Publications (31)
Volume of 4-polytopes from bivectors
Benjamin Bahr
In this article we prove a formula for the volume of 4-dimensional polytopes, in terms of their face bivectors, and the crossings within their boundary graph. This proves that the…
On knottings in the physical Hilbert space of LQG as given by the EPRL model
Benjamin Bahr
We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant u…
Deformation of the EPRL spin foam model by a cosmological constant
Benjamin Bahr, Giovanni Rabuffo
In this article, we consider an ad-hoc deformation of the EPRL model for quantum gravity by a cosmological constant term. This sort of deformation has been first introduced by Han…
Operator Spin Foam Models
Benjamin Bahr, Frank Hellmann, Wojciech KamiÅski +2
The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the mai…
Regge calculus from a new angle
Benjamin Bahr, Bianca Dittrich
In Regge calculus space time is usually approximated by a triangulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to…
Hypercuboidal renormalization in spin foam quantum gravity
Benjamin Bahr, Sebastian Steinhaus
In this article we apply background-independent renormalization group methods to spin foam quantum gravity. It is aimed at extending and elucidating the analysis of a companion let…
On the volume simplicity constraint in the EPRL spin foam model
Benjamin Bahr, Vadim Belov
We propose a quantum version of the quadratic volume simplicity constraint for the EPRL spin foam model. It relies on a formula for the volume of 4-dimensional polyhedra, depending…
Improved and Perfect Actions in Discrete Gravity
Benjamin Bahr, Bianca Dittrich
We consider the notion of improved and perfect actions within Regge calculus. These actions are constructed in such a way that they - although being defined on a triangulation - re…
Non-convex 4d polytopes in Spin Foam Models
Benjamin Bahr
In this article we consider non-convex polytopes in . The paper consist of two parts: Firstly, we extend the proof of the formula for the volume in terms of…
Properties of the Hamiltonian Renormalisation and its application to quantum mechanics on the circle
Benjamin Bahr, Klaus Liegener
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embeddi…
On background-independent renormalization of spin foam models
Benjamin Bahr
In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the conte…
Perfect discretization of reparametrization invariant path integrals
Benjamin Bahr, Bianca Dittrich, Sebastian Steinhaus
To obtain a well defined path integral one often employs discretizations. In the case of gravity and reparametrization invariant systems, the latter of which we consider here as a…
Hopf link volume simplicity constraints in spin foam models
Mehdi Assanioussi, Benjamin Bahr
In this article we consider specific bivector geometries which arise in the large-spin limit of the extension of the Engle-Pereira-Rovelli-Livine spin foam model for quantum gravit…
Approximating the physical inner product of Loop Quantum Cosmology
Benjamin Bahr, Thomas Thiemann
In this article, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product…
Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
Benjamin Bahr, Giovanni Rabuffo, Sebastian Steinhaus
We study the renormalization group flow of the Euclidean Engle-Pereira-Rovelli-Livine and Freidel-Krasnov (EPRL-FK) spin foam model in the large--limit. The vertex amplitude is…
Entanglement entropy of physical states in hypercuboidally truncated spin foam quantum gravity
Benjamin Bahr
In this article we consider physical states in the hypercuboidal truncation of the EPRL-FK spin foam quantum gravity model. In particular, these states are defined on graphs which…
Automorphisms in Loop Quantum Gravity
Benjamin Bahr, Thomas Thiemann
We investigate a certain distributional extension of the group of spatial diffeomorphisms in Loop Quantum Gravity. This extension, which is given by the automorphisms Aut(P) of the…
Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
Benjamin Bahr, Thomas Thiemann
This is the second paper concerning gauge-invariant coherent states for Loop Quantum Gravity. Here, we deal with the gauge group SU(2), this being a significant complication compar…
Holonomy Spin Foam Models: Definition and Coarse Graining
Benjamin Bahr, Bianca Dittrich, Frank Hellmann +1
We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbi…
A new realization of quantum geometry
Benjamin Bahr, Bianca Dittrich, Marc Geiller
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framew…
The Hot Bang state of massless fermions
Benjamin Bahr
In 2002, a method has been proposed by Buchholz et al. in the context of Local Quantum Physics, to characterize states that are locally in thermodynamic equilibrium. It could be sh…
Towards a Cosmological subsector of Spin Foam Quantum Gravity
Benjamin Bahr, Sebastian Kloser, Giovanni Rabuffo
We examine the four dimensional path integral for Euclidean quantum gravity in the context of the EPRL-FK spin foam model. The state sum is restricted to certain symmetric configur…
(Broken) Gauge Symmetries and Constraints in Regge Calculus
Benjamin Bahr, Bianca Dittrich
We will examine the issue of diffeomorphism symmetry in simplicial models of (quantum) gravity, in particular for Regge calculus. We find that for a solution with curvature there d…
Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
Benjamin Bahr, Sebastian Steinhaus
In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the Spin Foam model by Engle, Pereira, Rovelli, Livine, Freidel…
Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
Benjamin Bahr, Rodolfo Gambini, Jorge Pullin
In this review we discuss the interplay between discretization, constraint implementation, and diffeomorphism symmetry in Loop Quantum Gravity and Spin Foam models. To this end we…
Editorial: Coarse graining in quantum gravity -- Bridging the gap between microscopic models and spacetime physics
Astrid Eichhorn, Benjamin Bahr, Antonio D. Pereira
The Renormalization Group encodes three concepts that could be key to accelerate progress in quantum gravity. First, it provides a micro-macro connection that could connect microsc…
Operator Spin Foams: holonomy formulation and coarse graining
Benjamin Bahr
A dual holonomy version of operator spin foam models is presented, which is particularly adapted to the notion of coarse graining. We discuss how this leads to a natural way of com…
Coarse graining free theories with gauge symmetries: the linearized case
Benjamin Bahr, Bianca Dittrich, Song He
Discretizations of continuum theories often do not preserve the gauge symmetry content. This occurs in particular for diffeomorphism symmetry in general relativity, which leads to…
Numerical evidence for a phase transition in 4d spin foam quantum gravity
Benjamin Bahr, Sebastian Steinhaus
Building on recent advances in defining Wilsonian RG flows, and in particular the notion of scales, for background-independent theories, we present a first investigation of the ren…
Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
Benjamin Bahr, Thomas Thiemann
In this paper we investigate the properties of gauge-invariant coherent states for Loop Quantum Gravity, for the gauge group U(1). This is done by projecting the corresponding comp…
Spin foam models with finite groups
Benjamin Bahr, Bianca Dittrich, James P. Ryan
Spin foam models, loop quantum gravity and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to co…