaginary compacton BPS solutions that all have real energies. The reality of the energies for a particular solution is guaranteed when a modified antilinear CPT-symmetry maps the Hamiltonian functional to its parity time-reversed complex conjugate and the solution field to itself or a new field with degenerate energy. In addition to the known BPS Skyrmion configurations we find new types that we refer to as step, cusp, shell, and purely imaginary compacton solutions., 21 pages, 7 figures

Recently, black hole thermodynamics and phase transition have been studied in the extended phase space. Besides the VdW-like phase transition, more interesting phase transitions were found. More interestingly, combining with the thermodynamic geometry, the microstructure of black holes was investigated.In this paper, we give a brief review of recent progress on this subject., 4 pages, 1 figure. Invited News & Views by Science Bulletin

The paper is devoted to resonances playing an important role in direct and inverse scattering problems. A model of a relativistic particle on hybrid manifold consisting of a sphere with two semi-infinite wires attached is considered. The model is based on the theory of self-adjoint extensions of symmetric operators. Completeness of resonance states in the space of square integrable functions on the sphere is proved. The proof uses the relation between the completeness and the factorization of the characteristic function in Sz.-Nagy functional model. Keywords: Scattering, Resonance, Hybrid manifold, Dirac operator, MSC 2010: 47B38, 47E05