Related papers: Gauge Group and Topology Change
We study gauge theories and quantum gravity in a finite interval of time $\tau $, on a compact space manifold $\Omega $. The initial, final and boundary conditions are formulated in gauge invariant and general covariant ways by means of…
In this paper, we investigate the effects of a new version of the generalized uncertainty principle (modified GUP) on the dynamics of the Universe. As the modified GUP will modify the relation between the entropy and area of the apparent…
First, we review the basic mathematical structures and results concerning the gauge orbit space stratification. This includes general properties of the gauge group action, fibre bundle structures induced by this action, basic properties of…
Gauge theories formulated in a space-time manifold that includes compact extra dimensions can show a nontrivial gauge structure. Depending on whether the gauge parameters propagate or not in the extra dimensions, two different Kaluza--Klein…
This is the second paper of a series that develops a bordism-theoretic point of view on orientations in enumerative geometry. The first paper is arXiv:2312.06818. This paper focuses on those applications to gauge theory that can be…
If the Universe undergoes a phase transition, at which global monopoles are created or destroyed, topology of its spatial sections can change. More specifically, by making use of Myers' theorem, we show that, after a transition in which…
A gauge theory is associated with a principal bundle endowed with a connection permitting to define horizontal lifts of paths. The horizontal lifts of surfaces cannot be defined into a principal bundle structure. An higher gauge theory is…
A new approach extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states) is proposed. This new approach is based on an analogy between open quantum systems and dissipative…
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Sigma, the original functional is extended appropriately by additional…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
By fibering the duality between the $E_{8}\times E_{8}$ heterotic string on $T^{3}$ and M-theory on K3, we study heterotic duals of M-theory compactified on $G_{2}$ orbifolds of the form $T^{7}/\mathbb{Z}_{2}^{3}$. While the heterotic…
The minimal coupling principle is revisited under the quantum perspectives of the space-time symmetry. This revision is better realized on a Group Approach to Quantization (GAQ) where group cohomology and extensions of groups play a…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
We discuss the variation of gauge couplings in time in the framework of orbifold constructions, due to a change of the extra compact dimension's size. Models with gauge coupling unification allow to estimate the variation of the strong…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
Compactified Yang-Mills theories with one universal extra dimension were found [arXiv:1008.4638] to exhibit two types of gauge invariances: the standard gauge transformations (SGTs) and the nonstandard gauge transformations (NSGTs). In the…
A framework for higher gauge theory based on a 2-group is presented, by constructing a groupoid of connections on a manifold acted on by a 2-group of gauge transformations, following previous work by the authors where the general notion of…
We study the response of quantum many-body systems to coupling some of their degrees of freedom to external gauge fields. This serves to understand the current Green functions and transport properties of interacting many-body systems. Our…
A new point of view about the deep origin of thermodynamic phase transitions is sketched. The main idea is to link the appearance of phase transitions to some major topology change of suitable submanifolds of phase space instead of linking…
We investigate Type IIB compactifications with spatially varying fluxes and dilaton profiles in the setting of dynamical cobordism. In particular, we analyze a G-theory motivated compactification in which the fluxes and the dilaton depend…