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Tsvetkov T.D.,Institute for Cryobiology and Food Technologies | Petrov G.,Bulgarian Academy of Science
Bulgarian Journal of Agricultural Science | Year: 2012

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 scalarye) 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, Belous 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.


Petrov G.,Bulgarian Academy of Science | Hadzhy A.,Bulgarian Academy of Science | Tsvetkov T.D.,Institute for Cryobiology and Food Technologies
Bulgarian Journal of Agricultural Science | Year: 2016

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 andfurthermore even it is based on the fine play between the continuity and the discrete too.Following the classical Einstein’s gravitational theory Weyl in 1918 attempt to incorporate electromagnetism into thetheory by gauging the metric tensor i.e.by letting: gμν = exp(-γ∫dxμWμ(x))gμν, where γ was a constant and the vector field Wμ was to be identified with the electromagnetic vector potential.Although this idea was attractive, following Einstein, it was physically untenable because it would imply that the spacing of spectral lines would depend on the history of the emitting atoms, in manifest disagreement with experiment to this time by the quantum understandings of the nature.However, after the advent of Wave Mechanics in 1926, the idea was resurrected by application to other physical situations.This new observation that the usual electromagnetic differential minimal principle was equivalent to the integral minimal principle and that this was the correct version of Weyl’s proposal in which the constant was chosen pure imaginary γ = i/ћ, where ћ is the Planck constant h divided by 2π and the electromagnetic factor was chosen to multiply more the Schrödinger wave functional Ψ*ακ”(φκ’, t) by t ∈ (t-2(n - ½j), t2(n - ½j)], n = 0,1,2,…, j ≤ 2n, understanding mathematical as an operator acting on everyone function which described the relativistic quantum systems considered for simplicity by us only for relativistic scalars particles systems: (Formula presented), where j is the number of the virtual (“potential”) scalar Dirac particles called by us scalarino fulfilled anticommutative relations and occupied the local place localized (micro causality in the Casimir world) by the neighbourhood of the 4-ponts yμ-2(n-½j) in the coordinate Minkowski space-time.Moreover they have a helicity (projection of the spin on the longitudinal direction of the moving) also at the left at the mirror at the rest act the helicity operator on the vacuum state λ|ℓ0> = |-½> and at the right λ|r0> = |½> and the same is for the moved mirror.Between the mirrors is the helicity zero.Further for ϰ → ϰ’ or by localization ϰ, ϰ’→ 0 is defined: ∫Dφακ(Ψφακ(ακ, t-2(n-½j))δ(ακ‘-φακ)Ψ*ακ“(φακ’, t-2(n-½j) + ε½))Dακ‘= 1, for the Dirac δ-functional by definition δ(ακ‘-φακ) = <φακ|ακ‘> and then is (Formula presented).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 better the Whitney’s singularities theory applied on the vacuum and the black holes, also the dark energy and the dark matter from one uniformly point of view.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 in the relativistic theory of quantum wave fields by the contemporary considerations of the quantum vacuum as a ground state of anyone relativistic quantum fields e.g.j = 0 and n →∞.This 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 by Hilbert space 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 of the indefinite functional metrics (Bogolubov at al., 1987).Also the many miracle properties of so defined living cells and fossils apparent enchanting by consideration of hisfunctions yet are putting besides in the molecules but in the fundamental quantum field interactions between the quantum vacuum of anyone quantum fields 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.So also it is possible to be solving the many body problems by our so called Gedanken experiment with hyperbolic turns and reflections for Casimir world defined by two mirrors moving parallel to another i.e.the one can be at the rest and the other move with a constant velocity v.Aside from this, the essential difference is that external forces other than gravity, e.g.such as Casimir force, play a major role in the phenomena, i.e.remember there is not observed in our seeing world a local classical relativistic electromagnetic field potential Aμ(x) caused this force.And also it is possible to describe the fundamental interactions between anyone concrete fundamental relativistic quantum field with anyone other or with the external and innerness material objects as a additional boundary conditions (localizing) by the proving of the fulfilling of the causality conditions and consider they as an external classical fields and everyone internal background fields.At the first in his famous work “To the Electrodynamics of moved bodies”, Leipzig, 1905, Einstein has proved the possibility to understand the nature from the relativistic point of view in the classical physics.Moreover it can be represented the symmetrical selfadjoint field operator Φ taken for simplicity for the relativistic quantum scalar fields by definition obtained as functional virtual (potential) vector valued state in the functional state Hilbert space with indefinite metric.That is the quantum field operator obtained by anyone wave fields solution at the fixed time known as a virtual or “potential” quantum field operator.This is acting on the vector valued functional virtual vacuum 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 and is Lorenz invariant.So we have in this case the vacuum state which has global properties too and also can be understand better by definition in the global Lorenzian geometry for the events points connected in pairs by the seeing time like or may be at least one seeing non space like geodesic line with a length non less as the length of every other non-space like curve.So also it is realizable the possibility to be obtained the local or non-local quantum force currents by the help of the ensembles of the so called virtual current particles e.g.scalars and his scalarino.They interacts minimal local or global by phase integration over the field potential with the field force carrier knowing as the so called virial