Related papers: Parallel Objects and Field Equations
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
Differential forms is a highly geometric formalism for physics used from field theories to General Relativity (GR) which has been a great upgrade over vector calculus with the advantages of being coordinate-free and carrying a high degree…
This work provides a general overview for the treatment of symmetries in classical field theories and (pre)multisymplectic geometry. The geometric characteristics of the relation between how symmetries are interpreted in theoretical physics…
We formulate a theory combining the principles of a scalar-tensor gravity and Rastall's proposal of a violation of the usual conservation laws. We obtain a scalar-tensor theory with two parameters $\omega$ and $\lambda$, the latter…
Quantum theory is applicable, in principle, to both the microscopic and macroscopic realms. It is therefore worthwhile to investigate whether it is possible to evolve a quantum-compatible view of the properties and states of macroscopic…
The Standard Model of particle physics and the theory of General Relativity (GR) currently provide a good description of almost all phenomena of particle physics and gravitation that have received controlled experimental tests. However, the…
The classical gravitational two-body problem is generalized in order to be applicable also to weak gravitational fields. The equation of motion holds both for terrestrial and large cosmic scales, the Newtonian gravitational law represents a…
The dynamics of "dipolar particles", i.e. particles endowed with a four-vector mass dipole moment, is investigated using an action principle in general relativity. The action is a specific functional of the particle's world line, and of the…
The standard model of particle physics represents the cornerstone of our understanding of the microscopic world. In these lectures we review its contents and structure, with a particular emphasis on the central role played by symmetries and…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
In this note we show how to construct a number of nonconvex quadratic inequalities for a variety of physics equations appearing in physical design problems. These nonconvex quadratic inequalities can then be used to construct bounds on…
Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters…
The general concept of symmetry is realized in manifold ways in different realms of reality, such as plants, animals, minerals, mathematical objects or human artefacts in literature, fine arts and society. In order to arrive at a common…
The formalism of classical particle dynamics is reinvestigated according to the basic requirement of causal consistency, and a new equation of particle dynamics, which is more general and more in line with classical mechanics experiments…
The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4-dimensional space where time intervals are always a measure of geodesic arc lengths, i.e.…
Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical…
Process Philosophy endeavours to replace the classical ontology of substances by a process ontology centered on notions of changes and transitions. We argue, that the substantial and processual approach are mutually complementary. Here,…
In the first part of the talk, I give a low-resolution overview of the current state of particle physics - the triumph of the Standard Model and its discontents. I review and re-endorse the remarkably direct and (to me) compelling argument…
It is shown that the geometry of parallelizable manifolds can be extended to non-parallelizable ones by extending the connection that a global frame field would define on a parallelizable manifold to a connection that a singular frame field…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…