Space-time Symmetries Research Articles

Total Momentum and Other Noether Charges for Particles Interacting in a Quantum Spacetime

There has been strong interest in the fate of relativistic symmetries in some quantum spacetimes, partly because of its possible relevance for high-precision experimental tests of relativistic properties. However, the main technical results obtained so far concern the description of suitably deformed relativistic symmetry transformation rules, whereas the properties of the associated Noether charges, which are crucial for the phenomenology, are still poorly understood. Here, we tackle this problem focusing on first-quantized particles described within a Hamiltonian framework and using as a toy model the so-called “spatial kappa-Minkowski noncommutative spacetime”, where all the relevant conceptual challenges are present but, as here shown, in technically manageable fashion. We derive the Noether charges, including the much-debated total momentum charges, and we reveal a strong link between the properties of these Noether charges and the structure of the laws of interaction among particles.

Gravity from Pre-geometry

Abstract The gravitational interaction, as described by the Einstein–Cartan theory, is shown to emerge as the by-product of the spontaneous symmetry breaking of a gauge symmetry in a pre-geometric four-dimensional spacetime. Starting from a formulation a ` la Yang–Mills on an SO ( 1 , 4 ) or SO ( 3 , 2 ) principal bundle and not accounting for a spacetime metric, the Einstein–Hilbert action is recovered after the identification of the effective spacetime metric and spin connection for the residual SO ( 1 , 3 ) gauge symmetry of the spontaneously broken phase—i.e. the stabiliser of the SO ( 1 , 4 ) or SO ( 3 , 2 ) gauge group. Thus, the two fundamental tenets of general relativity, i.e. diffeomorphism invariance and the equivalence principle, can arise from a more fundamental gauge principle. The two mass parameters that characterise Einstein gravity, namely the Planck mass and the cosmological constant, are likewise shown to be emergent. The phase transition from the unbroken to the spontaneously broken phase is expected to happen close to the Planck temperature. This is conjectured to be dynamically driven by a scalar field that implements a Higgs mechanism, hence providing mass to new particles, with consequences for cosmology and high-energy physics. The couplings of gravity to matter are discussed after drawing up a dictionary that interconnects pre-geometric and effective geometric quantities. In the unbroken phase where the fundamental gauge symmetry is restored, the theory is potentially power-counting renormalisable without matter, offering a novel path towards a UV completion of Einstein gravity.

Observation of broadband super-absorption of electromagnetic waves through space-time symmetry breaking.

Using time as an additional design parameter in electromagnetism, photonics, and wave physics is attracting considerable research interest, motivated by the possibility to explore physical phenomena and engineering opportunities beyond the limits of time-invariant systems. Here, we report the experimental demonstration of enhanced broadband absorption of electromagnetic waves in a continuously modulated time-varying system, exceeding one of the key theoretical limits of linear time-invariant absorbers. This is achieved by harnessing the frequency-wave vector transitions and enhanced interference effects enabled by breaking both continuous space- and time-translation symmetries in a periodically time-modulated absorbing structure operating at radio frequencies. Furthermore, we demonstrate broadband coherent wave absorption using a secondary control wave, observing a nearly perfect, reconfigurable, antireflection effect over a broad continuous bandwidth. Our findings provide insights into enhanced wave absorption in time-varying scenarios and may enable the development of devices operating in a regime fundamentally beyond the reach of linear time-invariant systems.

Discrete spacetime crystal: Intertwined spacetime symmetry breaking in a driven-dissipative spin system

Discrete spacetime crystal: Intertwined spacetime symmetry breaking in a driven-dissipative spin system

Mass independent Klein Gordon equation

We transform the Klein–Gordon equation into a mass-independent form that treats space–time more symmetrically. The mass-independent Klein–Gordon equation (MIKE) is first order in a variable that plays the role of time, the approach taken in parametric time formulations. MIKE is useful for studying the effects of noise because we can borrow techniques from the theory of quantum open systems, where first order master equations often appear. Moreover, we can maintain space–time symmetry while carrying out calculations. Specifically, we use MIKE to study the noisy Feynman propagator, a correlation function of two fields in the presence of noise. One characteristic of the Feynman propagator (its sign) is important to ensure that probabilities properly range from zero to one. We find that the sign is preserved in the presence of electromagnetic noise.

