Ts. D. TSVETKOV^{1} and G. PETROV^{2}

^{1} *Institute for Cryobiology and Food Technologies, BG - 1111 Sofia, Bulgaria*

^{2} *Institute for Nuclear Researches and Nuclear Energy, BG – 1113 Sofia, Bulgaria*

TSVETKOV, Ts. D. and G. PETROV, 2012. The scalar particles in Casimir vacuum state of the relativistic quantum field system in living cells. *Bulg. J. Agric. Sci., *18: 819-826

The mathematical description of the Casimir world is based on the fine play between the continuity and the discrete. The discrete is more remarkable than the continuity things in this case as any one wave quantum field Casimir vacuum state defined on the involutes algebraic entities so that the quantum wave functional, i.e. the ground state, is non positive as remembers of the Hilbert space with indefinite metric and can be consider as a solution of the Schrödinger functional equation with impulse effect. The discrete things can be singularities, bifurcations and destroyed scaling behavior of the relativistic scalar quantum field system and his Casimir ground state in living cells as global properties of the quantum vacuum state interacting with external classical field modelled in our case by boundary conditions. The classical field theory is a theory of the continuity also describes the principle of the shot-range interaction in the nature. The twenty century has given the quantum field

theory that is the theory of the discrete world of the quantum entities. The global effects from the quantum field theory by the interactions of the elementary particle are the studying of the phenomenon of structure of the elementary particle hadrons by deep inelastic scattering and a vacuums structure of every one quantum field system, e g. the relativistic quantum field and his vacuum state with a given boundary conditions.

The question above the possibility to find the complicate phenomenon connected with the existence of the life and the living systems his place in the mathematical frame by the intersection between the classical and the quantum describing of the world of any one concrete quantum field theory by the contemporary ground state of the theoretical biological and nanophysics problems is open by the consideration of high topographical complementarities by the London- and Casimir forces involved importantly in the highly specific and strong but purely classical physical thermodynamically and quantum physically complexity of elementary living cells by enzymes with substrates, of antigens with antibodies, etc.

The theory of the “super transportation” based on the “Einstein condensation” of the bosons particles are given strong mathematical by N.N. Bogolubov in 1946 and has been defined a quasiparticles as excitations in a so-called collective state as a superposition between an excited particles state and the ground state of the quantum system.

By the consideration of the living cells, it is necessary to consider the quantum field concepts by Casimir vacuum state in observation scalars (here called as Pterophillum scalarе) of the sea relativistic quantum scalar field system.

From the new results by the contributions of the environmental freezing-drying and vacuum sublimation (Zwetkow 1985; Tsvetkov, Belоus 1986, Tsvetkov et al. 1989, Tsvetkov et al. 2004 – 2012) is hopped that by the significant form expressed e.g. by the scaling behaviours of the invariant entities by the energy impulse tensor described the elementary living cells and systems will be possibly to describe the biological expressions at the standpoint of the nanophysics by means the behaviour of the concrete relativistic quantum field system, e.g. sea virtual quantum scalars in the physical Casimir vacuum with a boundary conditions on every one surface S too. At the molecular level (Mitter and Robaschik, 1999) the thermodynamics behaviour is considered by quantum electromagnetic field system with additional boundaries as by the Casimir effect between the two parallel, perfectly conducting square plates (side L, distance d, L > d), embedded in a large cube (side L) with one of the plates at face. For further considerations we can suppose that the demon of Maxwell slide the moved plate with a constant velocity v and counted the seeing scalars for j = 0, …, 2n, where j is the number of the scalars with the minimum energy equal to the energy of the “zero fluctuations” levels by the hyperbolical rotation and reflection of the fixed 4-point y0 μ from Minkowski space between the plates from the demon of Maxwell counted.