Related papers: Zitterbewegung by Quantum Field Theory Considerati…
The theory of gravitation field within the special theory of relativity is analyzed.
The second quantization of the quaternionic fermionic field is undertaken using the real Hilbert space approach to quaternionic quantum mechanics ($\mathbbm H$QM). The solution responds to an open problem of quaternionic quantum theory, and…
This version corrects an inportant typographical error in Eq. 17. COMMENTS, FOR THE RECORD: A referees reoprt from Phys. Rev. Lett. read in part ``The first named author has appreciated my exceptionally long report. He has read and well…
We comment on the present status, the concepts and their limitations, and the successes and open problems of the various approaches to a relativistic quantum theory of elementary particles, with a hindsight to questions concerning quantum…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
Quantum Field Theory with fields as Operator Valued Distributions with adequate test functions, -the basis of Epstein-Glaser approach known now as Causal Perturbation Theory-, is recalled. Its recent revival is due to new developments in…
The status of lattice calculations in Quantum Field Theory is reviewed. A major part is devoted to recent progress in formulating exact chiral symmetry on the lattice. Another topic which has received a lot of attention is the influence of…
I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general…
We give a rough description of the 'categories' formed by quantum field theories. A few recent mathematical conjectures derived from quantum field theories, some of which are now proven theorems, will be presented in this language.
We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which in particular ascribes trajectories to…
The Riemann hypothesis is proved by quantum-extending the zeta Riemann function to a quantum mapping between quantum $1$-spheres with quantum algebra $A=\mathbb{C}$, in the sense of A. Pr\'astaro \cite{PRAS01, PRAS02}. Algebraic topologic…
Using Dirac equation together with the Wigner distribution function,the trembling motion,known as Zitterbewegung effect,of moving electrons in quasi-one-dimensional relativistic quantum plasma is theoretically investigated.The relativistic…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
In the current paper the properties of a quantum field theory based on certain sets of Lorentz-violating coefficients in the nonminimal fermion sector of the Standard-Model Extension are analyzed. In particular, three families of…
What follows is a broad-brush overview of the recent synergistic interactions between mathematics and theoretical physics of quantum field theory and string theory. The discussion is forward-looking, suggesting potentially useful and…
After a long technical and consequently philosophical disgression about the necessity of the construction presented in this book, a logically consistent and precise theory of quantum gravity is presented. The construction of this theory…
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…
We expect quantum field theories for matter to acquire intricate corrections due to their coupling to quantum fluctuations of the gravitational field. This can be precisely worked out in 3d quantum gravity: after integrating out quantum…
The canonical commutation relations of quantum field theory require all pairs of observables located in spacelike-separated regions to commute. In the theory as it is currently constituted, this implies that the information-carrying…