Related papers: General study and basic properties of causal symme…
We describe up to finite coverings causal flat affine complete Lorentzian manifolds such that the past and the future of any point are closed near this point. We say that these manifolds are strictly causal. In particular, we prove that…
A program of wide interest in modern conformal bootstrap studies is to numerically solve general conformal field theories, based on a critical assumption that the dynamics is encoded in the conformal four-point crossing equations and…
The simplicial endofunctor induced by a comonad in some category may underly a cyclic object in its category of endofunctors. The cyclic symmetry is then given by a sequence of natural transformations. We write down the commutation…
We study local variations of causal curves in a space-time with respect to b-length (or generalised affine parameter length). In a convex normal neighbourhood, causal curves of maximal metric length are geodesics. Using variational…
Based on the principle of relativity and the postulate on universal invariant constants (c,l), all possible kinematics can be set up with sub-symmetries of the Umov-Weyl-Fock transformations for the inertial motions. Further, in the…
The boundary at $\Cal I^+$, future null infinity, for a standard static, spherically symmetric spactime is examined for possible linear connections. Two independent methods are employed, one for treating $\Cal I^+$ as the future causal…
It was recently suggested that causal structures are both dynamical, because of general relativity, and indefinite, due to quantum theory. The process matrix formalism furnishes a framework for quantum mechanics on indefinite causal…
We present a computational tool that can be used to obtain the "spatial" homology groups of a causal set. Localisation in the causal set is seeded by an inextendible antichain, which is the analog of a spacelike hypersurface, and a one…
We develop a geometric criterion that unambiguously characterizes and also provides a systematic and effective computational procedure for finding all the residual symmetries of any gravitational Ansatz . We apply the criterion to several…
Let $v_1, ..., v_m$ be a finite set of unit vectors in $\RR^n$. Suppose that an infinite sequence of Steiner symmetrizations are applied to a compact convex set $K$ in $\RR^n$, where each of the symmetrizations is taken with respect to a…
A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's…
Cosmological models that are locally consistent with general relativity and the standard model in which an object transported around the universe undergoes P, C and CP transformations, are constructed. This leads to generalization of the…
Causal modelling is a tool for generating causal explanations of observed correlations and has led to a deeper understanding of correlations in quantum networks. Existing frameworks for quantum causality tend to focus on acyclic causal…
We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…
This paper presents a simple generalization of causal consistency suited to any object defined by a sequential specification. As causality is captured by a partial order on the set of operations issued by the processes on shared objects…
Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…
Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the…
Let $G$ be a compact connected subgroup of $SO(n+1)$. In $\mathbb{R}^{n+1}$, we gain interior $G$-symmetry for minimal hypersurfaces and hypersurfaces of constant mean curvature (CMC) which have $G$-invariant boundaries and $G$-invariant…
We consider examples of the $\mathbb H$-type groups with the natural horizontal distribution generated by the commutation relations of the group. In the contrast with the previous studies we furnish the horizontal distribution with the…
Dependent symmetries, symmetries that depend on the situation of the subsystem in a larger closed system, are explored by looking at simple examples. This is a new kind of symmetry in the open quantum dynamics of a subsystem Each symmetry…