arXiv subjects

Roberto Tanzi

Publications and source records attributed to Roberto Tanzi.

4 recordsLinked to original sources

arXiv2021

Hamiltonian study of the asymptotic symmetries of gauge theories

Asymptotic symmetries are a general and important feature of theories with long-ranging fields, such as gravity, electromagnetism, and Yang-Mills. They appear in the formalism once the analytic behaviour of fields near infinity is specified and have received a renewed interest in the last years after a possible connection with the information-loss paradox has been conjectured. One of the various methods used to study the asymptotic symmetries of field theories relies on the Hamiltonian formalism and was introduced in the seminal work of Henneaux and Troessaert, who successfully applied it to the case of gravity and electrodynamics. The main advantage of this approach is that the study of the asymptotic symmetries ensues from clear-cut first principles. After an extensive review of how the Hamiltonian approach to study asymptotic symmetries of gauge theories works, we apply these methods to two specific situations of physical interest. First, we deal with the non-abelian Yang-Mills case and we show that the above principles lead to trivial asymptotic symmetries (nothing else than the Poincaré group) and, as a consequence, to a vanishing total colour charge. This is a new and somewhat unexpected result. It implies that no globally colour-charged states exist in classical non-abelian Yang-Mills theory. The second situation considered is a scalar field minimally-coupled to an abelian gauge field, which can be used to study, at the same time, two specific cases: scalar electrodynamics and the abelian Higgs model. We show that the situation in scalar electrodynamics amply depends on whether the scalar field is massive or massless, insofar as, in the latter case, one cannot canonically implement asymptotic symmetries. Furthermore, we illustrate that, in the abelian Higgs model, the asymptotic canonical symmetries reduce to the Poincaré group in an unproblematic fashion.

hep-th↗

arXiv2021

Asymptotic symmetries of scalar electrodynamics and of the abelian Higgs model in Hamiltonian formulation

We investigate the asymptotic symmetry group of a scalar field minimally-coupled to an abelian gauge field using the Hamiltonian formulation. This extends previous work by Henneaux and Troessaert on the pure electromagnetic case. We deal with minimally coupled massive and massless scalar fields and find that they behave differently insofar as the latter do not allow for canonically implemented asymptotic boost symmetries. We also consider the abelian Higgs model and show that its asymptotic canonical symmetries reduce to the Poincaré group in an unproblematic fashion.

hep-th↗

arXiv2020

Asymptotic symmetries of Yang-Mills fields in Hamiltonian formulation

We investigate the asymptotic symmetry group of the free SU(N)-Yang-Mills theory using the Hamiltonian formalism. We closely follow the strategy of Henneaux and Troessaert who successfully applied the Hamiltonian formalism to the case of gravity and electrodynamics, thereby deriving the respective asymptotic symmetry groups of these theories from clear-cut first principles. These principles include the minimal assumptions that are necessary to ensure the existence of Hamiltonian structures (phase space, symplectic form, differentiable Hamiltonian) and, in case of Poincaré invariant theories, a canonical action of the Poincaré group. In the first part of the paper we show how these requirements can be met in the non-abelian SU(N)-Yang-Mills case by imposing suitable fall-off and parity conditions on the fields. We observe that these conditions admit neither non-trivial asymptotic symmetries nor non-zero global charges. In the second part of the paper we discuss possible gradual relaxations of these conditions by following the same strategy that Henneaux and Troessaert had employed to remedy a similar situation in the electromagnetic case. Contrary to our expectation and the findings of Henneaux and Troessaert for the abelian case, there seems to be no relaxation that meets the requirements of a Hamiltonian formalism and allows for non-trivial asymptotic symmetries and charges. Non-trivial asymptotic symmetries and charges are only possible if either the Poincaré group fails to act canonically or if the formal expression for the symplectic form diverges, i.e. the form does not exist. This seems to hint at a kind of colour-confinement built into the classical Hamiltonian formulation of non-abelian gauge theories.

hep-th↗

arXiv2020

Gravitational effects in birefringent quantum electrodynamics

The most general classical electrodynamics which still respect the linear superposition principle but allow for otherwise arbitrary birefringence require, and imply, a refined spacetime geometry described by a fourth-rank tensor field. Canonical gravitational dynamics for this geometry, if required to co-evolve in causally consistent fashion with the electromagnetic field, were shown to be constructively determined by gravitational closure of the birefringent electromagnetic field equations. For weak gravitational fields of the resulting birefringent refinement of classical Einstein-Maxwell theory, we show in this article that the corresponding quantum electrodynamics is locally renormalizable at every loop order in gauge-invariant fashion and then employ this result to compute various fundamental processes. Combining quantum field theoretic results in locally essentially flat regions with the global spacetime structure predicted by the refined gravitational dynamics, we find that the anomalous magnetic moment of the electron, the cross sections of Bhabha scattering, and the hyperfine splitting of the hydrogen all pick up a dependence on position in the gravitational field. Particularly the measurement of the hyperfine line of hydrogen, but quite generally the measurement of any local quantum electrodynamical process, is thus able to inform the search for vacuum birefringence and its effects in a new way, since the gravitational theory allows to predict where the effects will be most pronounced.

hep-ph↗