Network model for magnetic higher-order topological phases

We propose a network-model realization of magnetic higher-order topological phases (HOTPs) in the presence of the combined space-time symmetry C4T—the product of a fourfold rotation and time-reversal symmetry. We show that the system possesses two types of HOTPs. The first type, analogous to Floquet topology, generates a total of eight corner modes at 0 or π eigenphase, while the second type, hidden behind a weak topological phase, yields a unique phase with eight corner modes at ±π/2 eigenphase (after gapping out the counterpropagating edge states), arising from the product of particle-hole and phase-rotation symmetry. By using a bulk Z4 topological index (Q), we found both HOTPs have Q=2, whereas Q=0 for the trivial and the conventional weak topological phase. Together with a Z2 topological index associated with the reflection matrix, we are able to fully distinguish all phases. Our work motivates further studies on magnetic topological phases and symmetry-protected 2π/n boundary modes, as well as suggesting that such phases may find their experimental realization in coupled-ring-resonator networks. Published by the American Physical Society 2024

Late-time accelerating cosmological models in [formula omitted]-gravity with observational constraints

In the present paper, we investigate cosmological models in the most recent proposed modified f(R,Lm,T)-gravity theory in the context of a flat, homogeneous, and isotropic spacetime with perfect fluid source. We solve the field equations for the constant equation of state ω=1,13,0,−23,−1 with matter Lagrangian Lm=p and obtain five cosmological models. We make observational constraints on the model parameters involved in these four derived models using MCMC (Monte Carlo Markov Chain) analysis of cosmic chronometer Hubble datasets. After that, we investigate the effective equation of state and deceleration parameter for each model. We find that the first four models are transit-phase accelerating in the late-time universe, whereas the last one model shows only the accelerating phase of the expanding universe. We also discussed the information criteria for model selection (AIC and BIC) for the four models in the context of the standard ΛCDM model. Finally, we discussed the stability of the model in the context of the Hubble parameter and energy density.

Quantum Valley Hall Effect without Berry Curvature.

The quantum valley Hall effect (QVHE) is characterized by the valley Chern number (VCN) in a way that one-dimensional (1D) chiral metallic states are guaranteed to appear at the domain walls (DW) between two domains with opposite VCN for a given valley. Although in the case of QVHE, the total Berry curvature (BC) of the system is zero, the BC distributed locally around each valley makes the VCN well defined as long as intervalley scattering is negligible. Here, we propose a new type of valley-dependent topological phenomenon that occurs when the BC is strictly zero at each momentum. Such zero Berry curvature (ZBC) QVHE is characterized by the valley Euler number (VEN) which is computed by integrating the Euler curvature around a given valley in two-dimensional (2D) systems with space-time inversion symmetry. 1D helical metallic states can be topologically protected at the DW between two domains with the opposite VENs when the DW configuration preserves either the mirror symmetry with respect to the DW or the combination of the DW space-time inversion and chiral symmetries. We establish the fundamental origin of ZBC QVHE. Also, by combining tight-binding model study and first-principles calculations, we propose stacked hexagonal bilayer lattices including h-BX (X=As, P) and large-angle twisted bilayer graphenes as candidate systems with robust helical DW states protected by VEN.

Reflection parity and space-time parity photonic conservation laws in parametric nonlinear optics

Conservation laws are some of the most generic and useful concepts in physics. In nonlinear optical parametric processes, conservation of photonic energy, momenta and parity often lead to selection rules, restricting the allowed polarization and frequencies of the emitted radiation. Here we present a scheme to derive conservation laws in optical parametric processes in which many photons are annihilated and a single photon is emitted. We first rederive with it the known nonlinear optical conservation laws, and then utilize it to predict and explore conservations of reflection parity and space-time parity. Conservation of arises from a generalized reflection symmetry of the polarization in a superspace, analogous to the superspace employed in the study of quasicrystals. Conservation of similarly arises from space-time reversal symmetry in superspace. We explore these conservation laws numerically in the context of high-harmonic generation and outline experimental setups where they can be tested. Published by the American Physical Society 2024

Existence of remnants of regular black holes with de Sitter centers

We address the question of the end point of the quantum evaporation of regular black holes with the de Sitter centers specified by the algebraic structure of their stress–energy tensors [Formula: see text]. Most of the presented in the literature regular solutions belong to this class. In the case of a nonzero background cosmological constant stress–energy tensors with [Formula: see text] connect smoothly two de Sitter vacua, in the center and at infinity, and generate regular solutions to the Einstein equations, which describe the spacetime structure of regular black holes and their remnants. We show that for this class black holes their spacetime symmetry prevents a complete evaporation and provides the existence of thermodynamically stable remnants.

