Related papers: Quantum Fields as Category Algebras
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a…
A discussion of the meaning of a physical concept cannot be separated from discussion of the conditions for its ideal measurement. We assert that quantization is no more than the invocation of the quantum of action in the explanation of…
A manifestly covariant formulation of quantum field Maslov complex-WKB theory (semiclassical field theory) is investigated for the case of scalar field. The main object of the theory is "semiclassical bundle". Its base is the set of all…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the…
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…
A conformal field theory (CFT) is a quantum field theory which is invariant under conformal transformations; a group action that preserve angles but not necessarily lengths. There are two traditional approaches to the construction of CFTs:…
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…
In these notes, we describe an interesting connection between unitary representations of Lie groups and nets of local algebras, as they appear in Algebraic Quantum Field Theory (AQFT). It is based on first translating the axioms for nets of…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
The wave-particle duality of the vacuum states of quantum fields is considered and the particle-like property of the vacuum state of a quantum field is proposed as a vacuum-particle which carries the vacuum-energy and the vacuum-momentum of…
The author's attempt to construct a local causal model of quantum theory (QT) that includes quantum field theory (QFT) resulted in the identification of "quantum objects" as the elementary units of causality and locality. Quantum objects…
A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states),…
In the framework of Category Theory, we study the association between finite--dimensional representations of a compact quantum group and quantum vector bundles with linear connections for a given quantum principal bundle with a principal…
Quantum fields are considered as generators of infinite-dimensional Clifford algebra $Cl(\infty)$, which can be either orthogonal (in case of fermions) or symplectic (in case of bosons). A generic quantum state can be expressed as a…
Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
Quantum-matter theory (QMT), based on the Schr\"odinger or Dirac equations, is firmly established for both intra- and intermolecular interactions. However, there are two key issues with QMT. First, its applicability to large molecular…
We explore finite-field frameworks for quantum theory and quantum computation. The simplest theory, defined over unrestricted finite fields, is unnaturally strong. A second framework employs only finite fields with no solution to x^2+1=0,…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
We explore a wider theoretical framework that has quantum field theory built-in, taking the fact that quantum mechanics is reconstructed from quantum field theory as a hint. We formulate a quantum theory with an embedded structure by…