Towards relativistic quantum geometry

Abstract

We obtain a gauge-invariant relativistic quantum geometry by using a Weylian-like manifold with a geometric scalar field which provides a gauge-invariant relativistic quantum theory in which the algebra of the Weylian-like field depends on observers. An example for a Reissner-Nordstr\"om black-hole is studied.Comment: 9 pages, no figures, improved versio

Quantum thermodynamics in a static de Sitter space-time and initial state of the universe

“…where δσ = σ µ dx µ is an exact differential and V = √ −ĝ is the volume of the Riemannian manifold. The relativistic quantum algebra is given by [10,11] [σ(x), σ α (y)] = −iΘ α δ (4)…”

Exponential collapse with variable time scale driven by a scalar field

“…In order to describe GW during the exponential collapse, we shall use the formalism revisited in (II B), with the equation (19), which in our example holds:…”

Charged and Electromagnetic Fields from Relativistic Quantum Geometry

“…Another important fact is that since δΦ(x α ) g αβ = Λ δg αβ , the existence of the Hubble horizon is related to the existence of the Gaussian-like hypersurface. The variation of the metric tensor must be done in a Weylian integrable manifold [11] using an auxiliary geometrical scalar field θ, in order to the Einstein tensor (and the Einstein equations) can be represented on a Weyl-like manifold, in agreement with the gauge-invariant transformations Equation (3). If we consider a zero covariant derivative of the metric tensor in the Riemannian manifold (we denote with "; " the Riemannian-covariant derivative): ∆g αβ = g αβ;γ dx γ = 0, hence the Weylian covariant derivative g αβ|γ = θ γ g αβ , described with respect to the Weylian connections (To simplify the notation we shall denote θ α ≡ θ ,α ).…”

“…In a previous work [11] the possibility was explored that the variation of the tensor metric must be done in a Weylian integrable manifold using a geometric displacement, from a Riemannian to a Weylian integrable manifold, described by the dynamics of an auxiliary geometrical scalar field θ, in order that the Einstein tensor (and the Einstein equations) can be represented on a Weyl-like manifold. An important fact is that the Einstein tensor complies with the gauge-invariant transformations studied in a previous work [12].…”