Related papers: Quantum Fields as Category Algebras
In this talk I briefly review recent developments in quantum field theories on a noncommutative Euclidean space, with Heisenberg-like commutation relations between coordinates. I will be concentrated on new physics learned from this…
We propose a generalization of the description of Bell's inequalities in algebraic quantum field theory (AQFT) to the context of locally covariant quantum field theory (LCQFT). We use the functorial formulation of the state space as…
In orthodox Standard Quantum Mechanics (SQM) bases and factorizations are considered to define quantum states and entanglement in relativistic terms. While the choice of a basis (interpreted as a measurement context) defines a state…
The challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of space-time, the meaning of physical states, etc. Among them the…
The role of acceleration in particle physics can provide an alternative method for probing the properties of quantum gravity. To analyze acceleration-induced processes one utilizes the formalism of quantum field theory in curved spacetime.…
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…
Quantum information is about the entanglement of states. To this starting point we add parameters whereby a single state becomes a non-vanishing section of a bundle. We consider through examples the possible entanglement patterns of…
We use classes of Hilbert lattice equations for an alternative representation of Hilbert lattices and Hilbert spaces of arbitrary quantum systems that might enable a direct introduction of the states of the systems into quantum computers.…
Quantum field theory (QFT) based on the principles of special relativity (SR) and it is in fact the \emph{kinematic theory of fields}. The root assumption is that there is "relativistic description" of \emph{any} isolated quantum system in…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
We define a new concept of local states in the framework of algebraic quantum field theory (AQFT). Local states are a natural generalization of states and give a clear vision of localization in the context of QFT. In terms of them, we can…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of "noncommutative fields". Our description permits to break the usual particle-antiparticle…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
An algebraic formalism for description of quantum states of charged particle with spin moving in two-dimensional space under influence of singular magnetic field is developed in terms of graded algebras. The fundamental assumption is that…
Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…
One of the most basic notions in physics is the partitioning of a system into subsystems, and the study of correlations among its parts. In this work, we explore these notions in the context of quantum reference frame (QRF) covariance, in…
Quantum Field Theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantum mechanics to QFT for students at early…
We highlight the general notion of a relative quantum field theory, which occurs in several contexts. One is in gauge theory based on a compact Lie algebra, rather than a compact Lie group. This is relevant to the maximal superconformal…
This survey gives a comprehensive account of quantum correlations understood as a phenomenon stemming from the rules of quantization. Centered on quantum probability it describes the physical concepts related to correlations (both classical…