Related papers: The Principle of the Fermionic Projector, Appendic…
Differentiable physics provides a new approach for modeling and understanding the physical systems by pairing the new technology of differentiable programming with classical numerical methods for physical simulation. We survey the rapidly…
The purpose of this book is to give an exposition of geometry, from a point of view which complements Klein's Erlangen program. The emphasis is on extending the classical Euclidean geometry to the finite case, but it goes beyond that. After…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
The Standard Model of particle physics is derived from first principles from the free Dirac Lagrangian in 8-dimensional spacetime. Motivated by second quantization arguments, we embed the 4-dimensional Clifford algebra of the Dirac…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
Differential geomtrical methods for deriving the Dirac equation in Curved Spacetime are presented. Einstein's field equation is applied in a novel manner; in the most current standard reference, Birrell and Davies, 1994 [1], the suggestions…
The recently proposed physical projector approach to the quantisation of gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1 dimensions as one of the simplest examples of a topological quantum field theory. The…
We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal…
The phenomenon of emergent physics in condensed-matter many-body systems has become the paradigm of modern physics, and can probably also be applied to high-energy physics and cosmology. This encouraging fact comes from the universal…
We discuss the theoretical basis for the search of the possible experimental manifestations of the torsion field at low energies. First, the quantum field theory in an external gravitational field with torsion is reviewed. The…
The physical interpretation of cold dark matter perturbations is clarified by associating Bertschinger's Poisson gauge with a Eulerian/observer's frame of reference. We obtain such an association by using a Lagrangian approach to…
The classical and quantum dynamics of the Friedmann-Robertson-Walker Universe with massless scalar and massive fermion matter field as a source is discussed in the framework of the Dirac generalized Hamiltonian formalism. The Hamiltonian…
The ad-hoc imposition of normal ordering on the Lagrangian, energy-momentum tensor and currents is a standard tool in quantum field theory (QFT) to eliminate infinite vacuum expectation values (v.e.v.) However, for fermionic expressions…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
There is a substantial curricular overlap between calculus and physics, yet introductory physics students often struggle to connect the two. We introduce a quantity-based framing of the Fundamental Theorem of Calculus (FTC) to help unify…
The Standard Model of the electroweak and strong interactions of particle physics is a quantum field theory. Elementary particles are not indivisible `pieces' of matter but energy bundles of fields, whose properties and interactions are a…
This article reports on a student summer project performed in 2006 at the University of Frankfurt. It is addressed to undergraduate students familiar with the basic principles of relativistic quantum mechanics and general relativity. The…
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the…
Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two…