Related papers: Feynman geometry
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…
A framework for quantum field theory coupled to three-dimensional quantum gravity is proposed. The coupling with quantum gravity regulates the Feynman diagrams. One recovers the usual Feynman amplitudes in the limit as the cosmological…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold.…
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams…
Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
General Relativity describes gravity in geometrical terms. This suggests that quantizing such theory is the same as quantizing geometry. The subject can therefore be called quantum geometry and one may think that mathematicians are…
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…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…
This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we develop a theory of what we call (weak) quantum vertex $\F((t))$-algebras…
General relativity successfully describes space-times at scales that we can observe and probe today, but it cannot be complete as a consequence of singularity theorems. For a long time there have been indications that quantum gravity will…
We discuss how basic notions of graph theory and associated graph polynomials define questions for algebraic geometry, with an emphasis given to an analysis of the structure of Feynman rules as determined by those graph polynomials as well…
We find that, in presence of the Snyder geometry, the notion of translational invariance needs to be modified, allowing a momentum dependence of this symmetry. This step is necessary to build the maximally localized states and the Feynman…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
There are still no interacting models of the Wightman axioms, suggesting that the axioms are too tightly drawn. Here a weakening of linearity for quantum fields is proposed, with the algebra still linear but with the quantum fields no…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…