Space-time Theory Research Articles

Hilbert space of quantum field theory in de Sitter spacetime

We study the decomposition of the Hilbert space of quantum field theory in (d+1)-dimensional de Sitter spacetime into unitary irreducible representations (UIRs) of its isometry group SO(1,d+1). First, we consider multiparticle states in free theories starting from the tensor product of single-particle UIRs. Second, we study conformal multiplets of a bulk conformal field theory with symmetry group SO(2,d+1). Our main tools are the Harish-Chandra characters and the numerical diagonalization of the (truncated) quadratic Casimir of SO(1,d+1). We introduce a continuous density that encodes the spectrum of irreducible representations contained in a reducible one of SO(1,d+1). Our results are complete for d=1 and d=2. In higher dimensions, we rederive and extend several results previously known in the literature. Our work provides the foundation for future nonperturbative bootstrap studies of quantum field theory in de Sitter spacetime. Published by the American Physical Society 2025

Geodesics connecting endpoints of timelike interval in an asymptotically AdS spacetime

In the duality of 3-dimensional anti de-Sitter (AdS) spacetime and 2-dimensional conformal field theory (CFT), it was argued that the holographic entanglement entropy between two timelike separated events needs both timelike and spacelike geodesics. This paper studies the possibility of using smooth spacelike geodesics to connect two timelike separated events of boundary. We find that in a spherically symmetry Schwarzschild anti-de Sitter spacetime black hole, smooth spacelike geodesics can connect timelike-separated points by winding around the horizon multiple times. A similar result will also happen in a three-dimensional asymptotically AdS black hole that contains a photon ring in the bulk. Our result suggests that, if there is a photon ring, then the timelike entanglement entropy in the AdS3/CFT2 duality may not have an imaginary part. The result implies that the bulk photon ring may play an important role in understanding analytical behaviors of the entanglement spectrum for AdS3/CFT2 duality. Published by the American Physical Society 2025

Accurate Predictions of Gravity without Mass, Null Dark Matter Results, Muon Precession and Solutions to the Hubble Tension, Final Parsec Problem, Information Paradox, Inter Alia: A 3.5-Year Status Report on the Probabilistic Spacetime Theory

Accurate Predictions of Gravity without Mass, Null Dark Matter Results, Muon Precession and Solutions to the Hubble Tension, Final Parsec Problem, Information Paradox, Inter Alia: A 3.5-Year Status Report on the Probabilistic Spacetime Theory

Tourism Demand Forecasting based on Adaptive Neural Network Technology in Business Intelligence

In order to improve the effect of demand forecasting, this paper combines the adaptive neural network technology to construct a demand forecasting model, and proposes an adaptive fault-tolerant PI control strategy for multiple-input and multiple-output systems. In order to verify the effectiveness and stability of the designed adaptive fault-tolerant PI control strategy, this paper uses an iterative algorithm to improve the tracking control accuracy. Moreover, this paper integrates temporal geography with the theory of probabilistic temporal geography, system analysis theory, and tourist flow space-time bayonet theory to propose a research framework for forecasting tourist flow spatio-temporal bayonet based on the WITNESS simulation system. The research shows that the tourism demand forecasting model based on adaptive neural network technology proposed in this paper has good tourism demand forecasting effect, and has a certain effect on promoting the development of tourism.

Degenerate higher-order Maxwell theories in flat space-time

We consider, in Minkowski spacetime, higher-order Maxwell Lagrangians with terms quadratic in the derivatives of the field strength tensor, and study their degrees of freedom. Using a 3+1 decomposition of these Lagrangians, we extract the kinetic matrix for the components of the electric field, corresponding to second time derivatives of the gauge field. If the kinetic matrix is invertible, the theory admits five degrees of freedom, namely the usual two polarisations of a photon plus three extra degrees of freedom which are shown to be Ostrogradski ghosts. We also classify the cases where the kinetic matrix is non-invertible and, using analogous simple models, we argue that, even though the degeneracy conditions reduce the number of degrees of freedom, it does not seem possible to fully eliminate all potential Ostrogradski ghosts.

