Related papers: Structural Algebraic Quantum Field Theory
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the…
The formation of cosmic structures is an important diagnostic for both the dynamics of the cosmological model and the underlying theory of gravity. At the linear level of these structures, certain degeneracies remain between different…
In modern physics, one of the greatest divides is that between space-time and quantum fields, as the fiber bundle of the Standard Model indicates. However on the operational grounds the fields and spacetime are not very different. To…
In order to support students in the development of expertise in quantum mechanics, we asked which concepts and structures can act as organizing principles of the non-relativistic theory. The research question has been addressed in a…
The interior structure of arbitrary sets of quaternion units is analyzed using general methods of the theory of matrices. It is shown that the units are composed of quadratic combinations of fundamental objects having a dual mathematical…
A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral…
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
We construct a Heisenberg-like algebra for the one dimensional quantum free Klein-Gordon equation defined on the interval of the real line of length $L$. Using the realization of the ladder operators of this type Heisenberg algebra in terms…
Algebraic quantum field theory, or AQFT for short, is a rigorous analysis of the structure of relativistic quantum mechanics. It is formulated in terms of a net of operator algebras indexed by regions of a Lorentzian manifold. In several…
When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infrared. Using the octonions as space-time coordinates, we construct a pre-spacetime,…
We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using…
We give a very concise review of the group field theory formalism for non-perturbative quantum gravity, a higher dimensional generalisation of matrix models. We motivate it as a simplicial and local realisation of the idea of 3rd…
In this paper is considered relativistic quantum field theory expressed by elementary units of quantum information as they are considered as fundamental entity of nature by Carl Friedrich von Weizsaecker. Through quantization of a Weyl…
By exploring possible physical sense of notions, structures, and logic in a class of noncommutative geometries, we try to unify the four fundamental interactions within an axiomatic quantum picture. We identify the objects and algebraic…
We briefly review the r\^ole played by algebraic structures like combinatorial Hopf algebras in the renormalizability of (noncommutative) quantum field theory. After sketching the commutative case, we analyze the noncommutative…
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts. Firstly as field theories on noncommutative spacetimes they come with natural…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
We announce results about the nonperturbative mathematically rigorous construction of the $:\!\phi^4_4\!:$ quantum field theory in four-dimensional space-time. The complex structure of solutions of the classical nonlinear (real-valued) wave…
Using the complex Klein-Gordon field as a model, we quantize the quaternionic scalar field in the real Hilbert space. The lagrangian formulation has accordingly been obtained, as well as the hamiltonian formulation, and the energy and…
A quantum picture of the causal structure of Minkowski space M is presented. The mathematical model employed to this end is a non-classical version of the classical topos {H} of real quaternion algebras used elsewhere to organize the…