Related papers: Universal gauge-invariant cellular automata
We study one-loop quantum corrections to gauge couplings in heterotic vacua with spontaneous supersymmetry breaking. Although in non-supersymmetric constructions these corrections are not protected and are typically model dependent, we show…
Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to a point; and the fact that they have a well-defined notion of…
Positing complex adaptive systems made of agents with relations between them that can be composed, it follows that they can be described by gauge theories similar to elementary particle theory and general relativity. By definition, a…
Causal Graph Dynamics generalize Cellular Automata, extending them to bounded degree, time varying graphs. The dynamics rewrite the graph at each time step with respect to two physics-like symmetries: causality (bounded speed of…
A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…
I discuss gauge and global symmetries in particle physics, condensed matter physics, and quantum gravity. In a modern understanding, global symmetries are approximate and gauge symmetries may be emergent. (Based on a lecture at the April,…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…
Gauge invariance is essential for making physically meaningful predictions. In superconductors, mean-field Hamiltonians that explicitly break $U(1)$ symmetry often yield gauge-dependent results. While this issue has been resolved for linear…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
Endomorphisms algebras can replace the concept of principal fiber bundle. Gauge theories are reformulated within this algebraic framework and further generalized to unify ordinary connections and Higgs fields. A 'noncommutative Maxwell'…
We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with…
Phenomena in gauge theory are often described in the physics literature via a specific choice of gauge. In foundational and philosophical discussions this is often criticized as introducing gauge dependence, and contrasted against (often…
Local gauge symmetry underlies fundamental interactions and strongly correlated quantum matter, yet existing machine-learning approaches lack a general, principled framework for learning under site-dependent symmetries, particularly for…
Cellular automata (CA) is an important modelling paradigm for complex systems. In the design of cellular automata, the most difficult task is to find the transformation rules that describe the temporal evolution or pattern of a modelled…
We consider the relational approach to construct gauge-invariant observables in cosmological perturbation theory using synchronous coordinates. We construct dynamical synchronous coordinates as non-local scalar functionals of the metric…
In a traditional gauge theory, the matter fields \phi^a and the gauge fields A^c_\mu are fundamental objects of the theory. The traditional gauge field is similar to the connection coefficient in the Riemannian geometry covariant…
Cellular automata are a fundamental computational model with applications in mathematics, computer science, and physics. In this work, we explore the study of cellular automata to cases where the universe is a group, introducing the concept…
Unitarity of the global evolution is an extremely stringent condition on finite state models in discrete spacetime. Quantum cellular automata, in particular, are tightly constrained. In previous work we proved a simple No-go Theorem which…