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

Ts. D. Tsvetkov, G. Petrov

Abstract: By the living cells and organisms as an object of the fundamental cryobiological researches i.e. in this case the metabolisms is minimal and fossils e.g. the mystery by the mammoth baby Lyuba it is possible to be taken in the account the problem of a “time’s arrow” at the microscopic level by the help of the axiomatic-physical methods by the relativistic theory of quantum fields systems by the contemporary considerations of the quantum vacuum as a ground state of anyone relativistic quantum fields system. It can be defined by anyone field operator algebra becomes a fixture by the lyophilized elementary living cells

and fossils. So the possibility to understand the geometrical quantum functional theory of the indefinite metric for the further considerations i.e. in this case we consider only relativistic quantum system and the word elementary understands a one structure idealization of the living cells and fossils is to be used the Hilbert functional methods for the indefinite functional metrics (Bogolubov et al.,). Also the many miracle properties of so defined living cells and fossils apparent enchanting by consideration of his functions yet are putting besides in the molecules but in the fundamental quantum field interactions between the quantum vacuum of anyone quantum fields system in the Microsoft matter and the molecules but taken in the Minkowski space-time or in the flat space-time defined by so called oriented in the time global Lorenzian geometry too. Moreover it can be represented the symmetrical selfadjoint Hamiltonian operator Φ taken by as for simplicity for the relativistic quantum scalar fields by definition obtained as virtual (potential) element in the Hilbert functional space with indefinite metric. That is the quantum field operator obtained by everyone wave fields solution at the fixed time known as a virtual or “potential” quantum field operator. This is acting on the virtual vacuum vector valued functional states as a local entities of the Hilbert functional space with indefinite metric, e.g. the Minkowski space-time has a indefinite quadrate of the interval between events points. Furthermore the Hilbert functional space understands by means of the space of the test functions from his completion by

anyone norm 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 field operators defined in the Hilbert functional space with indefinite metric. Then so one 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 out of the Hilbert functional spaces with indefinite metric. Furthermore the vacuum state in the Schrödinger picture defined over this algebra can be negative too as remembering of the indefinite metric but that is only a one algebraic problem. It can be shown that, on scaling-invariant time like paths of the virtual quantum particles, there is a redeﬁnition of the dilatation current by the virial current that leads to virtual generators of dilatations operators.

and fossils. So the possibility to understand the geometrical quantum functional theory of the indefinite metric for the further considerations i.e. in this case we consider only relativistic quantum system and the word elementary understands a one structure idealization of the living cells and fossils is to be used the Hilbert functional methods for the indefinite functional metrics (Bogolubov et al.,). Also the many miracle properties of so defined living cells and fossils apparent enchanting by consideration of his functions yet are putting besides in the molecules but in the fundamental quantum field interactions between the quantum vacuum of anyone quantum fields system in the Microsoft matter and the molecules but taken in the Minkowski space-time or in the flat space-time defined by so called oriented in the time global Lorenzian geometry too. Moreover it can be represented the symmetrical selfadjoint Hamiltonian operator Φ taken by as for simplicity for the relativistic quantum scalar fields by definition obtained as virtual (potential) element in the Hilbert functional space with indefinite metric. That is the quantum field operator obtained by everyone wave fields solution at the fixed time known as a virtual or “potential” quantum field operator. This is acting on the virtual vacuum vector valued functional states as a local entities of the Hilbert functional space with indefinite metric, e.g. the Minkowski space-time has a indefinite quadrate of the interval between events points. Furthermore the Hilbert functional space understands by means of the space of the test functions from his completion by

anyone norm 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 field operators defined in the Hilbert functional space with indefinite metric. Then so one 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 out of the Hilbert functional spaces with indefinite metric. Furthermore the vacuum state in the Schrödinger picture defined over this algebra can be negative too as remembering of the indefinite metric but that is only a one algebraic problem. It can be shown that, on scaling-invariant time like paths of the virtual quantum 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: 2017-10-11

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