current (vis via as a quantum point source in three dimensional space or quantum sink in two dimensional space at a given time) i.e.that impact near local or global by interactions at the distance with the classical local neighborhood in the Microsoft matter in the Minkowski space-time.The probability interpretation of the spectral family give us the physical interpretation of the observed quantum invariant entity by the relativistic quantum systems even for the dynamically (not thermodynamically) fine structure of the ground state as potential state also as virtual vector valued functional state, i.e.as the element of the Hilbert functional state space with indefinite metric by the vacuum interactions in the Casimir world.It knows yet the Casimir force today is measured with exactness by 5%.Precisely the impact of this force on the molecular biology (genetics) is still not clear, i.e.there is a new situation of the so called quantum cryobiology.The additional boundary conditions (localization) must be taken under account, e.g.in the cosmogony models it is not possible to consider additional boundary conditions.So also it is possible to understand better the molecules by the molecular biology as a classical object interacting with the ground state of the every one relativistic quantum field.So also by definition it is considered the relevant operator valued functional Banach algebra or in the Schrodinger picture the vacuum wave functional as a solution of the wave equation describing the same relativistic quantum system in the Minkowski space-time or oriented in the time space-time, e.g.the so called global Lorenz geometry.With other words as in the non-relativistic case (Goodwin, 1963), by the help of the so called S-matrix theory in the quantum mechanics where this theory is very gut proved we hope to understand better the nature under consideration in the relativistic sense of the axiomatically S-matrix theory by the relativistic quantum systems in the living cells and the fossils too.So also the Casimir vacuum in the asymptotic past at the left “ℓ” side of the one perfectly conductor plate at the rest contains then from the micro-causal point of view propagation of the virtual particles for the initial observer understanding as referent system (a map).In the asymptotic future at the right “r“side of the same plate and the left side of the second parallel moved perfectly conductor plate towards the plate at the rest with a constant velocity v contains the propagation of some see massive particles for the late-time observer, e.g.the Maxwell demon for the events point bounded with time or non-space like geodesic line.Moreover at the right side of the moved plate anew there is a propagation of the relativistic quantum virtual particles system, e.g.the Maxwell demon for the events point bounded with time or non-space like causal geodesic paths.In mathematical sense it is possible to be defined the topology of Aleksandrov on the everyone space-time (M, g) – also a topology, that can be given in M by the choice of them as base of the topologies of the all sets in the form (Formula presented) - where the non-local events points kxm, k’xm ∈ M are defined in the past and future cone of the space-time.Precisely the mass less relativistic quantum field give us then that his local operators algebras are unitary equivalent in the bounded domains of the locally algebras by the matter field and also they have the same structure properties which is from more great importance for the theory than the definiteness of the metric of the Hilbert or Banach functional vector valued state space.So it is possible to be defined the double singularities which will be given by the ground state of local relativistic quantum system too.The symmetries and structure properties are mathematical described by the Banach algebra of the operators valued field’s defined in the Hilbert functional vector valued state space with indefinite metric.Farther the ground state is defined over the Banach algebra but it can be negative too as remember from the indefinite metric of the Hilbert functional state space.However then there are a number of additional properties generated from the physical distinctions by the massless systems: his scale i.e.the group of the scale transformations represented by the dilatations and special conformal transformations and conformal symmetries also obtained by the group of the conformal transformations give a double singularities of the relativistic quantum systems and the vacuum vector valued state, but scale invariance does not imply necessary a conformal invariance and as well the infrared effects leaded to manifest the global structure of the relativistic quantum systems and the vacuum state.Quantum Field Theory QFT and the Renormierungs groups theory RG-groups are classified by scale invariant, Infrared IR fixed point (Wilson’s philosophy).In the Doctor paper (G.Petrov, 1978) (the Thesis) it is showed by the help of the mathematical generalized Fourier analysis that the scaling behaviors of the some quantum entities are destroyed in longitudinal and conserved in the cross section’s direction by fulfilling the causality condition for non-forward deep inelastic scattering of leptons and hadrons.Also the scale invariance is not from the same nature as the conformal invariance by the massless quantum fields and the scale invariance lead yet not necessarily to the conformal invariance.It is possible to consider in the double cone with Alexandrov topology in the Lorenz manifold of the Casimir world by the help of the mirror reflections and hyperbolical turns between two mirror one at the rest and the second parallel moved with a constant velocity v at the face a domain of the sequence of fixed events points in Minkowski space-time without accumulative point.So in this case it is remarkable to understand the possibility to distinguish the chronology and the causality by the ensemble from assembling and folding surfaces of bounded events points in the space-time for n → ∞ where n is the number of the mirror reflections at the moved mirror.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 Schrodinger 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 (“potential”) generators of dilatations operators. © 2016, National Centre for Agrarian Sciences.All rights reserved.


