Related papers: Syntactic Structure, Quantum Weights
Quasi-probabilities appear across diverse areas of physics, but their conceptual foundations remain unclear: they are often treated merely as computational tools, and operations like conditioning and Bayes' theorem become ambiguous. We…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
It is shown that if the Euclidean path integral measure of a minimally coupled free quantum scalar field on a classical metric background is interpreted as probability of observing the field configuration given the background metric then…
In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is…
We consider Delone sets with finite local complexity. We characterize validity of a subadditive ergodic theorem by uniform positivity of certain weights. The latter can be considered to be an averaged version of linear repetitivity. In this…
The basic problem of semantic compression is to minimize the length of a message while preserving its meaning. This differs from classical notions of compression in that the distortion is not measured directly at the level of bits, but…
Classical and quantum mechanical descriptions of physical world are seamlessly abridged within the framework of Lagrangian formalism which, besides revealing the essence of nonlocally correlated dynamic evolution, helps understanding abrupt…
Euclidean quantum gravity (EQG) separates into a local theory and a global theory. The local theory operates in every compact $d$-manifold with boundary to produce a state on the boundary. The global theory then sums these boundary states…
A central property of a classical geometry is that the geodesic distance between two events is \emph{additive}. When considering quantum fluctuations in the metric or a quantum or statistical superposition of different spacetimes,…
Languages may encode similar meanings using different sentence structures. This makes it a challenge to provide a single set of formal rules that can derive meanings from sentences in many languages at once. To overcome the challenge, we…
We analyze both the feasibility and reasonableness of a classical Euclidean Theory of Everything (TOE), which we understand as a TOE based on an Euclidean space and an absolute time over which deterministic models of particles and forces…
This paper discusses the general structure of reflection positive Euclidean covariant distributions that can be used to construct Euclidean representations of relativistic quantum mechanical models of systems of a finite number of degrees…
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
The Euler characteristic, thought of as a function that assigns a numerical value to every finite simplicial complex, is locally determined in both a combinatorial sense and a geometric sense. In this note we show that not every function…
We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has…
Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…
A variational phase space is constructed for a system of fields on Euclidean space with periodic boundary conditions. An extended action functional is defined such that the Euler-Lagrange equations generate a symplectic flow on the…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
Token representation strategies within large-scale neural architectures often rely on contextually refined embeddings, yet conventional approaches seldom encode structured relationships explicitly within token interactions. Self-attention…