Spacetime symmetry breaking on nongeodesic leaves and a new form of matter

We examine the permanent damage caused by the historical breakdown of full diffeomorphism invariance induced by a foliation. We focus on the case where the foliation is allowed to be nongeodesic after the interactions with the foliation switch off. Gravity and other forms of matter recover full diffeomorphism invariance only at the expense of introducing a new matterlike component, carrying the nonvanishing Hamiltonian (and momentum, as it turns out) left over from the violating past interactions. This matter form must be stress-free in the preferred frame; this is the only way a matter action can mimic the evolution of the leftover Hamiltonian (and momentum) driven by the Dirac hypersurface deformation algebra. Hence, if the preferred frame is nongeodesic, the equivalent matter component must have energy and a momentum current in this frame, but still no spatial stresses: an unusual form of “matter.” It is equivalent to a fluid with anisotropic stress in some regimes, reducing to dust in others, or even displaying completely new features in extreme situations. Its stress energy tensor is conserved. We provide two examples based on accelerated frames: Rindler space-time and the canonical Schwarzchild frame. Published by the American Physical Society 2024

Geometrically thick equilibrium tori around a Schwarzschild black hole in swirling universes

We study geometrically thick non-self gravitating equilibrium tori orbiting a Schwarzschild black hole immersed in swirling universes. This solution is axially symmetric and non-asymptotically flat, and its north and south hemispheres spin in opposite directions. Due to repulsive effects arising from the swirl of the background spacetime, the equilibrium torus exists only in the small swirling case. With the increase of the swirling parameter, the disk structure becomes small and the excretion of matter near the black hole becomes strong. Moreover, the odd Z2 symmetry of spacetimes originating from the swirling parameter yields that the orientation of closed equipotential surfaces deviates away from the horizontal axis and the corresponding disk does not longer possess the symmetry with respect to the equatorial plane. These significant features could help to further understand the equilibrium tori and geometrically thick accretion disks around black holes in swirling universes.

A dynamical system analysis of non-interacting cold dark matter and dark energy at perturbative level

This work deals with a cosmological model consisting of cold dark matter and dark energy without any interaction. The study has been done both at the background level and at the perturbative level for the homogeneous and isotropic FLRW spacetime. By suitable transformation of the variables, the cosmic evolution equations are converted into an autonomous system. A discrete dynamical system analysis has been employed for cosmic inferences.

Real Topological Phonons in 3D Carbon Allotropes.

There has been a significant focus on real topological systems that enjoy space-time inversion symmetry and lack spin-orbit coupling. While the theoretical classification of the real topology has been established, more progress has yet to be made in the materials realization of real topological phononic states in 3D. To address this crucial issue, high-throughput computing is performed to inspect the real topology in the phonon spectrums of the 3D carbon allotropes. Among 1661 carbon allotropes listed in the Samara Carbon Allotrope Database (SACADA), 79 candidates host a phononic real Chern insulating (PRCI) state, 2 candidates host a phononic real nodal line (PRNL) state, 12 candidates host a phononic real Dirac point (PRDP) state, and 10 candidates host a phononic real triple-point pair (PRTPP) state. The PRCI, PRNL, PRTPP, and PRDP states of 27-SG. 166-pcu-h, 1081-SG. 194-42T13-CA, 52-SG. 141-gis, and 132-SG. 191-3,4T157 are exhibited as illustrative examples, and the second-order phononic hinge modes are explored. This study broadens the understanding of 3D topological phonons and expands the material candidates with phononic hinge modes and phononic realtopology.

Fractal Biology — Evolution from Molecular to Cognitive, and Psychological Dimensions

Biological and artificial intelligence (BI and AI) share the fundamental principles of space-time information processing based on symmetry transformation. Therefore, cognitive-science-inspired AI represents a promising area of exploration. A convincing example are the fractal structure of human languages and protein assembly. Biological processes’ temporal and spatial plasticity links them to basic laws of physics. Continuous advances in fundamental physical theories allow understanding of all aspects of space-time symmetry (STS) natively intertwined with the principle of relativity and causality. Spatial aspects of symmetry represented by three sub-domains such as chirality, fractality, and topology, are widely studied in biology. The role of chirality in biology has been analyzed in several recent reviews. However, the fractals and topological states of biological structures is a relatively new and fast-developing branch of science. Here, we trace publications exploring the role of fractal symmetry in all hierarchical states of biological organization, including at the molecular, cellular, morphological, physiological, perceptual, cognitive, and psychological levels. The coverage of the above-listed areas in current studies is sharply unequal and unsystematic. A broad view of biological fractality opens a unique opportunity to discriminate between a healthy state and a wide range of disease conditions. Psychiatric, neurological, and immune disorders are associated with aberrant molecular assembly and morphological changes in neural circuits, suggesting that the chain of chirality/fractality transfer through all levels of physiological organization deserves persistent attention.

