相关论文: Gauge Theory And Wild Ramification
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge…
We propose a geometric method to measure the wild ramification of a smooth etale sheaf along the boundary. Using the method, we study the graded quotients of the logarithmic ramification groups of a local field of positive characteristic…
In this review we summarize the ongoing effort to study extra-dimensional gauge theories with lattice simulations. In these models the Higgs field is identified with extra-dimensional components of the gauge field. The Higgs potential is…
In classical external gauge fields that fall off less fast than the inverse of the evolution parameter (time) of the system the implementability of a unitary perturbative scattering operator ($S$-matrix) is not guaranteed, although the…
We introduce new techniques for calculations in Gauge theories with extended supersymmetry. We are working in Projective Superspace where the $SU(2)$ R-symmetry is realized geometrically by including an auxilliary $\mathbb{CP}^1$ component…
In this thesis noncommutative gauge theory is extended beyond the canonical case, i.e. to structures where the commutator no longer is a constant. In the first part noncommutative spaces created by star-products are studied. We are able to…
We prove that under suitable graded and local hypothesis, a formally unramified algebra over a field must be reduced. We detail examples, including one due to Gabber, to show that it is not possible to generalize these results further.
Despite widespread interest and practical use, the theoretical properties of random forests are still not well understood. In this paper we contribute to this understanding in two ways. We present a new theoretically tractable variant of…
We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but…
The quantum theory of a free particle in two dimensions with non-local boundary conditions on a circle is known to lead to surface and bulk states. Such a scheme is here generalized to the quantized Maxwell field, subject to mixed boundary…
Positing complex adaptive systems made of agents with relations between them that can be composed, it follows that they can be described by gauge theories similar to elementary particle theory and general relativity. By definition, a…
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…
Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual…
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive…
Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in…
A modification of the gauge theory is proposed, in which the set of generalized coordinates is supplemented with symmetry transformation parameters, and a condition is additionally imposed on the latter that ensures the classical character…
Tropical algebraic geometry offers new tools for elimination theory and implicitization. We determine the tropicalization of the image of a subvariety of an algebraic torus under any homomorphism from that torus to another torus.
We argue that the mathematical structure, enabling certain cascading and emergent phenomena to intuitively emerge, coincides with Galois connections. We introduce the notion of generative effects to formally capture such phenomena. We…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
GR can be interpreted as a theory of evolving 3-geometries. A recent such formulation, the 3-space approach of Barbour, Foster and \'{O} Murchadha, also permits the construction of a limited number of other theories of evolving…