Five-dimensional compact stars in Einstein-Gauss-Bonnet gravity

Within the framework of Einstein-Gauss-Bonnet theory in five-dimensional spacetime (5D EGB), we derive the hydrostatic equilibrium equations and solve them numerically to obtain neutron stars for both isotropic and anisotropic distribution of matter. The mass-radius relations are obtained for SLy equation of state, which describes both the solid crust and the liquid core of neutron stars, and for a wide range of the Gauss-Bonnet coupling parameter α. More specifically, we find that the contribution of the Gauss-Bonnet term leads to substantial deviations from Einstein gravity. We also discuss that after a certain value of α, the theory admits higher maximum masses compared with general relativity, however, the causality condition is violated in the high-mass region. Finally, our results are compared with the recent observations data on mass-radius diagram.

Flat-space limit of holographic pseudoentropy in (A)dS spacetimes

The real part of pseudoentropy in conformal field theories is holographically calculated by the area of some extremal spacelike surfaces in the dual de Sitter (dS) and anti–de Sitter (AdS) spacetimes. We show that the flat-space limit of these curves in three-dimensional (A)dS spacetimes is well defined. We find that, if the length of the curves is calculated from the radial coordinate where the retarded time is extremum, then after taking the flat-space limit, the entanglement entropy of the dual theory of three-dimensional flat spacetime is obtained. For dS spacetime, the radial coordinate corresponding to the extremum of retarded time is located inside the cosmological horizon. Our results suggest that, on the field theory side, the entanglement entropy in the dual theory of flat spacetimes should be obtained from the ultrarelativistic limit of pseudoentropy in the dual conformal field theory to (A)dS spacetimes. Published by the American Physical Society 2024

Interpolating gauge-fixing for Yang–Mills–Chern–Simons theory in D=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=3$$\\end{document}

The Yang–Mills–Chern–Simons theory in three-dimensional Minkowski space-time is studied in a gauge-fixing scheme which interpolates between the covariant gauge and light-cone gauge, the interpolating gauge-fixing. The ultraviolet finiteness of the theory is proved via the Becchi–Rouet–Stora (BRS) algebraic renormalization procedure, which allows us to demonstrate the vanishing of all β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-functions and all anomalous dimensions to all orders in perturbation theory.

On the Non-identity Causal Theory of Spacetime from Causal Set Theory

AbstractThe aim to provide a causal theory of spacetime is not new. The overall program, however, was largely deemed unsuccessful, chiefly due to criticism voiced by Smart (Monist 53:385–395, 1969), Nerlich (Br J Philos Sci 33(4):361–388, 1982) and Earman (Synthese 24:74–86, 1972). Recently, Baron and Le Bihan (Noûs 58:202–224, 2023) have argued that developments in contemporary physics should make us reconsider this verdict. More precisely, they argue the emergence of spacetime from causal set theory (CST), where “the metric structure of spacetime can be recovered from its causal structure” (Baron and Le Bihan 2023, 2), “suggests a very natural way to reformulate the causal theory of spacetime” (ibid., 9)—an account which they end up dubbing the non-identity causal theory. This paper questions the success of Baron and Le Bihan’s non-identity theory. It is shown that (1) the specific grounding Baron and Le Bihan propose for timelike and spacelike relations is not plausible even when charitably reconstructed; and (2) that a causal theory of spacetime based on general relativity is just as successful for establishing a non-identity theory as a theory based on CST. In short then, we argue that the causal theory of spacetime proposed by Baron and Le Bihan is supported just as well (or badly) by the physics that already took centre stage in the original discussions of the causal theory of spacetime.

A new perspective on Kaluza–Klein theories

Assuming that the geometry of spacetime is uniquely determined by the energy–momentum tensor of matter alone, i.e. without any interactions, enables us to construct the Lagrangian from which the metric of higher dimensional spacetime follows. From the geodesic equations that follow, it becomes clear that the incorrect mass of elementary particles predicted by Kaluza–Klein theories arises from the assumption that in the absence of gravity the solution to the Einstein field equations reduces to the Minkowski metric. From construction of a consistent theory of 4D electromagnetism, we find that this assumption does not only result in the incorrect mass of elementary particles, but also the incorrect value of the cosmological constant. This suggests that these incorrect predictions, which are often regarded as major flaws of Kaluza–Klein theories, just reflect the inconsistency of the assumption that the solution to Einstein field equations reduces to Minkowski metric in the absence of gravity and Weyl invariance which is the symmetry of gauge theories in 4D spacetime. Abandoning this assumption results in modification of general relativity. We show that the unified description of fundamental interactions naturally incorporates the Higgs mechanism. For non-Abelian gauge fields, we find that the manifold comprising the extra dimensions has to be a group manifold and show that the standard model is realized in 16D spacetime. We show that charge and spin are the same concept, but what makes them different is that the former follows from symmetry of 4D spacetime while the latter follows from symmetry of the internal space.

