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Vielbeins are necessary when coupling General Relativity (GR) to fermionic matter. This enhances the gauge group of GR to include local Lorentz transformations. In view of a reduced phase space formulation of quantum gravity, in this work…
First, we briefly review the description of gravity theories as gauge theories in three and four dimensions. Specifically, we recall the procedure in which the results of General Relativity in three and four dimensions are recovered in a…
We examine a covariant quantization of electromagnetic fields by using an operator derived from a constant scalar that can be called extended Lorentz gauge. The quantization can avoid an inconsistency between Lorentz gauge and a commutation…
The concept of electric-magnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the Pauli-Fierz action (quadratic part of the Einstein-Hilbert action) can be cast in a form that is…
In the past decade the phenomenology of quantum gravity has been dominated by the search of violations of Lorentz invariance. However, there are very serious arguments that led us to assume that this invariance is a symmetry in Nature. This…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
The quantum gravity is formulated based on gauge principle. The model discussed in this paper has local gravitational gauge symmetry and gravitational field is represented by gauge potential. A preliminary study on gravitational gauge group…
The compatibility of special relativity and Quantum Mechanics has been questioned by several authors. The origin of this tension can be traced back mainly to the introduction of the measurement processes and the corresponding wave function…
In this work some issues in the context of Noncommutative Quantum Mechanics (NCQM) are addressed. The main focus is on finding whether symmetries present in Quantum Mechanics still hold in the phase-space noncommutative version. In…
We develop an unified algebraic approach to the description of gauge interactions within the framework of a new concept of quantum mechanics. The next step in generalizing the space-time and the action vector space is made. The gauge field…
We extend the theory of the gauging of classical quadratically nonlinear algebras without a central charge but with a coset structure, to the quantum level. Inserting the minimal anomalies into the classical transformation rules of the…
We perform a general computation of the off-shell one-loop divergences in Einstein gravity, in a two-parameter family of path integral measures, corresponding to different ways of parametrizing the graviton field, and a two-parameter family…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
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…
Recently, the authors presented a covariant extension of the Generalized Uncertainty Principle (GUP) with a Lorentz invariant minimum length. This opens the way for constructing and exploring the observable consequences of minimum length in…
Any metric theory of gravity whose interaction with quantum particles is described by a covariant wave equation is equivalent to a vector theory that satisfies Maxwell-type equations identically. This result does not depend on any…
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter', and features a global symmetry. One then…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and…