Related papers: The Lorentz Group, a Galilean Approach

We construct a canonical formulation of general relativity for the case of a timelike foliation of spacetime. The formulation possesses explicit covariance with respect to Lorentz transformations in the tangent space. Applying the loop…

We consider a complex covariant form of the macroscopic Maxwell equations, in a moving medium or at rest, following the original ideas of Minkowski. A compact, Lorentz invariant, derivation of the energy-momentum tensor and the…

Admitting the validity of Lorentz transformations for the space as time coordinates of the same event we derive their differential form in order to underline the correct prerequisites for the application of time and length contraction or…

This paper describes a particularly didactic and transparent derivation of basic properties of the Lorentz group. The generators for rotations and boosts along an arbitrary direction, as well as their commutation relations, are written as…

Matrix elements of irreducible representations of the Lorentz group are calculated on the basis of complex angular momentum. It is shown that Laplace-Beltrami operators, defined in this basis, give rise to Fuchsian differential equations.…

In this note we formulate and prove a version of Cartan decomposition for holomorphic loop groups, similar to Cartan decomposition for $p$-adic loop groups, discussed proved by Garland (and later by the authors by geometric mathods). The…

It is possible to construct representations of the Lorentz group using four-dimensional harmonic oscillators. This allows us to construct three-dimensional wave functions with the usual rotational symmetry for space-like coordinates and…

The aim of this work is to show, on the example of the behaviour of the spinless charged particle in the homogeneous electric field, that one can quantized the velocity of particle by the special gauge fixation. The work gives also the some…

Irreversibility implies a preferred flow of time, yet special relativity denies the existence of a preferred clock. This tension has long obstructed the formulation of a relativistic master equation: standard Markovian approximations either…

The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group averaging method to solve constraints one…

The paper presents a relativistic space-time diagram, which displays in true values the space (Cartesian and polar) and the time coordinates of the same event detected from two inertial reference frames in relative motion related by the…

We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field…

This paper presents some ideas which might assist teachers incorporating special relativity into an introductory physics curriculum. One can define the proper-time/velocity pair, as well as the coordinate-time/velocity pair, of a traveler…

We show that the Lorentz transformations for the space-time coordinates of the same event are a direct consequence of the principle of relativity and of Einstein's distant clocks synchronization procedure. In our approach, imposing the…

The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he…

I tell about different mathematical tool that is important in general relativity. The text of the book includes definition of geometrical object, concept of reference frame, geometry of metric-affinne manifold. Using this concept I learn…

In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after solving the second-class constraints inherited from the…

Empirical understanding teaches us that space is three dimensional while relativity merges space with time. We tried to show that it is possible to model space as three complex coordinates. In our construction, the usual spatial coordinate…

Quasi-Riemannian theories of gravity have smaller gauge groups acting on the tangent spacetime than the full Lorentz group. Among others, the spatial rotation group can be gauged to obtain spacetime asymmetric gravity with general…

In this paper, we classify space-time curves up to Galilean group of transformations with Cartan's method of equivalence. As an aim, we elicit invariats from action of special Galilean group on space-time curves, that are, in fact,…