Related papers: Why Gauge?
Gauge theory is a theory with constraints and, for that reason, the space of physical states is not a manifold but a stratified space (orbifold) with singularities. The classification of strata for smooth (and generalized) connections is…
We analyze the notion that physical theories are quantitative and testable by observations in experiments. This leads us to propose a new, Bayesian, interpretation of probabilities in physics that unifies their current use in classical…
When a theory shall be described at all scales, it is necessary to start from its elementary degrees of freedom. Herein, one possible chain of steps for this purpose will be briefly outlined for the example of a gauge theory, like QCD.…
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing…
Gauge theories with and without matter are formulated in the derivative expansion. Amplitudues are derived as a power series in the energy scales; there are simplifications as compared with the usual loop expansion. The incorporation and…
The interpretations of solutions of Einstein field's equations led to the prediction and the observation of physical phenomena which confirm the important role of general relativity, as well as other relativistic theories in physics. In…
We offer a fresh perspective on the relational interpretation of quantum mechanics as a way of thinking about the world described by quantum theory based on quantifiable notions of information. This allows us to provide a definition of a…
The idea that gauge theory has 'surplus' structure poses a puzzle: in one much discussed sense, this structure is redundant; but on the other hand, it is also widely held to play an essential role in the theory. In this paper, we employ…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…
We discuss some aspects of the relation between dualities and gauge symmetries. Both of these ideas are of course multi-faceted, and we confine ourselves to making two points. Both points are about dualities in string theory, and both have…
The conventional cosmological perturbation theory has been performed under the assumption that we know the whole spatial region of the universe with infinite volume. This is, however, not the case in the actual observations because…
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be…
The application of the notion of `observable' from gauge theory to diffeomorphism-invariant theories -- most relevantly to general relativity -- has led to numerous conceptual and technical issues when interpreting classical theories with…
The question of what is real is familiar in physics. This paper addresses this question through the notions of reality in the models of of the world (schemata) that are created by the information gathering and utilizing systems (IGUSes) in…
A space for gauge theories is defined, using projective limits as subsets of Cartesian products of homomorphisms from a lattice on the structure group. In this space, non-interacting and interacting measures are defined as well as functions…
As in the case of the other gauge field theories, there is so called ``gauge'' also in general relativity. This ``gauge'' is unphysical degree of freedom. There are two kinds of ``gauges'' in general relativity. These are called the first-…
We review the present status of gauge theories built on various quantum space-times described by noncommutative space-times. The mathematical tools and notions underlying their construction are given. Different formulations of gauge theory…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…