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The inconsistence of Dirac-Weyl field equations with the universal U(1) gauge invariance of neutrinos in quantum mechanics led to generalize the special relativity to the generic relativity, which was composed of the special relativity and…
Teleparallel gravity and its popular generalization $f(T)$ gravity can be formulated as fully invariant (under both coordinate transformations and local Lorentz transformations) theories of gravity. Several misconceptions about teleparallel…
A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is…
A gauge theory for a superalgebra that includes an internal gauge (G) and local Lorentz algebras, and that could describe the low energy particle phenomenology is constructed. These two symmetries are connected by fermionic supercharges.…
We show that in theories of generalised teleparallel gravity, whose Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the action and the field equations are not invariant under local Lorentz transformations. We also…
Effective field theories describing gravity coupled to matter are investigated, allowing for operators of arbitrary mass dimension. Terms violating local Lorentz and diffeomorphism invariance while preserving internal gauge symmetries 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…
The local symmetry transformations of the quantum effective action for general gauge theory are found. Additional symmetries arise under consideration of background gauges. Together with "trivial" gauge transformations, vanishing on mass…
We suggest an extension of the gauge principle which includes tensor gauge fields. In this extension of the Yang-Mills theory the vector gauge boson becomes a member of a bigger family of gauge bosons of arbitrary large integer spins. The…
We consider the standard gauge theory of Poincar\'{e} group, realizing as a subgroup of $GL(5. R)$. The main problem of this theory was appearing of the fields connected with non-Lorentz symmetries, whose physical sense was unclear. In this…
In a new theory, local Lorentz invariance is a low-energy symmetry which no longer holds when a fermion energy E is well above 1 TeV. Here we find that the modified E(p) relation is consistent with observation, and is in fact nearly the…
A recent result concerning interacting theories of self-dual tensor gauge fields in six dimensions is generalized to include coupling to gravity. The formalism makes five of the six general coordinate invariances manifest, whereas the sixth…
A gauge theory of the Lorentz group with a mass-dimension one gauge field coupling to matter of any spin is developed. As a completely new feature the "Vierbein" assuring local gauge invariance enters not as an independent dynamical field,…
First-order general relativity in $n$ dimensions ($n \geq 3$) has an internal gauge symmetry that is the higher-dimensional generalization of three-dimensional local translations. We report the extension of this symmetry for $n$-dimensional…
We study the possible affine gauge transformations of the torsion tensor that make up Lie algebras. We find two such non-trivial structures, in which the gauge parameters are a $2$-form and a scalar. The first one gives rise to a…
The f(T) gravity is nowadays being widely used for cosmological model building, as well as for constructing spherically symmetric solutions. In its classical pure tetrad formulation it violates the local Lorentz symmetry in the space of…
We propose a regularized lattice model for quantum gravity purely formulated in terms of fermions. The lattice action exhibits local Lorentz symmetry, and the continuum limit is invariant under general coordinate transformations. The metric…
We suggest an extension of the Yang-Mills theory which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large…
We explore generalized symmetry in the context of nonlinear dynamical gravity. Our basic strategy is to transcribe known results from Yang-Mills theory directly to gravity via the tetrad formalism, which recasts general relativity as a…
We introduce the generalized Lorentz gauge condition in the theory of quantum electrodynamics into the general vector-tensor theories of gravity. Then we explore the cosmic evolution and the static, spherically symmetric solution of the…