Related papers: Self Duality and Quantization
The well-known fact that classical automorphisms of (compactified) Minkowski spacetime (Poincare or conformal trandsformations) also allow a natural derivation/interpretation in the modular setting (in the operator-algebraic sense of Tomita…
Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…
In the foundational logical framework of homotopy-type theory we discuss a natural formalization of secondary integral transforms in stable geometric homotopy theory. We observe that this yields a process of non-perturbative cohomological…
We consider a local formalism in quantum field theory, in which no reference is made to infinitely extended spacial surfaces, infinite past or infinite future. This can be obtained in terms of a functional W[f,S] of the field f on a closed…
The quantum theory of ur objects postulates that all existing physical objects and their properties are constructed from fundamental objects called ur objects being described by an element of a two dimensional complex Hilbert space. This…
It is natural to consider a quantum system in the continuum limit of space-time configuration. Incorporating also, Einstein's special relativity, leads to the quantum theory of fields. Non-relativistic quantum mechanics and classical…
In this paper the quantization of the 2$+$1-dimensional gravity couplet to the massless Dirac field is carried out. The problem is solved by the application of the new Dynamic Quantization Method [1,2]. It is well-known that in general…
Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
A method has been recently proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example a version of quantized space-time is considered here. It is found that there is a…
We derive Maxwell equations for electric and magnetic fields in curved spacetime from first principles, relaxing an unnecessary assumption on the structure of the four-potential inherent to the standard approach and thus restoring the full…
We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer…
Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number - interpreted as area - which behaves additively…
We present an effective theory to describe the quantization of spherically symmetric vacuum in loop quantum gravity. We include anomaly-free holonomy corrections through a canonical transformation of the Hamiltonian of general relativity,…
We generalize $1+1$-dimensional formalism derived by Ahmadi et. al. [Phys. Rev. D \textbf{93}, 124031] to investigate an effect of relativistic acceleration on localized two-mode Gaussian quantum states in $3+1$-dimensional spacetime. The…
It is shown using both conventional and algebraic approach to quantum field theory that it is impossible to perform quantization on Unruh modes in Minkowski spacetime. Such quantization implies setting boundary condition for the quantum…
The $q$-theory approach to the cosmological constant problem is reconsidered. The new observation is that the effective classical $q$-theory gets modified due to the backreaction of quantum-mechanical particle production by spacetime…
The philosophy of the Loop Quantum Gravity approach is to construct the canonical variables by using the duality of infinitesimal connections and holonomies along loops. Based on this fundamental property for example the holonomy-flux…
General relativity becomes vastly simpler in three spacetime dimensions: all vacuum solutions have constant curvature, and the moduli space of solutions can be almost completely characterized. As a result, this lower dimensional setting…
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…