Related papers: A Generalized Crystalline Equivalence Principle
Crystallographic tilings of the Euclidean space $\mathbb{E}^n$ are defined as simple tilings whose group of isometric automorphisms is crystallographic. To classify crystallographic tilings by their automorphism groups it is necessary to…
The Equivalence Principle is considered in the framework of metric-affine gravity. We show that it naturally emerges as a Noether symmetry starting from a general non-metric theory. In particular, we discuss the Einstein Equivalence…
We demonstrate that, in certain cases, quantization and the classical limit provide functors that are "almost inverse" to each other. These functors map between categories of algebraic structures for classical and quantum physics,…
We present a comprehensive theoretical analysis of the General Standard Model (GSM), a recently proposed framework that unifies particle physics and cosmology within the Gravitational Quantum Field Theory (GQFT). Constructed from first…
Free fall in a uniform gravitational field is revisited in the case of quantum states with and without classical analogue. The interplay between kinematics and dynamics in the evolution of a falling quantum test particle is discussed…
We propose the Symmetry TFT for theories with a $U(1)$ symmetry in arbitrary dimension. The Symmetry TFT describes the structure of the symmetry, its anomalies, and the possible topological manipulations. It is constructed as a BF theory of…
A general theory of topological classification of defects is introduced. We illustrate the application of tools from algebraic topology, including homotopy and cohomology groups, to classify defects including several explicit calculations…
A categoricity theorem is established for patterns of resemblance of order 2 showing that the order in which patterns arise in a wide range of hierarchies is the same.
Let A and B be normal matrices with coefficients that are continuous complex-valued functions on a topological space X that has the homotopy type of a CW complex, and suppose these matrices have the same distinct eigenvalues at each point…
The ordinary Structure Identity Principle states that any property of set-level structures (e.g., posets, groups, rings, fields) definable in Univalent Foundations is invariant under isomorphism: more specifically, identifications of…
We define the symmetry category in 1+1d for continuous 0-form $G$-symmetry to be $\textbf{Sky}^\tau(G)$, the category of skyscraper sheaves of finite dimensional vector spaces with finite support on the group manifold of $G$, where $\tau…
A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic…
A comprehensive symmetry resolution of the entanglement entropy (EE) in $(1+1)$-d rational conformal field theories (RCFT) with categorical non-invertible symmetries is presented. This amounts to symmetry resolving the entanglement with…
We provide a geometric condition that guarantees strong Wilf equivalence in the generalized factor order. This provides a powerful tool for proving specific and general Wilf equivalence results, and several such examples are given.
We study a metric-like structure on categories, showing that the concept of the limit of a sequence in a metric space and the concept of the colimit of a sequence in a category have a common generalization. The main concept is a norm on a…
We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
We challenge the view that there is a basic conflict between the fundamental principles of Quantum Theory and General Relativity, and in particular the fact that a superposition of massive bodies would lead to a violation of the Equivalence…
The gauge symmetry of classical general relativity under space-time diffeomorphisms implies that any path integral quantization which can be interpreted as a sum over space-time geometries, gives rise to a formal invariant of smooth…