Minkowski Space Research Articles

On Yang–Mills fields from anti-de Sitter spaces

Motivated by some recent progress involving a non-compact gauge group, we obtain classical gauge fields using non-compact foliations of anti-de Sitter space in 4 dimensions (required dimensionality for conformal invariance of Yang–Mills theory) and transfer these to Minkowski spacetime using a series of conformal maps. This construction also builds upon some previous works involving SU(2) gauge group in that we now use its non-compact counterpart SU(1, 1) here. We note down gauge fields in both Abelian as well as non-Abelian settings and find them to be divergent at some hyperboloid, which is a hypersurface of co-dimension 1 inside the conformal boundary of AdS4. In spite of this hurdle we find a physically relevant field configuration in the Abelian case, reproducing a known result.

Bootstrapping gravity and its extension to metric-affine theories

In this work we study diffeomorphism-invariant metric-affine theories of gravity from the point of view of self-interacting field theories on top of Minkowski spacetime (or other background). We revise how standard metric theories couple to their own energy-momentum tensor, and discuss the generalization of these ideas when torsion and nonmetricity are also present. We review the computation of the corresponding currents through the Hilbert and canonical (Noether) prescriptions, emphasizing the potential ambiguities arising from both. We also provide the extension of this consistent self-coupling procedure to the vielbein formalism, so that fermions can be included in the matter sector. In addition, we clarify some subtle issues regarding previous discussions on the self-coupling problem for metric theories, both General Relativity and its higher derivative generalizations. We also suggest a connection between Lovelock theorem and the ambiguities in the bootstrapping procedure arising from those in the definition of conserved currents.

Study of topological and physical properties of Schwarzschild and Kerr space-time equipped with Zeeman topology

The Zeeman topology, first proposed by E. C. Zeeman in 1967, is a topology for Minkowski space that is physically well-motivated, but more intricate than the standard Euclidean topology. Later, it was extended to general relativity in 1976 by R. Göbel. Despite its compatibility with pseudo-Riemannian geometry, the Zeeman topology is rarely used in the literature due to its lack of second-countability. This work aims to explore the implications of the Zeeman topology for Schwarzschild and Kerr space-time. Specifically, we investigate the compactness of trapped surfaces and the validity of the singularity theorem. Our findings suggest that the Zeeman topology may offer alternative views to certain physical phenomena in general relativity.

The Feynman chessboard model in 3 + 1 dimensions

The chessboard model was Feynman’s adaptation of his path integral method to a two-dimensional relativistic domain. It is shown that chessboard paths encode information about the contiguous pairs of paths in a spacetime plane, as required by discrete worldlines in Minkowski space. The application of coding by pairs in a four-dimensional spacetime is then restricted by the requirements of the Lorentz transformation, and the implementation of these restrictions provides an extension of the model to 4D, illuminating the relationship between relativity and quantum propagation.

Mapping between space-like curve flows and soliton equations in Minkowski space

In this study, we demonstrate that when three distinct moving space-like curves with the time-like binormal vectors satisfy the generalizations of the Heisenberg spin chain model, these models are equivalent to the third-order system of the AKNS hierarchy and the complex KdV-type equations.

On pseudo-Riemannian quartics in Finsler geometry

Finsler geometry usually describes an extension of Riemannian geometry into a direction-dependent geometric structure. Historically, the well-known Riemann quartic length element example served as the inspiration for this construction. Surprisingly, the same quartic expression emerges as a fundamental dispersion relationcovariant Fresnel equationin solid-state electrodynamics. As a result, it is possible to conceive of the Riemann quartic length expression as a mathematical representation of a well-known physical phenomenon. This paper provides a number of Riemann quartic examples that show Finsler geometry to be overly constrictive for many applications, even when the signature space is positive definite in the Euclidean sense. The strong axioms of Finsler geometry are broken down on many more singular hypersurfaces for the spaces having an indefinite (Minkowski) signature. We suggest a more flexible definition of a Finsler structure that only has to hold for open subsets of a manifold’s tangent bundle. We demonstrate the distinctive singular hypersurfaces connected to the Riemann quartic and discuss the potential physics explanations for them. As an illustration of the pseudo-Riemannian quartic, we took into consideration the dispersion relation that appears in electromagnetic wave propagation in uniaxial crystal. Our analysis suggests that the signature of the Finsler measure may be altered for large anisotropy factors.

Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields

We develop the BRST approach to construct the general off-shell local Lorentz covariant cubic interaction vertices for irreducible massless and massive higher spin fields on d-dimensional Minkowski space. We consider two different cases for interacting higher spin fields: with one massive and two massless; two massive, both with coinciding and with different masses and one massless field of spins s1,s2,s3. Unlike the previous results on cubic vertices we extend our earlier result in (Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470) for massless fields and employ the complete BRST operator, including the trace constraints, which is used to formulate an irreducible representation with definite integer spin. We generalize the cubic vertices proposed for reducible higher spin fields in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) in the form of multiplicative and non-multiplicative BRST-closed constituents and calculate the new contributions to the vertex, which contains the additional terms with a smaller number of space-time derivatives. We prove that without traceless conditions for the cubic vertices in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) it is impossible to provide the noncontradictory Lagrangian dynamics and find explicit traceless solution for these vertices. As the examples, we explicitly construct the interacting Lagrangians for the massive spin of the s field and the massless scalars, both with and without auxiliary fields. The interacting models with different combinations of triples higher spin fields: massive spin s with massless scalar and vector fields and with two vector fields; massless helicity λ with massless scalar and massive vector fields; two massive fields of spins s, 0 and massless scalar is also considered.

Soft particles and infinite-dimensional geometry

In the sigma model, soft insertions of moduli scalars enact parallel transport of S-matrix elements about the finite-dimensional moduli space of vacua, and the antisymmetric double-soft theorem calculates the curvature of the vacuum manifold. We explore the analogs of these statements in gauge theory and gravity in asymptotically flat spacetimes, where the relevant moduli spaces are infinite-dimensional. These models have spaces of vacua parameterized by (trivial) flat connections on the celestial sphere, and soft insertions of photons, gluons, and gravitons parallel transport S-matrix elements about these infinite-dimensional manifolds. We argue that the antisymmetric double-soft gluon theorem in d + 2 bulk dimensions computes the curvature of a connection on the infinite-dimensional space Map, where G is the global part of the gauge group. The analogous metrics in abelian gauge theory and gravity are flat, as indicated by the vanishing of the antisymmetric double-soft theorems in those models. In other words, Feynman diagram calculations not only know about the vacuum manifold of Yang–Mills theory, they can also be used to compute its curvature. The results have interesting implications for flat space holography.

SO(1,3) Yang-Mills solutions on Minkowski space via cosets

We present a novel family of Yang-Mills solutions, with gauge group SO(1,3), on Minkowski space that are geometrically distinguished into two classes, viz. interior and exterior of the lightcone. We achieve this by foliating the former with SO(1,3)/SO(3) cosets and the latter with SO(1,3)/SO(1,2) cosets and analytically solving the Yang-Mills equation of an SO(1,3)-invariant gauge field. The resulting fields and their stress-energy tensor, when translated to the Minkowski space, diverge at the lightcone, but we demonstrate how this stress-energy tensor could be regularised due to its unique algebraic structure.

Harvesting correlations from vacuum quantum fields in the presence of a reflecting boundary

We explore correlations harvesting by two static detectors locally interacting with vacuum massless scalar fields in the presence of an infinite perfectly reflecting boundary. We study the phenomena of mutual information harvesting and entanglement harvesting for two detector-boundary alignments, i.e., parallel-to-boundary and orthogonal-to-boundary alignments. Our results show that the presence of the boundary generally inhibits mutual information harvesting relative to that in flat spacetime without any boundaries. In contrast, the boundary may play a doubled-edged role in entanglement harvesting, i.e., inhibiting entanglement harvesting in the near zone of the boundary while assisting it in the far zone of the boundary. Moreover, there exists an optimal detector energy gap difference between two nonidentical detectors that makes such detectors advantageous in correlations harvesting as long as the interdetector separation is large enough. The value of the optimal detector energy gap difference depends on both the interdetector separation and the detector-to-boundary distance. A comparison of the correlations harvesting in two different alignments shows that although correlations harvesting share qualitatively the same properties, they also display quantitative differences in that the detectors in orthogonal-to-boundary alignment always harvest comparatively more mutual information than the parallel-to-boundary ones, while they harvest comparatively more entanglement only near the boundary.

