SCALING WITHOUT CONFORMAL INVARIANTS AND THE CAUSALITY IN THE NON-LOCAL RELATIVISTIC QUANTUM SYSTEMS IN LIVING CELLS

G. Petrov, Ts. Tsvetkov

Abstract: Since the 1948 the mathematical description of the so-called Casimir world as a part of the physical observed space-time i.e. oriented in the relativistic sense in the time is to be considered by the help of the Hamiltonian quantum field’s theory and furthermore even it is based on the fine play between the continuity and the discrete too. The axiomatic-physical methods of the local quantum fields theory has given us the other possibility than the Lagrange quantum field’s theory and precisely on this rigorously mathematical way to understand the singularities theory of the zero point energy and the black holes, also the dark energy and the dark matter from one uniformly point of view. Furthermore by means of the space of the test functions from his completion by anyone norm the Hilbert functional space understands the possibility of the definition of the Casimir quantum vacuum state as well a ground state of the relativistic quantum field system in the Schrödinger picture over the involutes Banach algebra of the operators valued fields defined in the Hilbert functional state space with indefinite metric. Then so one virtual (“potential”) functional vector valued vacuum state can be negative as remember of the indefinite metric by definition but this is not from anyone significance for the theory. This question precisely spoken is a pure algebraically formulations of anyone relativistic quantum systems in the Hilbert functional state spaces with indefinite metric.
It can be shown that, on scaling-invariant time like or causally non space like paths of the virtual quantum point or sink sources, e.g. current particles, there is a redefinition of the dilatation current by the virial current that leads to virtual generators of dilatations operators.

Keywords: Casimir effect; causal and scaling principle; fossils; living cells; lyophilization; times arrow

Date published: 2017-09-20