On quasi-free dynamics on the resolvent algebra

The resolvent algebra is a new C*-algebra of the canonical commutation relations of a boson field given by Buchholz-Grundling. We study analytic properties of quasi-free dynamics on the resolvent algebra. Subsequently we consider a supersymmetric quasi-free dynamics on the graded C*-algebra made of a Clifford (fermion) algebra and a resolvent (boson) algebra. We establish an infinitesimal supersymmetry formula upon the GNS Hilbert space for any regular state satisfying some mild requirement which is standard in quantum field theory. We assert that the supersymmetric dynamics is given as a C*-dynamics.Comment: This paper has been withdrawn by the author due to its being based on some unjustified assumptions. Also there are mathematically incorrect arguments that stem from the assumption

A Dip after the Early Emission of Super-Luminous Supernovae: A Signature of Shock Breakout within Dense Circumstellar Media

The origin of super-luminous supernovae (SLSNe), especially the source of their huge luminosities, has not been clarified yet. While a strong interaction between SN ejecta and dense circumstellar media (CSM) is a leading scenario, alternative models have been proposed. In this Letter, we suggest new diagnostics to discriminate the strong SN-CSM interaction scenario from the others: a decline in the luminosity ('dip') before the main peak of the light curve. This dip is an unavoidable consequence of having a dense CSM within which the shock breakout occurs. If a dense CSM shell is located far at large radii from the progenitor inside, it takes time for the SN ejecta to reach it and the early light curve can be powered by the SN ejecta before the collision. Once the SN ejecta collides with the dense CSM, the electron density and thus the Thomson scattering opacity suddenly increase. Photons become unable to go out of the shock even if there is a source of emission inside, which results in the dip in the light curve. This dip is a solid prediction from the strong interaction scenario irrespective of a power source for the early emission. Eventually the forward shock breaks out from within the dense CSM, and the luminosity increases by the continuous strong SN-CSM interaction, resulting in an SLSN. The possible dip observed in the hydrogen-poor SLSN, 2006oz, could be the first example of this signature and give support to the SN-CSM interaction as the power source of SLSN 2006oz.Comment: 5 pages, 1 figure, 1 table, accepted by The Astrophysical Journal Letter

Markov property and strong additivity of von Neumann entropy for graded quantum systems

It is easy to verify the equivalence of the quantum Markov property and the strong additivity of entropy for graded quantum systems as well. However, the structure of Markov states for graded systems is different from that for tensor product systems. For three-composed graded systems there are U(1)-gauge invariant Markov states whose restriction to the pair of marginal subsystems is non-separable.Comment: 14 pages, to appear J. Math. Phy