Related papers: Why surplus structure is not superfluous
The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…
Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical…
Study of gauge symmetry is carried over the different interacting and noninteracting field theoretical models through a prescription based on lagrangian formulation. It is found that the prescription is capable of testing whether a given…
On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the…
Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…
The persistent challenge of formulating ontic structuralism in a rigorous manner, which prioritizes structures over the entities they contain, calls for a transformation of traditional logical frameworks. I argue that Univalent Foundations…
We equip the whole space of fields of the triplectic formalism of Lagrangian quantization with an even supersymplectic structure and clarify its geometric meaning. We also discuss its relation to a closed two-form arising naturally in the…
Topologically non-trivial gauge field configurations are an interesting aspect of non-abelian gauge theories. These become particularly important upon quantizing the theory, especially through their effect on the pseudo-scalar spectrum.…
This paper develops the basic theory of formal schemes over fields in the supersymmetric setting. We introduce the notion of a formal superscheme and investigate some of its fundamental properties. Particular emphasis is placed on the study…
We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…
In recent years philosophers of science have explored categorical equivalence as a promising criterion for when two (physical) theories are equivalent. On the one hand, philosophers have presented several examples of theories whose…
The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among the matters with different levels of hierarchy is appreciated. It is shown that the general…
Rationals are known to form interesting and computationally rich structures, such as Farey sequences and infinite trees. Little attention is being paid to more general, systematic exposition of the basic properties of fractions as a set.…
This paper is a continuation of Part I where the general setup was developed. Here we discuss the general equivalence problem for geometric structures and provide criteria for the equivalence, local and global, of transitive structures.…
Perhaps the most important contribution of gauge theory to general mathematics is to point out the importance of association functors. Emphasizing category theory we characterize association functors by two of their natural properties and…
Quantum field theory (QFT) in classical spacetime has revealed interesting and puzzling aspects about gravitational systems, in particular black hole thermodynamics and its information processing. Although quantum gravitational effects may…
In this paper we consider how the strong-coupling scale, or perturbative cutoff, in a multi-gravity theory depends upon the presence and structure of interactions between the different fields. This can elegantly be rephrased in terms of the…
Category theory has become central to certain aspects of theoretical physics. Bain [Synthese, 190:1621--1635 (2013)] has recently argued that this has significance for ontic structural realism. We argue against this claim. In so doing, we…
Constructive gravity allows to calculate the Lagrangian for gravity, provided one previously prescribes the Lagrangian for all matter fields on a spacetime geometry of choice. We explain the physical and mathematical foundation of this…
Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…