skip to main content

SciTech ConnectSciTech Connect

Title: A first look at Weyl anomalies in shape dynamics

One of the more popular objections towards shape dynamics is the suspicion that anomalies in the spatial Weyl symmetry will arise upon quantization. The purpose of this short paper is to establish the tools required for an investigation of the sort of anomalies that can possibly arise. The first step is to adapt to our setting Barnich and Henneaux's formulation of gauge cohomology in the Hamiltonian setting, which serve to decompose the anomaly into a spatial component and time component. The spatial part of the anomaly, i.e., the anomaly in the symmetry algebra itself ([Ω, Ω] ∝ ℏ instead of vanishing) is given by a projection of the second ghost cohomology of the Hamiltonian BRST differential associated to Ω, modulo spatial derivatives. The temporal part, [Ω, H] ∝ ℏ is given by a different projection of the first ghost cohomology and an extra piece arising from a solution to a functional differential equation. Assuming locality of the gauge cohomology groups involved, this part is always local. Assuming locality for the gauge cohomology groups, using Barnich and Henneaux's results, the classification of Weyl cohomology for higher ghost numbers performed by Boulanger, and following the descent equations, we find a complete characterizationsmore » of anomalies in 3+1 dimensions. The spatial part of the anomaly and the first component of the temporal anomaly are always local given these assumptions even in shape dynamics. The part emerging from the solution of the functional differential equations explicitly involves the shape dynamics Hamiltonian, and thus might be non-local. If one restricts this extra piece of the temporal anomaly to be also local, then overall no Weyl anomalies, either temporal or spatial, emerge in the 3+1 case.« less
Authors:
 [1]
  1. Department of Physics, University of California, Davis, California 95616 (United States)
Publication Date:
OSTI Identifier:
22251818
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 11; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; DIFFERENTIAL EQUATIONS; HAMILTONIANS; LOCALITY; MATHEMATICAL SOLUTIONS; QUANTIZATION; SYMMETRY