Related papers: Shape Quantities for Relational Quadrilateralland
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
Time dependent quadratic Hamiltonians are well known as well in classical mechanics and in quantum mechanics. In particular for them the correspondance between classical and quantum mechanics is exact. But explicit formulas are non trivial…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
Symmetries are a central concept in our understanding of physics. In quantum theories, a quantum reference frame (QRF) can be used to distinguish between observables related by a symmetry. The framework of operational QRFs provides a means…
** The primary topic of this dissertation is the study of the relationships between parts and wholes as described by particular physical theories, namely generalized probability theories in a quasi-classical physics framework and…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not…
This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…
A modified version of relational quantum mechanics is developed based on the three following ideas. An observer can develop an internally consistent description of the universe but it will, of necessity, differ in particulars from the…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
The shape space of k labelled points on a plane can be identified with the space of pure quantum states of dimension k-2. Hence, the machinery of quantum mechanics can be applied to the statistical analysis of planar configurations of…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
We study geometric consistency relations between angles of 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical…
The supersymmetric quantum mechanics of a two-dimensional non-relativistic particle subject to external magnetic and electric fields is studied in a superfield formulation and with the typical non-minimal coupling of (2+1) dimensions. Both…
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…
We review a recently developed theoretical approach to the experimental detection and quantification of bipartite quantum correlations between a qubit and a d dimensional system. Specifically, introducing a properly designed measure Q, the…
A $d$--dimensional quantum model in the spherical approximation confined to a general geometry of the form $L^{d-d^{\prime}} \times\infty^{d^{\prime}}\times L_{\tau}^{z}$ ($L$--linear space size and $L_{\tau}$--temporal size) and subjected…
This work deals with lump-like structures in models described by a single real scalar field in two-dimensional spacetime. We start with a model that supports lump-like configurations and use the deformation procedure to construct scalar…
All objects in 4D spacetime may in principle travel on null paths in a 5D mani-fold. We use this, together with a change in the extra coordinate and the signature of the metric, to construct a simple model of a classical universe and a…
Four-dimensional(4D) spacetime structures are investigated using the concept of the geodesic distance in the simplicial quantum gravity. On the analogy of the loop length distribution in 2D case, the scaling relations of the boundary volume…