Related papers: Quantum Gauge Theories and Noncommutative Geometry
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
The main purpose of this paper is to describe various phenomena and certain constructions arising in the process of studying derived noncommutative schemes. Derived noncommutative schemes are defined as differential graded categories of a…
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…
Quantum gauge theories with finite-dimensional representation spaces are constructed that can have canonical gauge field theories as singular limits. They describe nature as a recursive quantum assembly by iterating Fermi-Dirac…
A single geometric invariant fixes the relative normalization and structure of gravity, Yang-Mills theory, and fermion kinetic terms -- including ghost freedom in the gravitational sector -- without tuning. Our results establish a minimal…
Gauge theory is a well-established concept in quantum physics, electrodynamics, and cosmology. This theory has recently proliferated into new areas, such as mechanics and astrodynamics. In this paper, we discuss a few applications of gauge…
Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…
We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than 4 dimensions, a SU(n) gauge theory on a Moyal-Weyl space arises with…
In this talk some recent results in the quantization of Chern-Simons field theories in the Coulomb gauge will be presented. In the first part, the consistency of the Chern-Simons field theories in this gauge is proven using the Dirac's…
The aim of this contribution is to explain how Connes derives the standard model of electromagnetic, weak and strong forces from noncommutative geometry. The reader is supposed to be aware of two other derivations in fundamental physics:…
We argue that extra dimensions with a properly chosen compactification scheme could be a natural source for emergent gauge symmetries. Actually, some proposed vector field potential terms or polynomial vector field constraints introduced in…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
I briefly argue for logical necessity to incorporate, besides c, hbar, two fundamental length scales in the symmetries associated with the interface of gravitational and quantum realms. Next, in order to clear the proverbial bush, I discuss…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
We derive the interaction of fermions with a dynamical space-time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form-invariance of the fermion action under…
We define a natural generalized symmetry of the Yang-Mills equations as an infinitesimal transformation of the Yang-Mills field, built in a local, gauge invariant, and Poincar\'e invariant fashion from the Yang-Mills field strength and its…
We present a general analysis of gauge invariant, exact and metric independent forms which can be constructed using higher rank field-strength tensors. The integrals of these forms over the corresponding space-time coordinates provides new…
This is a brief review, in relatively non-technical terms, of recent advances in the theory of random field geometry. These advances have provided a collection of explicit new formulae describing mean values of a variety of geometric…
Some of the key cohomological features of the two $(1+1)$-dimensional (2D) free Abelian- and self-interacting non-Abelian gauge theories (having no interaction with matter fields) are briefly discussed first in the language of symmetry…
In the context of quantum field theory, an anomaly exists when a theory has a classical symmetry which is not a symmetry of the quantum theory. This short exposition aims at introducing a new point of view, which is that the proper setting…