Space-time Symmetries Research Articles

Inferring Fundamental Spacetime Symmetries with Gravitational-Wave Memory: From LISA to the Einstein Telescope

Inferring Fundamental Spacetime Symmetries with Gravitational-Wave Memory: From LISA to the Einstein Telescope

Gravitational-Wave Memory May Illustrate Spacetime Symmetries

Gravitational-Wave Memory May Illustrate Spacetime Symmetries

Six-dimensional correlators from a five-dimensional operator product expansion

In this letter we discuss the operator product expansion of scalar operators in five-dimensional field theories with an SU(1, 3) × U(1) spacetime symmetry. Such theories arise by a novel conformal null reduction of six-dimensional Lorentzian conformal field theories. Unlike Lorentzian conformal field theories, three-point functions of generic operators in such theories are not completely fixed by SU(1, 3) × U(1) symmetry. However, we show that in a special case the functional form of the OPE coefficients can be fully determined, and we use them to fix the form of the three-point function. The result is shown to agree with correlation functions obtained by reduction of six-dimensional conformal field theories.

Dark matter and spacetime symmetry restoration

We examine local physics in the presence of variables: variables associated with the whole of the spacelike surfaces of a foliation. These could be the (pseudo)constants of nature and their conjugate times, but our statements are more general. Interactions between the local and the global (for example, dependence of the local action on global times dual to constants) degrades full space-time diffeomorphism invariance down to spatial diffeomorphism invariance, and so an extra degree of freedom appears. When these presumably primordial global interactions switch off, the local action recovers full invariance and so the usual two gravitons, but a legacy matter component is left over, bearing the extra degree of freedom. Under the assumption that the preferred foliation is geodesic, this component behaves like dark matter, except that 3 of its 4 local degrees of freedom are frozen, forcing its rest frame to coincide with the preferred foliation. The nonfrozen degree of freedom (the number density of the effective fluid) is the survivor of the extra “graviton” present in the initial theory and keeps memory of all the past global interactions that took place in a given location in the preferred foliation. Such “painted-on” dark matter is best distinguished from the conventional one in situations where the preferred frame would be preposterous if all 4 degrees of freedom of dark matter were available. We provide one example: an outflowing halo of legacy matter with exact escape speed at each point and a very specific profile, surrounding a condensed structure made of normal matter. Published by the American Physical Society 2024

The crucial role of Lagrange multipliers in a space-time symmetry preserving discretization scheme for IVPs

In a recently developed variational discretization scheme for second order initial value problems [1], it was shown that the Noether charge associated with time translation symmetry is exactly preserved in the interior of the simulated domain. The obtained solution also fulfils the naively discretized equations of motions inside the domain, except for the last two grid points. Here we provide an explanation for the deviations at the boundary as stemming from the effect of Lagrange multipliers used to implement initial and connecting conditions. We show explicitly that the Noether charge including the boundary corrections is exactly preserved at its continuum value over the whole simulation domain, including the boundary points.

Cosmographic and matter bounce scenario in modified torsion gravity

In this manuscript, we investigate the matter bounce cosmological implications in the context of f(T,τ) gravity (T represents the torsion scalar whereas τ is the trace of the energy–momentum tensor). We construct the field equations for spatially flat homogeneous and isotropic space–time with perfect fluid configuration. We consider the two particular forms of scale factor inspired by loop-quantum cosmology to investigate the matter bounce mechanism. In this regard, we examine the graphical behavior of cosmological as well as dynamical parameters at and in the neighborhood of bounce point. Furthermore, the stability via perturbation technique and energy conditions are also discussed. It is concluded that all the cosmographic tests favor the bouncing cosmology for an appropriate choice of model parameters. It is worth mentioning that considered models are stable and energy conditions are violated at the bouncing point as well as in its vicinity leading to a successful bouncing scenario.

