Related papers: Quantum Field Theory of Geometry
Quantum Information and the new informational paradigm are entering the domain of quantum field theory and gravity, suggesting the quantum automata framework. The quantum automaton is the minimal-assumption extension to the Planck and…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
Free scalar field theory on 2 dimensional flat spacetime, cast in diffeomorphism invariant guise by treating the inertial coordinates of the spacetime as dynamical variables, is quantized using LQG type `polymer' representations for the…
Axiomatic quantum field theory (QFT) provides a rigorous mathematical foundation for QFT, and it is the basis for proving some important general results, such as the well-known spin-statistics theorem. Free-field QFT meets the axioms of…
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…
Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalisation of symmetry groups for certain integrable systems, and on the other as part of a generalisation of geometry itself…
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…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder-Weyl formalism. To recover the standard noncovariant formalism without violating covariance,…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
Quantum geometry defines the phase and amplitude distances between quantum states. The phase distance is characterized by the Berry curvature and thus relates to topological phenomena. The significance of the full quantum geometry,…
Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…
We set up a covariant renormalisation group equation on a foliated spacetime which preserves background diffeomorphism symmetry. As a first application of the new formalism, we study the effect of quantum fluctuations in Lorentz symmetry…
A quantum scalar field theory with spacetime-dependent coupling is studied. Surprisingly, while translation invariance is explicitly broken in the classical theory, momentum conservation is recovered at the quantum level for some specific…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
Planck-scale physics challenges the classical smooth-spacetime picture by introducing quantum fluctuations that imply a nontrivial spacetime microstructure. We present a framework that encodes these fluctuations by promoting local scale…