Related papers: Weyl Geometry and Quantum Corrections
A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl's electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the…
We make biframe and quaternion extensions on the noncommutative geometry, and construct the biframe spacetime for the unification of gravity and quantum field theory. The extended geometry distinguishes between the ordinary spacetime based…
In homogeneous cosmologies, quantum geometry effects lead to a resolution of the classical singularity without having to invoke special boundary conditions at the singularity or introduce ad-hoc elements such as unphysical matter. The same…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
We review (non-supersymmetric) gauge theories of four-dimensional space-time symmetries and their quadratic action. The only true gauge theory of such a symmetry (with a physical gauge boson) that has an exact geometric interpretation,…
In the context of an extended General Relativity theory with boundary terms included, we introduce a new nonlinear quantum algebra involving a quantum differential operator, with the aim to calculate quantum geometric alterations when a…
A quantum cosmology in teleparallel gravity is presented in this article. Teleparallel gravity is used to perform such an analysis once in General Relativity (GR) the concept of gravitational energy is misleading preventing the…
In any quantum theory of gravity, it is of the utmost importance to recover the limit of quantum theory in an external spacetime. In quantum geometrodynamics (quantization of general relativity in the Schr\"odinger picture), this leads in…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
This article provides a cartoon of the quantization of General Relativity using the ideas of effective field theory. These ideas underpin the use of General Relativity as a theory from which precise predictions are possible, since they show…
Quantum geometry is a differential geometry based on quantum mechanics. It is related to various transport and optical properties in condensed matter physics. The Zeeman quantum geometry is a generalization of quantum geometry including the…
Familiar textbook quantum mechanics assumes a fixed background spacetime to define states on spacelike surfaces and their unitary evolution between them. Quantum theory has changed as our conceptions of space and time have evolved. But…
We consider the Principle of Equivalence along with Weyl theorem to discuss the interpretation of gravity as a geometric effect; we study what are the restrictions on the connections that must be required for this geometrization to occur in…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
We develop the properties of Weyl geometry, beginning with a review of the conformal properties of Riemannian spacetimes. Decomposition of the Riemann curvature into trace and traceless parts allows an easy proof that the Weyl curvature…
I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such…
A new geometry, called General geometry, is constructed. It is proven that its the most simplest special case is geometry underlying Electromagnetism. Another special case is Riemannian geometry. Action for electromagnetic field and Maxwell…