Gauss–Bonnet source of Brans–Dicke scalar field and accelerated expansion of universe

In this work, using a different theoretical approach, we study a homogeneous and isotropic cosmological spacetime filled with a perfect fluid. Using the framework of Brans–Dicke (BD) and Gauss–Bonnet (GB) theories and including a scalar potential, we obtain the analytical solution of the field equations and find the field functions and the relevant expansion parameter of the spacetime. We assume that the BD and GB media can interact with each other, and hence that there is an energy transfer between these two components. Using this approach, we assume that the BD scalar field is related to intrinsic properties of the GB medium. We introduced a power-law scalar field [Formula: see text] and found the appropriate dynamical functions for the different powers p. We found that the expansion rate of spacetime also behaves as a power-law, and the accelerating expansion is always satisfied for this model. We also analyze the stability for physically acceptable critical points for a given scale factor.

Classification of same-gate quantum circuits and their space-time symmetries with application to the level-spacing distribution

Classification of same-gate quantum circuits and their space-time symmetries with application to the level-spacing distribution

Photon quantization in cosmological spaces

Canonical quantization of the photon—a free massless vector field—is considered in cosmological spacetimes in a two-parameter family of linear gauges that treat all the vector potential components on equal footing. The goal is setting up a framework for computing photon two-point functions appropriate for loop computations in realistic inflationary spacetimes. The quantization is implemented without relying on spacetime symmetries, but rather it is based on the classical canonical structure. Special attention is paid to the quantization of the canonical first-class constraint structure that is implemented as the condition on the physical states. This condition gives rise to subsidiary conditions that the photon two-point functions must satisfy. Some of the de Sitter space photon propagators from the literature are found not to satisfy these subsidiary conditions, bringing into question their consistency. Published by the American Physical Society 2024

Breaking the cosmological principle into pieces: a prelude to the intrinsically homogeneous and isotropic spacetimes

In this manuscript, we show that there are three fundamental building blocks supporting the cosmological principle. The first of them states that there is a special frame in the Universe where the spatial geometry is intrinsically homogeneous and isotropic. The second demands the existence of a fiducial observer to whom the Hubble parameter is isotropic. The last piece states that matter and radiation behave as a perfect fluid. We show that these three hypotheses give us the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetimes, the central pillar of the standard model of cosmology. We keep with the first of them and start to investigate the so-called intrinsically homogeneous and isotropic spacetimes. They emerge after the decoupling of the CMB with the geometric frame of reference. Furthermore, a ‘ΛCDM-like’ effective theory arises naturally in those backgrounds, together with some new density parameters relating to the local inhomogeneities, the internal energy density, and the local and global magnitudes of the Hubble anisotropy. All those properties make this class of inhomogeneous models, which roughly speaking, keeps ‘1/3’ of the cosmological principle, worth investigating in applications to cosmology, for it can accommodate the same ingredients of the standard model, as a geometric frame and a free-falling isotropic cosmic background radiation, and reduce to the latter when some observable parameters vanish.

Weyl quadratic gravity as a gauge theory and non-metricity vs torsion duality

We review (non-supersymmetric) gauge theories of four-dimensional space-time symmetries and their quadratic action. The only true gauge theory of such a symmetry (with a physical gauge boson) that has an exact geometric interpretation, generates Einstein gravity in its spontaneously broken phase and is anomaly-free, is that of Weyl gauge symmetry (of dilatations). Gauging the full conformal group does not generate a true gauge theory of physical (dynamical) associated gauge bosons. Regarding the Weyl gauge symmetry, it is naturally realised in Weyl conformal geometry, where it admits two different but equivalent geometric formulations, of same quadratic action: one non-metric but torsion-free, the other Weyl gauge-covariant and metric (with respect to a new differential operator). To clarify the origin of this intriguing result, a third equivalent formulation of this gauge symmetry is constructed using the standard, modern approach on the tangent space (uplifted to space-time by the vielbein), which is metric but has vectorial torsion. This shows an interesting duality vectorial non-metricity vs vectorial torsion of the corresponding formulations, related by a projective transformation. We comment on the physical meaning of these results.

