RT Journal Article
T1 Poisson brackets in Sobolev spaces: a mock holonomy-flux algebra
A1 Barbero G., J. Fernando
A1 Basquens, Marc
A1 Díaz Jiménez, Bogar
A1 Sánchez Villaseñor, Eduardo Jesús
AB The purpose of this paper is to discuss a number of issues that crop up in the computation of Poisson brackets in field theories. This is specially important for the canonical approaches to quantization and, in particular, for loop quantum gravity. We illustrate the main points by working out several examples. Due attention is paid to relevant analytic issues that are unavoidable in order to properly understand how computations should be carried out. Although the functional spaces that we use throughout the paper will likely have to be modified in order to deal with specific physical theories such as general relativity, many of the points that we will raise will also be relevant in that context. The specific example of the mock holonomy-flux algebra will be considered in some detail and used to draw some conclusions regarding the loop quantum gravity formalism.
PB IOP Publising
SN 0031-8949
YR 2022
FD 2022-10-31
LK http://hdl.handle.net/10016/36119
UL http://hdl.handle.net/10016/36119
LA eng
NO This work has been supported by the grant PID2020-116567GB-C22 funded byMCIN/AEI/10.13039/ 501100011033. E J S Villaseñor is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors(EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). Bogar Díaz acknowledges support from the CONEX-Plus programme funded by Universidad Carlos III de Madrid and the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 801538.
DS e-Archivo
RD 30 abr. 2024