Related papers: Note about the spin connection in general relativi…
The affine connection in a space-time with a maximally symmetric spatial subspace is derived using the properties of maximally symmetric tensors. The number of degrees of freedom in metric-affine gravity is thereby considerably reduced…
We generalize the integrable Heisenberg ferromagnet model according to each Hermitian symmetric spaces and address various new aspects of the generalized model. Using the first order formalism of generalized spins which are defined on the…
Complementarity plays a pivotal role in understanding a diverse range of quantum phenomena. Here, we show how the tradeoff between quantities of a complete complementarity relation is modified in an arbitrary spacetime for a particle with…
We derive the kinematic Hamiltonian for the so-called "new general relativity" class of teleparallel gravity theories, which is the most general class of theories whose Lagrangian is quadratic in the torsion tensor and does not contain…
I review the formalism of loop quantum gravity, in both its real and complex formulations, and spin foam theory which is its path integral counterpart. Spin networks for non-compact groups are introduced (following hep-th/0205268) to deal…
We show how an affine connection on a Riemannian manifold occurs naturally as a cochain in the complex for Leibniz cohomology of vector fields with coefficients in the adjoint representation. The Leibniz coboundary of the Levi-Civita…
It is a commonplace attributed to Kretschmann that any local physical theory can be represented in arbitrary coordinates using tensor calculus. But the literature also claims that spinors _as such_ cannot be represented in coordinates in a…
The different forms of the Hamiltonian formulations of linearized General Relativity/spin-two theories are discussed in order to show their similarities and differences. It is demonstrated that in the linear model, non-covariant…
A generalization of the $SU(2)$--spin systems on a lattice and their continuum limit to an arbitrary compact group $G$ is discussed. The continuum limits are, in general, non--relativistic $\sigma$--model type field theories targeted on a…
Spin network technique is usually generalized to relativistic case by changing $SO(4)$ group -- Euclidean counterpart of the Lorentz group -- to its universal spin covering $SU(2)\times SU(2)$, or by using the representations of $SO(3,1)$…
Although intrinsic spin is usually viewed as a purely quantum property with no classical analog, we present evidence here that fermion spin has a classical origin rooted in the geometry of three-dimensional physical space. Our approach to…
We remind how relationality arises as the core insight of general-relativistic gauge field theories from the articulation of the generalised hole and point-coincidence arguments. Hence, a compelling case for a manifestly relational…
In these continuation papers (VI and VII) we are interested in approach the problem of spin from a classical point of view. In this first paper we will show that the spin is neither basically relativistic nor quantum but reflects just a…
In this work we propose a new gravitational setup formulated in terms of two interacting vierbein fields. The theory is the fully diffeomorphism and local Lorentz invariant extension of a previous construction which involved a fixed…
We consider the quantum theory of the Lorentzian fermionic differential forms and the corresponding bi-spinor quantum fields, which are the expansion coefficients of the forms in the bi-spinor basis of Becher and Joos [7]. The canonical…
General Relativity in the noncommutative spacetime of ${\cal M}^4 \times Z_2 \times Z_2$ is constructed based on a new type of fermions in addition to the known chiral quark-leptons. While this theory has a finite physical spectrum, all the…
Stationary extended frames in general relativity are considered. The requirement of stationarity allows to treat the spacetime as a principal fiber bundle over the one-dimensional group of time translations. Over this bundle a connection…
We briefly review why the non-linear realisation of the semi-direct product of a group with one of its representations leads to a field theory defined on a generalised space-time equipped with a generalised vielbein. We give formulae, which…
In this brief article an internal symmetry of a generic metric compatible space-time connection, metric and generalized volume element is introduced. The symmetry arises naturally by considering a space-time connection containing a generic…
The system of two relativistic particles with einbein fields is quantized as a constrained system.A method of the introduction of the Newton--Wigner collective coordinate is discussed in presence of different gauge fixing conditions. Some…