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A recent idea, put forward by Mund, Rehren and Schroer, is discussed; it suggests that in gauge quantum field theory one can replace the point-localized gauge fields by string-localized vector potentials built from gauge invariant…
A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…
In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…
A simple theoretical model of scalar fields in one spatial dimension with internal symmetry is considered. Assuming the existence of localized classical field configurations, the Schr\"{o}dinger picture is used to describe their quantum…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…
We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class…
The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a…
Local gauge theories are in a complicated relationship with boundaries. Whereas fixing the gauge can often shave off unwanted redundancies, the coupling of different bounded regions requires the use of gauge-variant elements. Therefore,…
Quantum fluctuations, through quantum corrections, have the potential to lead to irreversibility in quantum field theory. We consider the virtual ``charge" distribution generated by quantum corrections in the leading log, short range…
We present a theoretical framework for a class of generalized $U(1)$ gauge effective field theories. These theories are defined by specifying geometric patterns of charge configurations that can be created by local operators, which then…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
The cosmological constant and the Higgs mass seem unnaturally small and anthropically selected. We show that both can be efficiently scanned in Quantum Field Theories with a large enough number of vacua controllable thanks to approximated…
We consider the Hamiltonian constraint formulation of classical field theories, which treats spacetime and the space of fields symmetrically, and utilizes the concept of momentum multivector. The gauge field is introduced to compensate for…
We discuss a possible framework for the construction of a quantum gravity theory where the principles of QFT and general relativity can coexist harmonically. Moreover, in order to fix the correct gauge group of the theory we study the most…
We outline, test, and apply a new scheme for nonpertubative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…
A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of…
I argue that questions of algorithmic decidability, computability and complexity should play a larger role in deciding the "ultimate" theoretical description of the Landscape of string vacua. More specifically, I examine the notion of the…