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Related papers: Homotopy approach to quantum gravity

200 papers

We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge…

Mathematical Physics · Physics 2014-08-04 Urs Schreiber , Michael Shulman

We show that the algebra of discretized spatial diffeomorphism constraints in Hamiltonian lattice quantum gravity closes without anomalies in the limit of small lattice spacing. The result holds for arbitrary factor-ordering and for a…

General Relativity and Quantum Cosmology · Physics 2009-10-30 R. Loll

Given a discrete group G and a spherical G-fusion category whose neutral component has invertible dimension, we use the state-sum method to construct a 3-dimensional Homotopy Quantum Field Theory (HQFT) with target the Eilenberg-MacLane…

Quantum Algebra · Mathematics 2012-06-20 Vladimir Turaev , Alexis Virelizier

We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…

Mathematical Physics · Physics 2008-09-19 Manuel Hohmann , Raffaele Punzi , Mattias N. R. Wohlfarth

The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…

General Relativity and Quantum Cosmology · Physics 2026-02-24 Shengzhi Li , Yongge Ma

Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product…

High Energy Physics - Theory · Physics 2015-06-26 M. Bojowald , H. A. Kastrup

This note is to bring to the reader's attention the fact that general relativity and quantum mechanics differ from each other in one main aspect. General relativity is based on the diffeomorphism covariant formulation of the laws of physics…

General Physics · Physics 2015-02-18 Andrei T. Patrascu

We generalize the Hamiltonian picture of General Relativity coupled to classical matter, known as geometrodynamics, to the case where such matter is described by a Quantum Field Theory in Curved Spacetime, but gravity is still described by…

General Relativity and Quantum Cosmology · Physics 2024-03-20 J. L. Alonso , C. Bouthelier-Madre , J. Clemente-Gallardo , D. Martínez-Crespo

In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theory and give description of so-called well-tempered elements…

Rings and Algebras · Mathematics 2020-05-05 Ilya Zhdanovskiy

Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…

General Relativity and Quantum Cosmology · Physics 2016-08-31 Jose A. Zapata

A "quantum-first" approach to gravity is described, where rather than quantizing general relativity, one seeks to formulate the physics of gravity within a quantum-mechanical framework with suitably general postulates. Important guides are…

High Energy Physics - Theory · Physics 2018-05-23 Steven B. Giddings

One of the approaches to quantum gravity is to formulate it in terms of De Rham algebra, choose a triangulation of space-time, and replace differential forms by cochains (that form a finite dimensional vector space). The key issue of…

Mathematical Physics · Physics 2024-06-27 Andrey Losev , Dmitrii Sheptunov , Xin Geng

We present the invariant structure of a Holomorphic Unified Field Theory in which gravity and gauge interactions arise from a single geometric framework. The theory is formulated using a product principal bundle, with one connection, and…

General Physics · Physics 2026-01-27 J. W. Moffat , E. J. Thompson

A theory of gravitation is constructed in which all homogeneous and isotropic solutions are nonsingular, and in which all curvature invariants are bounded. All solutions for which curvature invariants approach their limiting values approach…

General Relativity and Quantum Cosmology · Physics 2009-10-22 R. Brandenberger , V. Mukhanov , A. Sornborger

In this paper we construct a model for group field cosmology. The classical equations of motion for the non-interactive part of this model generate the Hamiltonian constraint of loop quantum gravity for a homogeneous isotropic universe…

General Relativity and Quantum Cosmology · Physics 2015-06-11 Mir Faizal

We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…

High Energy Physics - Theory · Physics 2009-11-10 C. Wetterich

We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…

General Relativity and Quantum Cosmology · Physics 2009-10-30 M. Heller , W. Sasin

We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural…

Mathematical Physics · Physics 2021-06-22 Andrzej Okolow

We review the approach to quantum gravity based on supersymmetry, strings, and holography. This includes a survey of black holes in higher-dimensions, supersymmetry and supergravity, as well as string theory, black hole microstates, and the…

General Relativity and Quantum Cosmology · Physics 2014-05-29 Henriette Elvang , Gary T. Horowitz

We consider the homothetic motion group. We construct a homothetic covariant Newtonian gravitation theory which unifies inertial homothetic forces and gravitational fields. This is achieved through an equivalence principle based on a local…

General Relativity and Quantum Cosmology · Physics 2015-06-18 Xavier Jaén , Alfred Molina