Bondi-Metzner-Sachs (BMS) symmetries have been attracting a great deal of interest in recent years. Originally discovered as being the symmetries of asymptotically flat spacetime geometries at null infinity in general relativity, BMS symmetries have also been shown to exist for free field theories over Minkowski spacetime. In wanting to better understand their status and the underlying reasons for their existence, this work proposes a general rationale toward identifying all possible global symmetries of a free field theory over Minkowski spacetime, by allowing the corresponding conserved generators not to be necessarily spatially local in phase space. As a preliminary toward a separate study of the role of asymptotic states for BMS symmetries in an unbounded Minkowski spacetime, the present discussion focuses first onto a 2 + 1 dimensional free scalar field theory in a bounded spatial domain with the topology of a disk and an arbitrary radial Robin boundary condition. The complete set of global symmetries of that system, most of which are dynamical symmetries but include as well those generated by the local total energy and angular-momentum of the field, is thereby identified.
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September 2019
Research Article|
September 10 2019
Nonlocal global symmetries of a free scalar field in a bounded spatial domain
Daddy Balondo Iyela
;
Daddy Balondo Iyela
a)
1
Département de Physique, Université de Kinshasa (UNIKIN)
, B.P. 190 Kinshasa XI, Democratic Republic of Congo
2
Centre for Cosmology, Particle Physics and Phenomenology (CP3), Institut de Recherche en Mathématique et Physique (IRMP), Université catholique de Louvain (UCLouvain)
, 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium
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Jan Govaerts
Jan Govaerts
b)
2
Centre for Cosmology, Particle Physics and Phenomenology (CP3), Institut de Recherche en Mathématique et Physique (IRMP), Université catholique de Louvain (UCLouvain)
, 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium
3
International Chair in Mathematical Physics and Applications (ICMPA–UNESCO Chair), University of Abomey-Calavi
, 072 B.P. 50 Cotonou, Republic of Benin
4
Fellow of the Stellenbosch Institute for Advanced Study (STIAS)
, Stellenbosch, Republic of South Africa
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Daddy Balondo Iyela
1,2,a)
Jan Govaerts
2,3,4,b)
1
Département de Physique, Université de Kinshasa (UNIKIN)
, B.P. 190 Kinshasa XI, Democratic Republic of Congo
2
Centre for Cosmology, Particle Physics and Phenomenology (CP3), Institut de Recherche en Mathématique et Physique (IRMP), Université catholique de Louvain (UCLouvain)
, 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium
3
International Chair in Mathematical Physics and Applications (ICMPA–UNESCO Chair), University of Abomey-Calavi
, 072 B.P. 50 Cotonou, Republic of Benin
4
Fellow of the Stellenbosch Institute for Advanced Study (STIAS)
, Stellenbosch, Republic of South Africa
a)
E-mail: [email protected]
b)
E-mail: [email protected]
J. Math. Phys. 60, 092302 (2019)
Article history
Received:
June 17 2019
Accepted:
August 22 2019
Citation
Daddy Balondo Iyela, Jan Govaerts; Nonlocal global symmetries of a free scalar field in a bounded spatial domain. J. Math. Phys. 1 September 2019; 60 (9): 092302. https://doi.org/10.1063/1.5115308
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