Related papers: The Principle of the Fermionic Projector, Appendic…
We introduce the key ideas and mathematical tools central to modern discussions of collapse. We assume knowledge of basic quantum mechanics -- the Schr\"{o}dinger evolution of states in Hilbert space, the Born probability rule, the Dirac…
This paper is dedicated to give a concise introduction to the theory of causal fermion systems. After putting the theory of causal fermion systems into the historical context, we recall fundamental physical preliminaries. Afterwards, we…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
Geometrical model for quantum objects is suggested. It is shown that equations for free material Dirac field and for Maxwell electromagnetic field can be considered as relations describing propagation of the space topological defects. This…
The concept of inertial frame of reference in classical physics and special theory of relativity is analysed. It has been shown that this fundamental concept of physics is not clear enough. A definition of inertial frame of reference is…
The classical theory of gravity is formulated as a gauge theory on a frame bundle with spontaneous symmetry breaking caused by the existence of Dirac fermionic fields. The pseudo-Riemannian metric (tetrad field) is the corresponding Higgs…
Spinors have played an essential but enigmatic role in modern physics since their discovery. Now that quantum-gravitational theories have started to become available, the inclusion of a description of spin in the development is natural and…
The model of point particle in general external fields is considered and the generalized equivalence principle is suggested identifying all backgrounds which give rise to equivalent particle dynamics. The equivalence transformations for…
An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows to recover quantum mechanics as mechanics on a non-differentiable (fractal) space-time. The…
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial…
It is shown that the manner of introducing theinteraction between a spin 1 particle and external classical gravitational field can be successfully uni- fied with the approach that occurred with regard to a spin 1/2 particle and was first…
Relations between the Friedmann observables of the expanding Universe and the Dirac observables in the generalized Hamiltonian approach are established for the Friedmann cosmological model of the Universe with the field excitations…
The basic ideas and the important role of gauge principles in modern elementary particle physics are outlined. There are three theoretically consistent gauge principles in quantum field theory: the spin-1 gauge principle of electromagnetism…
We consider a electron in a external field in D=5, through the Dirac equation in the Galilean symmetry approach, and in the Lorentz symmetry approach; from these we perform the nonrelativistic limit, then we procede the supersymmetry of the…
Based on the most general principles of reality, gauge and reparametrization invariance, a problem of constructing the action describing dynamics of a classical color-charged particle interacting with background non-Abelian gauge and…
A brief review of the different ways of the Dirac equation derivation is given. The foundations of the relativistic canonical quantum mechanics of a fermionic doublet are formulated. In our approach the Dirac equation is derived from the…
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of…
In terms of the relational approach to space-time geometry and physical interactions, we show that the Dirac equation for a free fermion in the momentum representation can be obtained starting from a binary system of complex relations…
This is the author Master's Thesis and its main purpose is to demonstrate that it is possible to formulate Einstein's field equations as an initial value problem. The first chapter concerns the hyperbolic equations theory. The definition of…