Related papers: Deformation principle as a foundation of physical …
We investigate the motion of test particles in quantum-gravitational backgrounds by introducing the concept of q--desics, quantum-corrected analogs of classical geodesics. Unlike standard approaches that rely solely on the expectation value…
The hypothesis is suggested that the equation for the Dirac free wave field is, in fact, a group-theoretical relation describing propagation of specific microscopic deviations of space geometry from the euclidean one (closed topological…
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime…
A strengthened canonical quantization scheme for the constrained motion on a curved hypersurface is proposed with introduction of the second category of fundamental commutation relations between Hamiltonian and positions/momenta, whereas…
Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to…
Plastic deformation is widely regarded as an intrinsically dissipative phenomenon and its theoretical description is largely phenomenological. We argue instead that plasticity possesses a non-dissipative, symmetry determined backbone:…
It is the author's belief that a perfect theory will eventually be formulated, where geometry and physics become indistinguishable, so that the complete understanding of space properties, together with proper assignments between geometric…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell…
A possible model for quantum kinematics of a test particle in a curved space-time is proposed. Every reasonable neighbourhood V_e of a curved space-time can be equipped with a nonassociative binary operation called the geodesic…
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…
This work presents a group-theoretic interpretation of the historical evolution of mechanics, proposing that each fundamental theory of motion corresponds to a distinct geometry in the sense of Felix Klein. The character of each geometry is…
These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…
This work investigates the geometrical properties of self-gravitating $N$-body systems from the perspective established by Henri Poincar\'e and Albert Einstein concerning the operational nature of measured geometry. Utilizing recent…
The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to…
A motivation of using noncommutative and nonarchimedean geometry on very short distances is given. Besides some mathematical preliminaries, we give a short introduction in adelic quantum mechanics. We also recall to basic ideas and tools…
It is proved that the set of geodesic circles in two dimensions may be given a variational description and the explicit form of it is presented. In the limit case of the Euclidean geometry a certain claim of uniqueness of such description…
The definition of a reference frame in General Relativity is achieved through the construction of a congruence of time-like world-lines. In this framework, splitting techniques enable us to express physical phenomena in analogy with Special…
Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…
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…