Related papers: Clifford Geometrodynamics
We study a new approach to generally covariant quantum mechanics applied in the case of an FLRW cosmological background. For positive spatial curvature we find a discrete series of solutions of the Klein-Gordon equation that can reasonably…
The mathematical foundations of relativistic quantum mechanics is largely based upon the discovery of the Pauli and Dirac matrices. An algebra which lies at an even more fundamental level is the geometric Clifford algebra with metric…
The brane-worlds model was inspired partly by Kaluza-Klein's theory, where the gravitation and the gauge fields are obtained of a geometry of higher dimension (bulk). Such a model has been showing positive in the sense of we find…
A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic…
The derivation of the exact and unique nilpotent Becchi-Rouet-Stora-Tyutin (BRST)- and anti-BRST symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem in the framework of…
Multidimensional theories still remain attractive from the point of view of better understanding fundamental interactions. In this paper a six-dimensional Kaluza-Klein type model at the classical, Einstein's gravity formulation is…
This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
Physical spacetime geometry follows from some effective thermodynamics of quantum states of all fields and particles described in frames of General Relativity. In the sense of pure field theoretical Einstein's point of view on gravitation…
In hybrid classical-quantum theories, the dynamics of the classical system induce the classicality of the quantum system, meaning that such models do not necessarily require a measurement postulate to describe probabilistic measurement…
In the review article in Progress in Particle and Nuclear Physics (vol.121(2021) 103890)) the authors present the achievements so far of the spin-charge-family theory, which offers the explanation for all the so far observed properties of…
Faced with the persisting problem of the unification of gravity with other fundamental interactions we investigate the possibility of a new paradigm, according to which the basic space of physics is a multidimensional space ${\cal C}$…
In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The…
We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…
We identify a class of condensate states in the group field theory (GFT) approach to quantum gravity that can be interpreted as macroscopic homogeneous spatial geometries. We then extract the dynamics of such condensate states directly from…
In a companion article, the Clifford bundle over spacetime was used as a geometric framework for obtaining coupled Dirac and Einstein equations. Other forces may be incorporated using minimal coupling. Here the fundamental forces that are…
We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…
In this article we present a possibility of imposing the unimodular condition within the 5-dimensional Kaluza-Klein theory including the scalar field. Unimodular gravity became an object of increasing interest in the late 80-ties; and was…
Nelson's stochastic mechanics links quantum mechanics to an underlying Brownian motion with the identification $\hbar = m\sigma$. Ghose's interpolating equation introduces a continuous parameter $\lambda$ that suppresses the quantum…
The Landau-Lifshitz-Gilbert equation for magnetization dynamics is recast into spinor form using the real-valued Clifford algebra (geometric algebra) of three-space. We show how the undamped case can be explicitly solved to obtain…