Related papers: Schwinger's variational principle in Einstein$-$Ca…
We analyse the Einstein-Cartan gravity in its standard form cal-R = R + cal-K^2, where cal-R and R are the Ricci scalar curvatures in the Einstein-Cartan and Einstein gravity, respectively, and cal-K^2 is the quadratic contribution of…
Starting with Newton's law of universal gravitation, we generalize it step-by-step to obtain Einstein's geometric theory of gravity. Newton's gravitational potential satisfies the Poisson equation. We relate the potential to a component of…
We introduce bosonic (p - 1)-form fields that couple to the spin connection of the Einstein-Cartan theory of gravity thus becoming a non-trivial source of space-time torsion. We analyze all the general features of both the matter and the…
We derive the chiral kinetic theory under the presence of a gravitational Riemann curvature. It is well-known that in the chiral kinetic theory there inevitably appears a redundant ambiguous vector corresponding to the choice of the Lorentz…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
For a conformally-coupled scalar field we obtain the conformally-related Einstein-Langevin equations, using appropriate transformations for all the quantities in the equations between two conformally-related spacetimes. In particular, we…
We generalize Einstein's General Relativity (GR) by assuming that all matter (including macro-objects) has quantum effects. An appropriate theory to fulfill this task is Gauge Theory Gravity (GTG) developed by the Cambridge group. GTG is a…
We consider the special and general relativistic extensions of the action principle behind the Schr\"odinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
In this paper, we analyze the variation of the gravitational action on a bounded region of spacetime whose boundary contains segments with various characters, including null. We develop a systematic approach to decompose the derivative of…
The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor…
We investigate a relation of the contravariant geometry to the emergent gravity from noncommutative gauge theories. We give a refined formulation of the contravariant gravity and provide solutions to the contravariant Einstein equation. We…
We investigate the axial vector torsion-spin coupling effects in the framework of the Poincar\'e gauge theory of gravity with the general Yang-Mills type Lagrangian. The dynamical equations for the ``electric'' and ``magnetic'' components…
We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from the most general Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity…
Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann…
We review the application of torsion in field theory. First we show how the notion of torsion emerges in differential geometry. In the context of a Cartan circuit, torsion is related to translations similar as curvature to rotations.…
We present a new approach to the covariant canonical formulation of Einstein-Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the…
Using the tools of q--differential calculus and quantum Lie algebras associated to quantum groups, we find a one--parameter family of q-gauge theories associated to the quantum group $ISO_q(3,1)$. Although the gauge fields, that is the…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…
An analysis of the Schwinger's action principle in Lagrangian quantum field theory is presented. A solution of a problem contained in it is proposed via a suitable definition of a derivative with respect to operator variables. This results…