Analyticity and the Unruh effect: a study of local modular flow

The Unruh effect can be formulated as the statement that the Minkowski vacuum in a Rindler wedge has a boost as its modular flow. In recent years, other examples of states with geometrically local modular flow have played important roles in understanding energy and entropy in quantum field theory and quantum gravity. Here I initiate a general study of the settings in which geometric modular flow can arise, showing (i) that any geometric modular flow must be a conformal symmetry of the background spacetime, and (ii) that in a well behaved class of “weakly analytic” states, geometric modular flow must be future-directed. I further argue that if a geometric transformation is conformal but not isometric, then it can only be realized as modular flow in a conformal field theory. Finally, I discuss a few settings in which converse results can be shown — i.e., settings in which a state can be constructed whose modular flow reproduces a given vector field.

The cosmological constant emerging from a symmetry invariant

The cosmological constant is normally introduced as an additional term entering the Einstein–Hilbert (EH) action. In this letter, we demonstrate that, instead, it appears naturally from the standard EH action as an invariant term emerging from spacetime symmetries. We then demonstrate that the same constraint emerging from this invariant suppresses the short wavelength modes and it favors the long wavelength ones. In this way, inside the proposed formulation, the observed value for the vacuum energy density is obtained naturally from the zero-point quantum fluctuations.

Asymptotic symmetries from the string worldsheet

In IIB string theory on AdS3 background with NS-NS fluxes, we show that Brown-Henneaux asymptotic Killing vectors can be derived by requiring both the worldsheet equations of motion and Virasoro constraints are preserved near the asymptotic boundary of the target spacetime. The charges on the worldsheet that generate the corresponding transformations can be written down in both the Lagrangian formalism and Hamiltonian formalism. This provides a method of studying asymptotic symmetry of the target spacetime directly from worldsheet string theories, without using results from the supergravity limit. As an example, we apply this method to flat spacetime in three dimensions and obtain the BMS3 generators on the worldsheet theory.

A topological Hund nodal line antiferromagnet

The interplay of topology, magnetism, and correlations gives rise to intriguing phases of matter. In this study, through state-of-the-art angle-resolved photoemission spectroscopy, density functional theory, and dynamical mean-field theory calculations, we visualize a fourfold degenerate Dirac nodal line at the boundary of the bulk Brillouin zone in the antiferromagnet YMn2Ge2. We further demonstrate that this gapless, antiferromagnetic Dirac nodal line is enforced by the combination of magnetism, space-time inversion symmetry, and nonsymmorphic lattice symmetry. The corresponding drumhead surface states traverse the whole surface Brillouin zone. YMn2Ge2 thus serves as a platform to exhibit the interplay of multiple degenerate nodal physics and antiferromagnetism. Interestingly, the magnetic nodal line displays a d-orbital dependent renormalization along its trajectory in momentum space, thereby manifesting Hund’s coupling. Our findings offer insights into the effect of electronic correlations on magnetic Dirac nodal lines, leading to an antiferromagnetic Hund nodal line.

Higher-group global symmetry and the bosonic M5 brane

Higher-group symmetries are combinations of higher-form symmetries which appear in various field theories. In this paper, we explain how higher-group symmetries arise in 10d and 11d supergravities when the latter are coupled to brane sources. Motivated by this observation, we study field theories at zero and finite temperature invariant under a class of continuous Abelian higher-group symmetries. We restrict the analysis to the low-energy regime where the dynamical field content exclusively consists of Goldstone fields arising from the spontaneous breaking of higher-group and spacetime symmetries. Invariant quantities are constructed and the phases of matter are classified according to the pattern of spontaneous symmetry breaking. With respect to supergravity, we highlight how such Goldstone effective theories provide a symmetry-based interpretation for the theories living on D/M-branes. As an explicit example we construct a 6-group invariant action for the bosonic M5 brane, consistent with the self-duality of the 3-form field strength on the brane. While the self-duality condition in the bosonic case needs to be imposed externally as a constraint at zero temperature, we find an equilibrium effective action for the bosonic M5 brane at finite temperature that inherently implements self-duality.