Related papers: Quantization, Holography and the Universal Coeffic…
I present a method of quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UCT). I also show that by using this method new features of…
Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
We review the definition of geometric quantization, which begins with defining a mathematical framework for the algebra of observables that holds equally well for classical and quantum mechanics. We then discuss prequantization, and go into…
We present a rigorous quantization scheme that yields a quantum field theory in general boundary form starting from a linear field theory. Following a geometric quantization approach in the K\"ahler case, state spaces arise as spaces of…
Some time ago we presented an article (which was in fact the outline of a research programme) in which we argued for the need to develop a nonommutative version of topological quantum field theories (NCTQFT for short). Recent work by C.J.…
This thesis develops recent work on the so called Volume-Complexity and Action-Complexity conjectures. According to this family of proposals, geometric quantities can be defined in some holographic gravitational theories that can be mapped…
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological…
An elementary introduction is provided to the phase space quantization method of Moyal and Wigner. We generalize the method so that it applies to 2-dimensional surfaces, where it has an interesting connection with quantum holography. In the…
In this talk we entertain the possibility that the synthesis of general covariance and quantum mechanics requires an extension of the basic kinematical setup of quantum mechanics. According to the holographic principle, regions of spacetime…
We present a fully quantum version of the holographic principle in terms of quantum systems, subsystems, and their interactions. We use the concept of environment induced decoherence to prove this principle. We discuss the conditions under…
The method of geometrical quantization of symplectic manifolds is applied to constructing infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(2)$. A formulation of the…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
Holography is a cornerstone characterisation and imaging technique that can be applied to the full electromagnetic spectrum, from X-rays to radio waves or even particles such as neutrons. The key property in all these holographic approaches…
Recently, a general tool called a holographic transformation, which transforms an expression of the partition function to another form, has been used for polynomial-time algorithms and for improvement and understanding of the belief…
I show how recent progress in real space renormalization group methods can be used to define a generalized notion of holography inspired by holographic dualities in quantum gravity. The generalization is based upon organizing information in…
Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
We develop a wave mechanics formalism for qubit geometry using holomorphic functions and Mobius transformations, providing a geometric perspective on quantum computation. This framework extends the standard Hilbert space description,…