相关论文: Fiber bundle structure in Ashtekar-Barbero-Immirzi…
The Standard Model of the theory of elementary particles is based on the $U(1)\times SU(2)\times SU(3)$ symmetry. In the presence of a gravitation field, i. e. in a non-flat space-time manifold, this symmetry is implemented through three…
In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…
This text describes the fiber bundle structure and shows its universality for writing the laws of classical physics: newtonian, relativistic and quantum mechanics.
We introduce a geometric construction of a gauge field theory of a complex adaptive system. It is based on a suitable simplicial formulation of a discrete geometry that manifests relevant properties valid in the classical differentiable…
In this paper, nonholonomic gerbes will be naturally derived for manifolds and vector bundle spaces provided with nonintegrable distributions (in brief, nonholonomic spaces). An important example of such gerbes is related to distributions…
In this work, we develop a generalization of Kaluza-Klein theory by considering a purely affine framework, without assuming a prior metric structure. We formulate the dimensional reduction using the geometry of principal fiber bundles and…
In this article we give the realization of the Klein's Program for geometrical structures (Riemannian spaces and fiber bundles with connection) with arbitrary variable curvature within the framework of infinite deformed groups. These groups…
The Immirzi parameter of loop quantum gravity is a one parameter ambiguity of the theory whose precise interpretation is not universally agreed upon. It is an inherent characteristic of the quantum theory as it appears in the spectra of…
A gauge theory of gravity based on a nonlinear realization (NLR) of the local Conform-Affine (CA) group of symmetry transformations is presented. The coframe fields and gauge connections of the theory are obtained. The tetrads and Lorentz…
The following work demonstrates the viability of Poincar\'e symmetry in a discrete universe. We develop the technology of the discrete principal Poincar\'e bundle to describe the pairing of (1) a hypercubic lattice `base manifold' labeled…
A new formalism for spinors on curved spaces is developed in the framework of variational calculus on fibre bundles. The theory has the same structure of a gauge theory and describes the interaction between the gravitational field and…
Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is…
This is the second in a series of papers discussing in the framework of gerbe theory canonical and geometric aspects of the 2d nonlinear sigma model in the presence of conformal defects in the worldsheet. Employing the formal tools worked…
This paper is a comprehensive investigation of the Affine Gauge Theory (AGT) as a gauge theory of gravity having the same mathematical structure as gauge theories of the other fundamental forces of nature. This mathematical structure…
The present work provides a mathematically rigorous account on super fiber bundle theory, connection forms and their parallel transport, that ties together various approaches. We begin with a detailed introduction to super fiber bundles. We…
There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincar\'{e} gauge theory and…
We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford -- Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off-diagonal…
We consider smooth families of Lie groups (group bundles) and connections that are compatible with the group operation. We characterize the space of group connections on a group bundle as an affine space modeled over the vector space of…
We present an intrinsic geometric classification of the supermanifold of maps from $\mathbb{R}^{0|2}$ to any smooth manifold $S$, avoiding auxiliary structures. The key isomorphism relates this space to the pullback of the decomposable…
The classical theory of Riemann ellipsoids is formulated naturally as a gauge theory based on a principal G-bundle ${\cal P}$. The structure group G=SO(3) is the vorticity group, and the bundle ${\cal P}=GL_+(3, R})$ is the connected…