相关论文: Five-Dimensional Tangent Vectors in Space-Time: II…

There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these frameworks make use of irreducible representations, some make…

We study five dimensional cosmological models with four dimensional hypersufaces of the Bianchi type I and V. In this way the five dimensional vacuum field equations $\rm G_{AB} = 0$, led us to four dimensional matter equations $\rm…

This paper is the second part of a series that develops the mathematical framework necessary for studying field theories on ``T-Minkowski'' noncommutative spacetimes. These spacetimes constitute a class of noncommutative geometries,…

We write down an explicit projection that maps any given 4-spinor to a point in 3+1 spacetime while commuting with the Lorentz action. This suggests that a Lorentz invariant theory - including spacetime itself - has a more natural…

It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be…

The problem is posed of further extending the axiomatic construction proposed in Part 1 for non-local point transformations mapping in each other different curved space times. The new transformations apply to curved space times when…

This paper deals with fundamental properties of Poincar\'e half-maps defined on a straight line for planar linear systems. Concretely, we focus on the analyticity of the Poincar\'e half-maps, their series expansions (Taylor and…

We wish to construct a minimal set of algebraically independent scalar curvature invariants formed by the contraction of the Riemann (Ricci) tensor and its covariant derivatives up to some order of differentiation in three dimensional (3D)…

This paper introduces and investigates a class of noncommutative spacetimes that I will call ``T-Minkowski,'' whose quantum Poincar\'e group of isometries exhibits unique and physically motivated characteristics. Notably, the coordinates on…

In a four-dimensional space I shall construct all of the conformally invariant, scalar-vector-tensor field theories that are consistent with conservation of charge, and flat space compatible. By the last assumption I mean that the…

We present an efficient method for finding the independent invariant tensors of a gauge theory. Our method uses a theorem relating invariant tensors and D-flat directions in field space. We apply our method to several examples-- SO(3) with…

By using invariant theory we show that a (higher-dimensional) Lorentzian metric that is not characterised by its invariants must be of aligned type II; i.e., there exists a frame such that all the curvature tensors are simultaneously of…

The non-Abelian tensor gauge fields take value in extended Poincar\'e algebra. In order to define the invariant Lagrangian we introduce a vector variable in two alternative ways: through the transversal representation of the extended…

We present general formulas for transverse and transverse-traceless (TT) symmetric tensors in flat spaces. TT tensors in conformally flat spaces can be obtained by means of a conformal transformation.

The rotations of rigid bodies in Euclidean space are characterized by their instantaneous angular velocity and angular momentum. In an arbitrary number of spatial dimensions, these quantities are represented by bivectors (antisymmetric…

Besides the well known scalar invariants, there exist also vectorial invariants in the realm of special relativity. It is shown that the three-vector $\left(\frac{d\vec{p}}{dt}\right)_{\parallel…

We give a complete description of semi-symmetric algebraic curvature tensors on a four-dimensional Lorentzian vector space and we use this description to determine all four-dimensional homogeneous semi-symmetric Lorentzian manifolds.

In this paper I shall show how notions of Finsler geometry can be used to construct a new type of geometry using a scalar field, f, on the cotangent bundle of a differentiable manifold, M. This new geometry will be called Lorentzian…

It is evident that the positions of 4 bodies in $d>2$ dimensional space can be identified with vertices of a tetrahedron. Square of volume of the tetrahedron, weighted sum of squared areas of four facets and weighted sum of squared edges…

The analytic continuation to an imaginary velocity $i\xi$ of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted…