Hamiltonian Renormalisation IV. Renormalisation Flow of D+1 dimensional free scalar fields and Rotation Invariance

Abstract

In this article we extend the test of Hamiltonian Renormalisation proposed in this series of articles to the D-dimensional case using a massive free scalar field. The concepts we introduce are explicitly computed for the D=2 case but transfer immediately to higher dimensions. In this article we define and verify a criterion that monitors, at finite resolution defined by a cubic lattice, whether the flow approaches a rotationally invariant fixed point.

28 pages

References in corpus (4)

• Cosmological Coherent State Expectation Values in LQG I. Isotropic Kinematics
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Hamiltonian Renormalization III. Renormalisation Flow of 1+1 dimensional free scalar fields: Properties
• Hamiltonian Renormalisation II. Renormalisation Flow of 1+1 dimensional free scalar fields: Derivation

Cited by in corpus (10)

• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Hamiltonian Renormalization III. Renormalisation Flow of 1+1 dimensional free scalar fields: Properties
• Hamiltonian Renormalisation II. Renormalisation Flow of 1+1 dimensional free scalar fields: Derivation
• Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity
• Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology
• Hamiltonian Renormalisation V: Free Vector Bosons
• Expectation values of Coherent States for $\mathrm{SU}(2)$ Lattice Gauge Theories
• Properties of the Hamiltonian Renormalisation and its application to quantum mechanics on the circle
• On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC