相关论文: Structure, classifcation, and conformal symmetry, …

It is well known that at distances shorter than Planck length, no length measurements are possible. The Volovich hypothesis asserts that at sub-Planckian distances and times, spacetime itself has a non-Archimedean geometry. We discuss the…

The classification of all possible induced representations arising from theories admitting a Poincar\'e symmetry has molded our very conception of particles in flat space. In this note, we argue that if one takes the same viewpoint on the…

In this paper, we construct a class of collapsing spacetimes in vacuum without any symmetries. The spacetime contains a black hole region which is bounded from the past by the future event horizon. It possesses a Cauchy hypersurface with…

Wigner's seminal work on the Poincar\'e group revealed one of the fundamental principles of quantum theory: symmetry groups are projectively represented. The condensed-matter counterparts of the Poincar\'e group could be the spacetime…

In this work, we show that extending the standard description of space-time symmetries from groups of isometries to the more flexible framework of kinematical groupoids allows for the extension of Wigner's program to curved space-times. We…

When developing a quantum theory for a physical system, one determines the system's symmetry group and its irreducible unitary representations. For Minkowski space, the symmetry group is the Poincar\'e group, $\mathbb{R}^4 \rtimes…

We construct the vector fields associated to the space-time invariances of relativistic particle theory in flat Euclidean space-time. We show that the vector fields associated to the massive theory give rise to a differential operator…

This review consists of two parts. The first part establishes certain astrophysical bounds on the smoothness of classical spacetime. Some of the best bounds to date are based on the absence of vacuum Cherenkov radiation in ultrahigh-energy…

This paper treats the global existence question for a collection of general relativistic collisionless particles, all having the same mass. The spacetimes considered are globally hyperbolic, with Cauchy surface a 3-torus. Furthermore, the…

One of the deepest insights from the general theory of relativity is the relational nature of spacetime. While it is a generally agreed on that the nature of spacetime must be drastically different at the Planck scale, it has been a common…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…

When spacetime is considered as a subspace of a wider complex spacetime manifold, there is a mismatch of the elementary linear representations of their symmetry groups, the real and complex Poincar\'{e} groups. In particular, no spinors are…

The theory of defects in ordered and ill-ordered media is a well-advanced part of condensed matter physics. Concepts developed in this field also occur in the study of spacetime singularities, namely: i)- the topological theory of quantized…

In relativistic quantum mechanics, elementary particles are described by irreducible unitary representations of the Poincare group. The same applies to the center-of-mass kinematics of a multi-particle system that is not subject to external…

The quest for a quantum gravity phenomenology has inspired a quantum notion of space-time, which motivates us to study the fate of the relativistic symmetries of a particular model of quantum space-time, as well as its intimate connection…

Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…

The complete classification of classical $r$-matrices generating quantum deformations of the (3+1)-dimensional (A)dS and Poincar\'e groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists…

We describe the short-distance properties of the spacetime of a system of D-particles by viewing their matrix-valued coordinates as coupling constants of a deformed worldsheet $\sigma$-model. We show that the Zamolodchikov metric on the…

Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…