AG Mathematische Physik, Leonardo Sangaletti (Leipzig): An L4 quantum energy inequality in the thermal sector

Leonardo Sangaletti (Leipzig)

An L4 quantum energy inequality in the thermal sector

Abstract:
Energy density and its positivity properties represent a fundamental
subject in classical and quantum physics. In this talk, we will
investigate this topic in the thermal representation of a free massive
quantum scalar field. After a brief review of the fundamental
mathematical tools at the base of this work, we will construct the GNS
representation of our QFT induced by a state at thermal equilibrium
(KMS). Therein, we will identify the generator of the time evolution and
its spatial density. The symmetry between the particles and holes
makes evident the impossibility for a lower bound of the expectation
value of the energy density in this representation. In order to tackle
this problem, we will investigate and extend some results of modular
theory and non-commutative Lp spaces. In this way, we obtain a general
result concerning the expectation value of an operator affiliated to a
von Neumann algebra. Finally, the proven results are used to derive an
L4 state dependent non-trivial QEI.