Enigma of Pyramidal Neurons: Chirality-Centric View on Biological Evolution. Congruence to Molecular, Cellular, Physiological, Cognitive, and Psychological Functions

The mechanism of brain information processing unfolds within spatial and temporal domains inherently linked to the concept of space–time symmetry. Biological evolution, beginning with the prevalent molecular chirality, results in the handedness of human cognitive and psychological functions (the phenomena known as biochirality). The key element in the chain of chirality transfer from the downstream to upstream processes is the pyramidal neuron (PyrN) morphology–function paradigm (archetype). The most apparent landmark of PyrNs is the geometry of the cell soma. However, “why/how PyrN’s soma gains the shape of quasi-tetrahedral symmetry” has never been explicitly articulated. Resolving the above inquiry is only possible based on the broad-view assumption that encoding 3D space requires specific 3D geometry of the neuronal detector and corresponding network. Accordingly, our hypothesis states that if the primary function of PyrNs, at the organism level, is sensory space symmetry perception, then the pyramidal shape of soma is the best evolutionary-selected geometry to support sensory-motor coupling. The biological system’s non-equilibrium (NE) state is fundamentally linked to an asymmetric, non-racemic, steady state of molecular constituents. The chiral theory of pyramidal soma shape conceptually agrees that living systems have evolved as non-equilibrium systems that exchange energy with the environment. The molecular mechanism involved in developing PyrN’s soma is studied in detail. However, the crucial missing element—the reference to the fundamental link between molecular chirality and the function of spatial navigation—is the main obstacle to resolving the question in demand: why did PyrNs’ soma gain the shape of quasi-tetrahedral symmetry?

Aharonov-Bohm effect for confined matter in lattice gauge theories

Gauge theories arise in physical systems displaying space-time local symmetries. They provide a powerful description of important realms of physics ranging from fundamental interactions to statistical mechanics, condensed matter, and, more recently, quantum computation. As such, a remarkably deep understanding has been achieved in the field. With the advent of quantum technology, lower energy analogs, capable of capturing important features of the original quantum field theories through quantum simulation, have been intensively studied. Here, we propose a specific scheme implementing an quantum simulation of lattice gauge theories constrained to mesoscopic spatial scales. To this end, we study the dynamics of mesons residing in a ring-shaped lattice of mesoscopic size pierced by an effective magnetic field. In particular, we find a type of Aharonov-Bohm effect that goes beyond the particlelike effect, reflecting the features of the confining gauge potential. The coherence properties of the meson are quantified by the persistent current and by specific features of the correlation functions. When the magnetic field is quenched, Aharonov-Bohm oscillations and correlations start a specific matter-wave current dynamics. Published by the American Physical Society 2024

Quantum Nonlocality: How Does Nature Do It?

In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space-time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality, Einstein -causality and global symmetries. Bell tests allow only rejecting probabilistic coupling provided by a local hidden variable model, but they do not justify metaphysical speculations about quantum nonlocality and objects which know about each other's state, even when separated by large distances. The violation of Bell inequalities in physics and in cognitive science can be explained using the notion of Bohr- contextuality. If contextual variables, describing varying experimental contexts, are correctly incorporated into a probabilistic model, then the Bell-CHSH inequalities cannot be proven and nonlocal correlations may be explained in an intuitive way. We also elucidate the meaning of statistical independence assumption incorrectly called free choice, measurement independence or no- conspiracy. Since correlation does not imply causation, the violation of statistical independence should be called contextuality; it does not restrict the experimenter's freedom of choice. Therefore, contrary to what is believed, closing the freedom-of choice loophole does not close the contextuality loophole.

