Towards the fundamental spectrum of the Quantum Yang-Mills Theory

Abstract

In this work we focus on the quantum Einstein-Yang-Mills sector quantised by the methods of Loop Quantum Gravity (LQG). We point out the improved UV behaviour of the coupled system as compared to pure quantum Yang-Mills theory on a fixed, classical background spacetime as was considered in a seminal work by Kogut and Susskind. Furthermore, we develop a calculational scheme by which the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed in principle and by which one can make contact to the Wilsonian renormalization group, possibly purely within the Hamiltonian framework. Finally, we comment on the relation of the fundamental spectrum to that of pure Yang-Mills theory on a (flat) classical spacetime.

51 pages

References in corpus (7)

• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Gravity quantized
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Spectral Analysis of the Volume Operator in Loop Quantum Gravity
• Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
• Quantum Field Theory: Where We Are
• Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries

Cited by in corpus (5)

• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Hamiltonian Renormalisation IV. Renormalisation Flow of D+1 dimensional free scalar fields and Rotation Invariance
• Hamiltonian Renormalisation V: Free Vector Bosons
• Quantum reduced loop gravity: extension to gauge vector field