Constrain the time variation of the gravitational constant via the propagation of gravitational waves

The gravitational constant variation means the breakdown of the strong equivalence principle. As the cornerstone of general relativity, the validity of general relativity can be examined by studying the gravitational constant variation. Such variations have the potential to affect both the generation and propagation of gravitational waves. Here, our focus lies on the effect of gravitational constant variation specifically on the propagation of gravitational waves. In a previous paper (An et al., 2023 [13]) we have studied such effect based on a Maxwell-like equation. That work admits two drawbacks. The assumption that describing gravitational waves with Maxwell-like equation is not solid. And more such treatment can only deal with space dependent gravitational constant. In the current paper we will remedy these two issues. We employ two analytical methods, namely based on the Fierz-Pauli action and the perturbation of Einstein-Hilbert action around Minkowski spacetime, both leading to the same gravitational wave equation. By solving this equation, we find the effects of gravitational constant variation on gravitational wave propagation. The result is consistent with previous investigations based on Maxwell-like equations for gravitational waves for space dependent gravitational constant cases. In addition we can constrain the time variation of the gravitational constant via the propagation of gravitational waves based on GW170817 data. And more, we find that small variations in the gravitational constant result in an amplitude correction at the leading order and a phase correction at the sub-leading order for gravitational waves. These results provide valuable insights for probing gravitational constant variation and can be directly applied to gravitational wave data analysis.

On separable states in relativistic quantum field theory

We initiate an investigation into separable, but physically reasonable, states in relativistic quantum field theory. In particular we will consider the minimum amount of energy density needed to ensure the existence of separable states between given spacelike separated regions. This is a first step towards improving our understanding of the balance between entanglement entropy and energy (density), which is of great physical interest in its own right and also in the context of black hole thermodynamics. We will focus concretely on a linear scalar quantum field in a topologically trivial, four-dimensional globally hyperbolic spacetime. For rather general spacelike separated regions A and B we prove the existence of a separable quasi-free Hadamard state. In Minkowski spacetime we provide a tighter construction for massive free scalar fields: given any R > 0 we construct a quasi-free Hadamard state which is stationary, homogeneous, spatially isotropic and separable between any two regions in an inertial time slice all of whose points have a distance . We also show that the normal ordered energy density of these states can be made (in Planck units). To achieve these results we use a rather explicit construction of test-functions f of positive type for which we can get sufficient control on lower bounds on .

Refocusing of the optical branched flow on a rough curved surface

The phenomenon of branched flow has attracted researchers since its inception, with recent observations of the light branching on soap bubbles. However, previous studies have primarily focused on the flat spacetime, overlooking the effect of surface curvature on branched flows. In this paper, we explore the branched flow phenomenon of light on a rough curved surface called constant Gaussian curvature surfaces (CGCSs). Compared with flat space, a CGCS demonstrates that the first branching point advances due to the focusing effect of the positive curvature of the surface. Furthermore, unlike on flat space, optical branches on curved surfaces do not consistently become chaotic during its transmission in a random potential field. On the contrary, the “entropy” decreases at specific positions, which reveals a sink flow phenomenon following the generation of branched flows. This result highlights the time inversion characteristics of CGCSs. Lastly, we demonstrated that the anomalous entropy reduction is related to the transverse and longitudinal coherence transformations of light. We suppose these efforts would fuel further investigation of the thermodynamic evolution and spatiotemporal inversion of random caustics, as well as their future application in the information transmission of random potentials in curved spacetime.

Quantum flux operators for Carrollian diffeomorphism in general dimensions

We construct Carrollian scalar field theories in general dimensions, mainly focusing on the boundaries of Minkowski and Rindler spacetime, whose quantum flux operators form a faithful representation of Carrollian diffeomorphism up to a central charge, respectively. At future/past null infinity, the fluxes are physically observable and encode rich information of the radiation. The central charge may be regularized to be finite by the spectral zeta function or heat kernel method on the unit sphere. For the theory at the Rindler horizon, the effective central charge is proportional to the area of the bifurcation surface after regularization. Moreover, the zero mode of supertranslation is identified as the modular Hamiltonian, linking Carrollian diffeomorphism to quantum information theory. Our results may hold for general null hypersurfaces and provide new insight in the study of the Carrollian field theory, asymptotic symmetry group and entanglement entropy.

The Relativistic Rotation Transformation and the Observer Manifold

We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore, not a parameterised motion on a background space or spacetime, but is determined by a particular sequence of tetrads related by specific special Lorentz transformations or boosts. Because such Lorentz boosts do not form a group, these tetrads represent distinct observers that cannot put together their local descriptions into a manifold in the usual sense. The choice of observer manifold depends on the dynamical situation under consideration, and is not solely determined by the kinematics. Three examples are given: Franklin’s rotation transformation for uniform plane rotation, the Thomas precession of a vector attached to an electron, and the motion of a charged particle in an electromagnetic field. In each case, at each point of its trajectory, there is a distinguished tetrad and a special Lorentz transformation that maps Minkowski space to the spacetime of the local observer on the curve.

GEMS Embeddings of Hayward Regular Black Holes in Massless and Massive Gravities

After finding a solution for the Hayward regular black hole (HRBH) in massive gravity, we embed the (3+1)-dimensional HRBHs both in massless and in massive gravities into (5+2)- and (6+3)-dimensional Minkowski spacetimes, respectively. Here, massive gravity denotes that a graviton acquires a mass holographically by broken momentum conservation in the HRBH. The original HRBH has no holographically added gravitons, which we call ‘massless’. Making use of newly found embedding coordinates, we obtain desired Unruh temperatures and compare them with the Hawking and local fiducial temperatures, showing that the Unruh effect for a uniformly accelerated observer in a higher-dimensional flat spacetime is equal to the Hawking effect for a fiducial observer in a black hole spacetime. We also obtain freely falling temperatures of the HRBHs in massless and massive gravities seen by freely falling observers, which remain finite even at the event horizons while becoming the Hawking temperatures in asymptotic infinity.

A duality for prescribed mean curvature graphs in Riemannian and Lorentzian Killing submersions

AbstractWe develop a conformal duality for space‐like graphs in Riemannian and Lorentzian three‐manifolds that admit a Riemannian submersion over a Riemannian surface whose fibers are the integral curves of a Killing vector field, which is time‐like in the Lorentzian case. The duality swaps mean curvature and bundle curvature and sends the length of the Killing vector field to its reciprocal while keeping invariant the base surface. We obtain two consequences of this result. On the one hand, we find entire graphs in Lorentz–Minkowski space with prescribed mean curvature a bounded function with bounded gradient. On the other hand, we obtain conditions for the existence and nonexistence of entire graphs which are related to a notion of the critical mean curvature.

Quantum mechanical Gaussian wavepackets of single relativistic particles

We study the evolutions of selected quasi-(1+1) dimensional wavepacket solutions to the Klein–Gordon equation for a relativistic charged particle in uniform motion or accelerated by a uniform electric field in Minkowski space. We explore how good the charge density of a Klein–Gordon wavepacket can be approximately described by a Gaussian state with the single-particle interpretation. We find that the minimal initial width of a wavepacket for a good Gaussian approximation in position space is about the Compton wavelength of the particle divided by its Lorentz factor at the initial moment. This can be considered as a manifestation of relativistic length contraction, which is also observed numerically in the spreading of the wavepacket’s charge density.

BMS modular covariance and structure constants

Two-dimensional (2d) field theories invariant under the Bondi-Metzner-Sachs algebra, or 2d BMSFTs in short, are putative holographic duals of Einstein gravity in 3d asymptotically flat spacetimes. When defined on a torus, these field theories come equipped with a modified modular structure. We use the modular covariance of the BMS torus two-point function to develop formulae for different three-point structure constants of the field theory. These structure constants indicate that BMSFTs follow the eigenstate thermalization hypothesis, albeit with some interesting changes to usual 2d CFTs. The singularity structures of the structure constants contain information on perturbations of cosmological horizons in 3d asymptotically flat spacetimes, which we show can also be obtained as a limit of BTZ quasinormal modes.

Gyroscopic gravitational memory

We study the motion of a gyroscope located far away from an isolated gravitational source in an asymptotically flat spacetime. As seen from a local frame tied to distant stars, the gyroscope precesses when gravitational waves cross its path, resulting in a net ‘orientation memory’ that carries information on the wave profile. At leading order in the inverse distance to the source, the memory consists of two terms: the first is linear in the metric perturbation and coincides with the spin memory effect, while the second is quadratic and measures the net helicity of the wave burst. Both are closely related to symmetries of the gravitational radiative phase space at null infinity: spin memory probes superrotation charges, while helicity is the canonical generator of local electric-magnetic duality on the celestial sphere.