Related papers: Standard and Hyperfinite Unifications for All Phys…

This work starts with the observation of a certain "rule" (up to now unexplored) in the fundamental laws of Nature. We show some evidence of this, and formulate it as a fundamental principle which exhibits a number physical consequences. In…

This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…

We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure…

For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises…

A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system.…

We derive the effective theories for heavy particles with a functional integral approach by integrating away the states with high velocity and with high virtuality. This formulation is non-perturbative and has a close connection with the…

While the traditional conception of inductive logic is Carnapian, I develop a Peircean alternative and use it to unify formal learning theory, statistics, and a significant part of machine learning: supervised learning. Some crucial…

We prove a unified convergence theorem, which presents in four equivalent forms of the famous Antosik-Mikusinski Theorems. In particular, we show that Swartz' three uniform convergence principles are all equivalent to the Antosik-Mikusinski…

There is a natural equivalence relation on representations of the states of a given quantum system in a Hilbert space, two representations being equivalent iff they are related by a unitary transformation. There are two equivalence classes,…

This report presents an elementary theory of unification for positive conjunctive queries. A positive conjunctive query is a formula constructed from propositional constants, equations and atoms using the conjunction $\wedge$ and the…

In this paper, we show that Higher-Order Coloured Unification - a form of unification developed for automated theorem proving - provides a general theory for modeling the interface between the interpretation process and other sources of…

We write the partition function for a lattice gauge theory, with compact gauge group, exactly in terms of unconstrained variables and show that, in the mean field approximation, the dynamics of pure gauge theories, invariant under compact,…

We canonically quantize $(2+1)$-dimensional electrodynamics including a higher-derivative Chern-Simons term. The effective theory describes a standard photon and an additional degree of freedom associated with a massive ghost. We find the…

We present a Mathematica package that takes any reductive gauge algebra and fully-reducible fermion representation, and outputs all semisimple gauge extensions under the condition that they have no additional fermions, and are free of local…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

The paper presents an interesting mathematical feedback between the formalism of coherent states and the field of integrals and integral representations involving special functions. This materializes through an easy and fast method to…

This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…

We study Euclidean lattice formulations of non-gauge supersymmetric models with up to four supercharges in various dimensions. We formulate the conditions under which the interacting lattice theory can exactly preserve one or more nilpotent…

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…

Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…