Unconstrained Lagrangian formulation for bosonic continuous spin theory in flat spacetime of arbitrary dimension

We have discovered two unconstrained forms of free Lagrangian for continuous spin(CS) theory in arbitrary flat spacetime dimension for bosonic case. These Lagrangians, unlike that by Schuster and Toro, do not include delta functions and are conventional. The first form consists of five kinds of totally symmetric helicity fields and one kind of gauge parameter. By introducing auxiliary creation and annihilation operators, each is combined into a state vector in Fock space, including all ranks one by one. The Lagrangian imposes no constraints, such as trace conditions, on these fields or the gauge parameter field. Additionally, the Lagrangian does not contain higher-order derivative terms. In the limit as CS parameter μ approaches zero, it naturally reproduces a Lagrangian for helicity fields in higher spin(HS) theory, known as unconstrained quartet formulation. Permitting third-order derivatives, we also obtain the second unconstrained form of Lagrangian that can be written in terms of three kinds of fields, including μ, similar to the formulation by Francia and Sagnotti. Partial gauge fixing and partial use of equations of motion (EOM) on this Lagrangian yield a Fronsdal-like Lagrangian with a single double-traceless field, including μ. By imposing further gauge fixing on the field in the EOM with respect to divergence and trace, we confirm the reproduction of the modified Wigner equations already known in literature.

Spectral flow and localisation in AdS3 string theory

We study string theory in three-dimensional Anti-de Sitter spacetime in the path integral formalism. We derive expressions for generic spectrally-flowed near-boundary vertex operators in the Wakimoto representation, and relate their correlation functions to covering maps from the worldsheet to the target space boundary. We show that the path integral structurally reproduces correlation functions of the dual symmetric orbifold theory. By rephrasing spectral flow as the introduction of a background gauge field, we provide a path integral derivation of the localisation property of the near boundary theory. We then focus on the case of IIB string theory on AdS3 × S3 × \U0001d54b4 with k = 1 units of NS-NS flux, where the relationship between correlation functions and covering maps can be made sharp. We also comment on the relation of the k = 1 theory and twistor theory.

Quantization of Yang–Mills theory in de Sitter spacetime

In this paper, we analyze the quantization of Yang–Mills theory in the de Sitter spacetime. It is observed that the Faddeev–Popov ghost propagator is divergent in this spacetime. However, this divergence is removed by using an effective propagator, which is suitable for perturbation theory. To show that the quantization of Yang–Mills theory in the de Sitter is consistent, we quantize it using first-class constraints in the temporal gauge. We also demonstrate that this is equivalent to quantizing the theory in the Lorentz gauge.

Emergent modified gravity

A complete canonical formulation of general covariance makes it possible to construct new modified theories of gravity that are not of higher-curvature form, as shown here in a spherically symmetric setting. The usual uniqueness theorems are evaded by using a crucial and novel ingredient, allowing for fundamental fields of gravity distinct from an emergent space-time metric that provides a geometrical structure to all solutions. As specific examples, there are new expansion-shear couplings in cosmological models, a form of modified Newtonian dynamics can appear in a space-time covariant theory without introducing extra fields, and related effects help to make effective models of canonical quantum gravity fully consistent with general covariance.

