Related papers: Noncommutative Geometry, Hodge Theorem and Hologra…
It is shown that it is possible to define quantum field theory of a massless scalar free field on the Killing horizon of a 2D-Rindler spacetime. Free quantum field theory on the horizon enjoys diffeomorphism invariance and turns out to be…
According to the holographic principle, the information content assigned to a gravitational region is processed by its lower dimensional boundary. As an example setup compatible with this principle, the AdS/CFT correspondence relies on the…
In the nonsymmetric gravitational theory (NGT) the space-time metric $g_{\mu\nu}$ departs from the flat-space Minkowski form $\eta_{\mu\nu}$ such that it is no longer symmetric, $i.e.$ $g_{\mu\nu} \ne g_{\nu\mu}$. We find that in the most…
Holography has provided valuable insights into the time evolution of strongly coupled gauge theories in a fixed spacetime. However, this framework is insufficient if this spacetime is dynamical. We present a scheme to evolve a…
The holographic principle posits that all quantum information in a region of spacetime is encoded on its boundary. While there is strong evidence for this principle in certain models of quantum gravity in asymptotically anti-de Sitter…
The holographic principle suggests that regions of space contain fewer physical degrees of freedom than would be implied by conventional quantum field theory. Meanwhile, in Hilbert spaces of large dimension $2^n$, it is possible to define…
Noncommutative geometry allows to unify the basic building blocks of particle physics, Yang-Mills-Higgs theory and General relativity, into a single geometrical framework. The resulting effective theory constrains the couplings of the…
We propose a novel codimension-n holography, called cone holography, between a gravitational theory in $(d+1)$-dimensional conical spacetime and a CFT on the $(d+1-n)$-dimensional defects. Similar to wedge holography, the cone holography…
The nilpotent BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral…
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory. The extended geometry distinguishes between the ordinary spacetime based…
This paper contains the first written exposition of some ideas (announced in a previous survey) on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of…
We apply one of the formalisms of noncommutative geometry to $R^N_q$, the quantum space covariant under the quantum group $SO_q(N)$. Over $R^N_q$ there are two $SO_q(N)$-covariant differential calculi. For each we find a frame, a metric and…
The holographic principle, being a generic feature of quantum gravity, should allow for the consideration of dualities other than AdS/CFT. The AdS/BCFT correspondence, in which the dual field theory has local conformal symmetry and is…
Undecidability, a hallmark of G\"odel incompleteness theorems, has recently emerged in quantum many-body physics through the spectral gap problem. We demonstrate how this logical limitation can be holographically transmitted to a class of…
This thesis explores Quantum Field Theory (QFT) on curved spacetimes using a geometric Hamiltonian approach to the Schr\"odinger-like representation. In particular it studies the theory of the scalar field described through its…
The holographic principle states that the number of degrees of freedom describing the physics inside a volume (including gravity) is bounded by the area of the boundary (also called the screen) which encloses this volume. A stronger…
Symmetry topological field theory (SymTFT) is a convenient tool for studying finite generalized symmetries of a given quantum field theory (QFT). In particular, SymTFTs encode all the symmetry structures and properties, including anomalies.…
We present a new formulation of quantum holonomy theory, which is a candidate for a non-perturbative and background independent theory of quantum gravity coupled to matter and gauge degrees of freedom. The new formulation is based on a…