Related papers: A Semi-Classical Approach to Gravitation, Mass and…
We discuss the fluctuation properties of diagonal matrix elements in the semiclassical limit in chaotic systems. For extended observables, covering a phase space area of many times Planck's constant, both classical and quantal distributions…
In recent years Quantum Superstrings and Quantum Gravity approaches have come to rely on non differenciable spacetime manifolds. These throw up a noncommutative spacetime geometry and we consider the origin of mass and a related…
The motion of a classical spinning test particle in the field of a weak plane gravitational wave is studied. It is found that the characteristic dimensions of the particle's orbit is sensitive to the ratio of the spin to the mass of the…
Basic notions of Dirac theory of constrained systems have their analogs in differential geometry. Combination of the two approaches gives more clear understanding of both classical and quantum mechanics, when we deal with a model with…
We consider the gravitational potential and the gravitational rotation field generated by an spherical mass distribution with exponential density, when the force between any two mass elements is not the usual Newtonian one, but some general…
This is a broad-brush introduction to the theory of spin in quantum field theory, presented at the 1993 SLAC Summer Institute. It may be useful for beginning students.
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where some arithmetic properties of a given number field can be…
In this paper we pose two fundamental ideas on the motion of an elementary particle supporting the internal "spin motion" or $\textit{Zitterbewegung}$ and a particle as concentrated energy. First, the particle moves randomly in a limited…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
The problem of quantum gravity is treated from a radically new viewpoint based on a detailed mathematical analysis of what the constitution of physical space is, which has been carried out by Michel Bounias and the author. The approach…
Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…
Newton introduced the concept of mass in his {\it Principia} and gave an intuitive explanation for what it meant. Centuries have passed and physicists as well as philosophers still argue over its meaning. Three types of mass are generally…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
Phase spaces with nontrivial geometry appear in different approaches to quantum gravity and can also play a role in e.g. condensed matter physics. However, so far such phase spaces have only been considered for particles or strings. We…
In this short review, we explain how and in which sense the causal action principle for causal fermion systems gives rise to classical gravity and the Einstein equations. Moreover, methods are presented for going beyond classical gravity,…
In these lectures I describe some of the open questions in the standard model relating to the nature and origin of mass, forces and matter and discuss some of the speculative theoretical ideas put forth in this regard. Some of the topics…
In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time…
Using very general and well established ideas of the statistical physics of macroscopic bodies, that is, of those composed of many degrees of freedom, we show how classical behavior of the center of mass motion arises from a fully quantum…
These are expanded lecture notes of a mini-course whose objectives were to introduce the basic concepts, constructions and techniques of noncommutative geometry, as well as their uses as a framework for modelling quantum spacetime. Key…