On the Emergence of Non Locality for Quantum Fields Enjoying Κ-Poincaŕe Symmetries (original) (raw)

Quantum Gravity from Noncommutative Spacetime

J.Korean Phys.Soc. 65 (2014) 1754-1798

We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of symplectic geometry rather than Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory and so gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, it is feasible to formulate a background independent quatum gravity where the prior existence of any spacetime structure is not a priori assumed but defined by fundamental ingredients in quantum gravity theory. This scheme for quantum gravity resolves many notorious problems in theoretical physics, for example, to resolve the cosmological constant problem, to understand the nature of dark energy and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture for what matter is. A matter field such as leptons and quarks simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative ⋆-algebra) of quantum gravity.

Fock space, quantum fields, and kappa-Poincar� symmetries

Phys Rev D, 2007

We study the quantization of a linear scalar field, whose symmetries are described by the κ-Poincaré Hopf-algebra, via deformed Fock space construction. The one-particle sector of the theory exhibits a natural (planckian) cutoff for the field modes. At the multi-particle level the non-trivial co-algebra structure of κ-Poincaré leads to a deformed bosonization in the construction of Fock space states. These physical states carry energy-momentum charges which are divergenceless and obey a deformed dispersion relation.

Canonical quantization, spacetime noncommutativity and deformed symmetries in field theory

Journal of Physics A: Mathematical and Theoretical, 2007

Within the spirit of Dirac's canonical quantization, noncommutative spacetime field theories are introduced by making use of the reparametrization invariance of the action and of an arbitrary non-canonical symplectic structure. This construction implies that the constraints need to be deformed, resulting in an automatic Drinfeld twisting of the generators of the symmetries associated with the reparametrized theory. We illustrate our procedure for the case of a scalar field in 1+1-spacetime dimensions, but it can be readily generalized to arbitrary dimensions and arbitrary types of fields.

Algebraic approach to Quantum Gravity II: noncommutative spacetime

Toward a New Understanding of Space, Time and Matter, 2009

We provide a self-contained introduction to the quantum group approach to noncommutative geometry as the next-to-classical effective geometry that might be expected from any successful quantum gravity theory. We focus particularly on a thorough account of the bicrossproduct model noncommutative spacetimes of the form [t, xi] = ıλxi and the correct formulation of predictions for it including a variable speed of light. We also study global issues in the Poincaré group in the model with the 2D case as illustration. We show that any off-shell momentum can be boosted to infinite negative energy by a finite Lorentz transformaton.

Fock space, quantum fields and kappa-Poincar\'e symmetries

Physical Review D, 2007

We study the quantization of a linear scalar field, whose symmetries are described by the kappa-Poincare' Hopf-algebra, via deformed Fock space construction. The one-particle sector of the theory exhibits a natural (planckian) cut-off for the field modes. At the multi-particle level the non-trivial co-algebra structure of kappa-Poincare' leads to a deformed bosonization in the construction of Fock space states. These physical states carry energy-momentum charges which are divergenceless and obey a deformed dispersion relation.

From quantum gravity to quantum field theory via noncommutative geometry

Classical and Quantum Gravity, 2014

A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a semi-classical limit, give a system of interacting fermions in an ambient gravitational field. The interaction involves flux tubes of the gravitational field. In the additional limit where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. *

Algebraic Approach to Quantum Gravity III: Non-Commutative Riemannian Geometry

Quantum Gravity Mathematical Models and Experimental Bounds, 2007

This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that arises naturally as the classical limit; a theory with nonsymmetric metric and a skew version of metric compatibilty. Meanwhile, in quantum gravity a key ingredient of our approach is the proposal that the differential structure of spacetime is something that itself must be summed over or 'quantised' as a physical degree of freedom. We illustrate such a scheme for quantum gravity on small finite sets.