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Register a new userThe global existence of small self-interacting scalar field propagating in the contracting universe
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We present a condition on the self-interaction term that guaranties the existence of the global in time solution of the Cauchy problem for the semilinear Klein-Gordon equation in the Friedmann-Lama$hat{i}$tre-Robertson-Walker model of the contracting universe. For the Klein-Gordon equation with the Higgs potential we give a lower estimate for the lifespan of solution.
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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 towards 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 since fields and their conjugate momenta are intrinsically spatially non local physical entities. As a preliminary towards 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.
This paper deals with the study of the two-dimensional Dirac operatorwith infinite mass boundary condition in a sector. We investigate the question ofself-adjointness depending on the aperture of the sector: when the sector is convexit is self-adjoint on a usual Sobolev space whereas when the sector is non-convexit has a family of self-adjoint extensions parametrized by a complex number of theunit circle. As a byproduct of this analysis we are able to give self-adjointnessresults on polygones. We also discuss the question of distinguished self-adjointextensions and study basic spectral properties of the operator in the sector.
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