A symmetry principle for gauge theories with fractons

Fractonic phases are new phases of matter that host excitations with restricted mobility. We show that a certain class of gapless fractonic phases are realized as a result of spontaneous breaking of continuous higher-form symmetries whose conserved charges do not commute with spatial translations. We refer to such symmetries as nonuniform higher-form symmetries. These symmetries fall within the standard definition of higher-form symmetries in quantum field theory, and the corresponding symmetry generators are topological. Worldlines of particles are regarded as the charged objects of 1-form symmetries, and mobility restrictions can be implemented by introducing additional 1-form symmetries whose generators do not commute with spatial translations. These features are realized by effective field theories associated with spontaneously broken nonuniform 1-form symmetries. At low energies, the theories reduce to known higher-rank gauge theories such as scalar/vector charge gauge theories, and the gapless excitations in these theories are interpreted as Nambu-Goldstone modes for higher-form symmetries. Due to the nonuniformity of the symmetry, some of the modes acquire a gap, which is the higher-form analogue of the inverse Higgs mechanism of spacetime symmetries. The gauge theories have emergent nonuniform magnetic symmetries, and some of the magnetic monopoles become fractonic. We identify the ’t Hooft anomalies of the nonuniform higher-form symmetries and the corresponding bulk symmetry-protected topological phases. By this method, the mobility restrictions are fully determined by the choice of the commutation relations of charges with translations. This approach allows us to view existing (gapless) fracton models such as the scalar/vector charge gauge theories and their variants from a unified perspective and enables us to engineer theories with desired mobility restrictions.

Large N Fractons.

We consider theories of N-component fields with exotic spacetime symmetries, including a conserved dipole moment. Microscopic charges are immobile by symmetry, and so resemble fractons. Using collective fields we solve these models to leading order in large N. The large N solution reveals that these models are strongly correlated, and that interactions dress the microscopic charges so that they become mobile, long-lived quasiparticles. Dipole symmetry is spontaneously broken throughout the phase diagram of these models, leading to a low-energy Goldstone description.

Apparent fine tunings for field theories with broken space-time symmetries

We exhibit a class of effective field theories that have hierarchically small Wilson coefficients for operators that are not protected by symmetries but are not finely tuned. These theories possess bounded target spaces and vacua that break space-time symmetries. We give a physical interpretation of these theories as generalized solids with open boundary conditions. We show that these theories realize unusual RG flows where higher dimensional (seemingly irrelevant) operators become relevant even at weak coupling. Finally, we present an example of a field theory whose vacuum energy relaxes to a hierarchically small value compared to the UV cut-off.

Spacetime symmetry breaking effects in gravitational-wave generation at the first post-Newtonian order

Spacetime symmetry breaking effects in gravitational-wave generation at the first post-Newtonian order

Quantum electrodynamics of non-Hermitian Dirac fermions

We develop an effective quantum electrodynamics for non-Hermitian (NH) Dirac materials interacting with photons. These systems are described by nonspatial symmetry protected Lorentz invariant NH Dirac operators, featuring two velocity parameters υH and υNH associated with the standard Hermitian and a masslike anti-Hermitian Dirac operators, respectively. They display linear energy-momentum relation, however, in terms of an effective Fermi velocity υF=υH2−υNH2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\upsilon}_{\ extrm{F}}=\\sqrt{\\upsilon_{\ extrm{H}}^2-{\\upsilon}_{\ extrm{NH}}^2} $$\\end{document} of NH Dirac fermions. Interaction with the fluctuating electromagnetic radiation then gives birth to an emergent Lorentz symmetry in this family of NH Dirac materials in the deep infrared regime, where the system possesses a unique terminal velocity υF = c, with c being the speed of light. While in two dimensions such a terminal velocity is set by the speed of light in the free space, dynamic screening in three spatial dimensions permits its nonuniversal values. Manifestations of such an emergent spacetime symmetry on the scale dependence of various physical observables in correlated NH Dirac materials are discussed.

The Symmetry of Primitive Root in Number Theory

Symmetry refers to the exact same characteristics on both sides of an object or figure on a central axis or plane. In science and daily life, symmetrical things give people a sense of dignity and contain the beauty of balance and stability. It includes concepts such as space symmetry, time symmetry and group theory. In this article, the author explores an interesting phenomenon of primitive roots in number theory–symmetry, by symmetry, all primitive roots can be quickly solved.