Related papers: Physical Principles Based on Geometric Properties
Relaxing the postulates of an axiomatic theory is a natural way to find more general theories, and historically, the discovery of non-Euclidean geometry is a famous example of this procedure. Here, we use this way to extend quantum…
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…
Quantum mechanics is formulated as a geometric theory on a Hilbert manifold. Images of charts on the manifold are allowed to belong to arbitrary Hilbert spaces of functions including spaces of generalized functions. Tensor equations in this…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
An extension of the classical action principle obtained in the framework of the gauge transformations, is used to describe the motion of a particle. This extension assigns many, but not all, paths to a particle. Properties of the particle…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
According to Schroedinger's ideas, classical dynamics of point particles should correspond to the " geometrical optics " limit of a linear wave equation, in the same way as ray optics is the limit of wave optics. It is shown that, using…
This is a brief review where some basic elements of non-commutative geometry are given. The rules and ingredients that enter in the construction of the standard model and grand unification models in non-commutative geometry are summarized.…
Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We develop both…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
I discuss the physical basis of classical mechanics, such as expressed commonly using the framework of Newton's Principia. Newton's formulation of the laws of motion is seen to have quite a few ambiguities and shortcomings. Therefore I…
Starting from the guiding principles of spacetime locality and operationalism, a general framework for a probabilistic description of nature is proposed. Crucially, no notion of time or metric is assumed, neither any specific physical…
We consider Hilbert's problem of the axioms of Physics at a qualitative or conceptual level. This issue is more pressing than ever as we seek to understand how both General Relativity and quantum theory could emerge from some deeper theory…
Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the…
There were many attempts to geometrize electromagnetic field and find out new interpretation for quantum mechanics formalism. The distinctive feature of this work is that it combines geometrization of electromagnetic field and…
This is a paper about geometry and how one can derive several fundamental laws of physics from a simple postulate of geometrical nature. The method uses monogenic functions analysed in the algebra of 5-dimensional spacetime, exploring the…
To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…