Related papers: No speedup for geometric theories
Poincar\'e held the view that geometry is a convention and cannot be tested experimentally. This position was apparently refuted by the general theory of relativity and the successful confirmation of its predictions; unfortunately,…
Physics is formulated in terms of timeless classical mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality.
Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
The classical theory of $G$-structures, which include almost-complex structures, explains the relationship between the curvature of compatible connections and integrability. This note is an effort to understand how the curvature of…
After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary…
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
The classical notions of continuity and mechanical causality are left in order to refor- mulate the Quantum Theory starting from two principles: I) the intrinsic randomness of quantum process at microphysical level, II) the projective…
We introduce a sequent calculus for the propositional team logic with both the split disjunction and the inquisitive disjunction consisting of a Gentzen-style system (G3-like) for classical propositional logic together with two…
The construction of a gauge field theory for elementary particles usually starts by promoting global invariance of the matter action to a local one, this in turn implying the introduction of gauge fields. We present here a procedure that…
Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize…
Landauer's principle states that the logical irreversibility of an operation, such as erasing one bit, whatever its physical implementation, necessarily implies its thermodynamical irreversibility. In this paper, a very simple…
We consider a maximal extension of the Hilbert-Einstein action and analyze several interesting features of the theory. More specifically, the motion is non-geodesic and takes place in the presence of an extra force. These models could lead…
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…
The Lorentzian metric structure used in any field theory allows one to implement the relativistic notion of causality and to define a notion of time dimension. This article investigates the possibility that at the microscopic level the…
The Palatini formalism is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, but we follow a completely covariant approach by…
Linear logic is a substructural logic proposed as a refinement of classical and intuitionistic logics, with applications in programming languages, game semantics, and quantum physics. We present a template for Gentzen-style linear logic…
The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity (or impredicativity) of second and higher order…
We investigate the structure common to causal theories that attempt to explain a (part of) the world. Causality implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalizing power of the…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…