The Hole Argument without the notion of isomorphism

In this paper, I argue that the Hole Argument can be formulated without using the notion of isomorphism, and for this reason it is not threatened by the criticism of Halvorson and Manchak (Br J Philos Sci, 2022. https://doi.org/10.1086/719193). Following Earman and Norton (Br J Philos Sci 38, pp. 515–525, 1987), I divide the Hole Argument into two steps: the proof of the Gauge Theorem and the transition from the Gauge Theorem to the conclusion of radical indeterminism. In the analaysis of the first step, I argue that the Gauge Theorem does not rely on the notion of isomorphism but on the notion of the diffeomorphism-invariance of the equations of local spacetime theories; however, for this approach to work, the definition of local spacetime theories needs certain amendments with respect to Earman and Norton’s formulation. In the analysis of the second step, I postulate that we should use the notion of radical indeterminism instead of indeterminism simpliciter and that we should not decide in advance what kind of maps are to be used in comparing models. Instead, we can tentatively choose some kind of maps for this purpose and check whether a given choice leads to radical indeterminism involving empirically indistinguishable models. In this way, the use of the notion of isomorphism is also avoided in the second step of the Hole Argument. A general picture is that physical equivalence can be established by means of an iterative procedure in which we examine various candidate classes of maps, and, depending on the outcomes, we need to broaden or narrow these classes. The Hole Argument can be viewed as a particular instance of this procedure.

Energy metrics and their Ricci flows

The framework of the Deformed Space-Time theory has been extended in the past from four to five dimensions, where the fifth coordinate is the energy exchanged by the interaction. In this theory, each fundamental interaction is described by an energy-dependent metric. This picture has been exploited in order to take care of the interaction behaviour both when Lorentz invariance holds and the spacetime is Minkowskian and when Lorentz is violated and must be recovered in a non-minkowskian spacetime. It has been successfully attempted to complete the pentadimensional metric of the four fundamental interactions calculating the fifth element of the metric corresponding to the fifth coordinate energy. The mathematical tool exploited is the method of the Ricci flow which gave the complete explicit form of the fifth element of the metric, answering in this way the question of "how the energy measure the energy" for each interaction, setting the electromagnetic interaction as the reference for the energy measure. In this sense it has been given meaning to the problem of the energy gauge for interaction, identifying the gauge with the fifth metric element. The consequences of the nuclear metamorphosis have been also examined for reaching the technological goal of a device stably producing this metamorphosis under the hadronic metric. The most valuable consequence is that in this pentadimensional picture, the old Einsteinian dream of a complete geometrization of the interactions is reached. The results achieved in the present work have allowed to design, build, and test of devices capable of exploiting the behavior of the fifth element of the metrics to obtain the production of electric charges directly from the nuclear metamorphosis of the matter.

New Classes of Solutions for Euclidean Scalar Field Theories

This paper presents new classes of exact radial solutions to the nonlinear ordinary differential equation that arises as a saddle-point condition for a Euclidean scalar field theory in D-dimensional spacetime. These solutions are found by exploiting the dimensional consistency of the radial differential equation for a single massless scalar field, which allows it to transform into an autonomous equation. For massive theories, the radial equation is not exactly solvable, but the massless solutions provide useful approximations to the results for the massive case. The solutions presented here depend on the power of the interaction and on the spatial dimension, both of which may be noninteger. Scalar equations arising in the study of conformal invariance fit into this framework, and classes of new solutions are found. These solutions exhibit two distinct behaviors as D→2 from above.

Spacetime Is Doomed: Time Is an Artifact

Abstract It is well known that spacetime has no operational meaning beyond the Planck scale. In consequence, many high-energy theoretical physicists are seeking, and finding, new structures entirely beyond spacetime. In light of these advances, we propose that time is not fundamental. The arrow of time is an artifact of projection of a stationary dynamics, entirely beyond spacetime and quantum theory, whose entropy does not increase.

Физическое состояние объектов прошлого и будущего

The theory of absolute space-time, on which the theory of relativity is based, thanks to Minkowski, says that the events of the past, present and future are equal in relation to their existence, i.e. they always exist and never disappear. The article examines the question of the physical state of their existence. A formalism is being built within the framework of the Relativity theory, according to which, since we do not see or interact with objects of the past and future, their states represent the socalled ghostly matter, characterized by a zero energy- momentum tensor. With the passage of coordinate (global) time, ghostly matter passes into the present and is discovered as reality, and then again passes into ghostly and becomes an object of the past.

Телекоммуникации между прошлыми и настоящей историческими эпохами

The theory of absolute space-time, known as general relativity, postulates the equal existence of the past, present, and future. This is the basis for the reality of constructing a time machine, which allows you to move bodies from the present to the past and back. The article describes the methods to transmit messages between a person who has moved into the past and people in the present.