Tsvetkov T.D.,Institute for Cryobiology and Food Technologies | Petrov G.,Bulgarian Academy of Science
Bulgarian Journal of Agricultural Science | Year: 2013

Since the 1948 the mathematical description of the so-called Casimir world as a part of the physical observed space-time in the relativistic sense is to be considered by the help of the Hamiltonian quantum field's theory and furthermore it is based on the fine play between the continuity and the discrete too while the Casimir force was stated. The axiomatic-physical methods of the local quantum fields theory has given the other possibility then the Lagrange quantum field's theory and rigorously mathematical way to understand the singularities and the black holes, also the dark energy and the dark matter from one uniformly point of view. Then it is possible to describe the fundamental interactions between the anyone concrete fundamental relativistic quantum field system with other someone or with the external and innerness material objects as an external classical fields, material boundaries and everyone internal background. It is also not only a question of mathematical but also philosophical-ideological problem too if it is at stake by nature systems. From the same nature is the problem connected with the "time's arrow". The same understanding must exist by the social scientifically, economical, mathematical and informatics systems. It is groundless this to be renounced or disguised. It is senseless that for the mathematic Scientifics there is not given the Nobel price from pure ideological and historical grounds and there is a price for piece from ideological point of view. However, the living cells are wiser then us. By the living cells as an object of the fundamental cryobiological researches i.e. the metabolisms is minimal and also by the help of the axiomatic-physical methods given by the relativistic quantum fields theory it is possible to be taken in the account the problem of a "time's arrow" at the microscopic level by the contemporary considerations of the quantum vacuum in the Casimir world as a ground state of anyone relativistic quantum system becomes a fixture by the lyophilized elementary living cells. It can be represented by the symmetrical selfaddjoint Hamiltonian operator taken for simplicity by definition of the quantum scalar field's operator Φ defined as potentially virtual entity in the Hilbert functional space with indefinite metric. So also the possibility to be obtained the local or non-local quantum currents the carrier of the force (see virial current) of the near actions of interactions with the classical neighborhood in the Minkowski space-time is realizable. The probability interpretation of his spectral family give us the physical interpretation of the observed quantum entity even for the dynamically (not thermodynamically) fine structure of his ground state as potential state and following this as element of the Hilbert functional space with indefinite metric. By the vacuum interactions in the Casimir world, the Casimir force today is measured with 5 % exactness. The action of this force of the molecular biology today is not clear. It knows the following fact then it is at stake of potentially force with a long-range action at the distance. Also with other words, it is asserted every experiment in this genetics domain without clearness of the role of his actions further in the living cells. That is to be taken very good under account from the point of view of the nanophysics also by distance at 10-9 m. May be he is the cause for non-observation of the so-called Goldstein massless bosons as it is the case by the Coulomb force. For the quantum electrodynamics the Coulomb force can be understand by the help of the carrier of the force the so-called virtual particles. Then it is to be supposed the virtual paths of these quantum entities in the Quantum Electrodynamics QED. In addition, the quantum vacuum state of the QED has virtual quantum fluctuations. Then the Casimir force is to be caused by those vacuum fluctuations. Moreover the Casimir vacuum state of the quantum relativistic scalar field system may be not belonging in the operator definition's domain of the field's operators, but fulfill the additional causal and boundary conditions for the carrier of the interaction force, the virtual fundamental scalar Goldstein mesons particles belonging to the domain structure of the Casimir world. So also the Casimir vacuum in the asymptotic past at the left of the non moved plate for this case from the micro causal point of view contains the virtual particles for the initial observer understanding as referent system (a map) and in the asymptotic future at the right of this plate and the left of the moved plate a few see particles for the late-time observer, e.g. the Maxwell demon, and moreover at the right of the moved plate anew the virtual relativistic quantum particles system.


The physical fundamental equations describing the absorption and emission of light waves by atoms are symmetric with respect to the sign of the time parameter also the principle of the detail equilibrium is in force - that is, there is no directionality of "time's arrow" at the microscopic level of this physical phenomena; it is only at the macroscopic level when following Einstein from the macro causality properties of view the irreversible character of time begins to assert itself in the classical sense of the Minkowski space-time, and then for no other reason than probability in the thermodynamically sense by the understanding of his nature. Following this thought it is to remark that the physical phenomena by the light absorption and emission has a relativistic character also the time parameter is not so gut understanding by definition in Minkowski space without Lorenz transformations between the Lorenz manifold's points of the Lorenz globally geometry whiles the gut understand thermodynamically "time's arrow" as a physical phenomena is non relativistic and the time is absolutely also the Galileo transformation between the Riemann manifold's points is in force. All that is connected with the more fine understanding of the symmetry by transformations of the vector valued functional state as the so called super symmetry as by the time inverse connected with the mutuality principles and the principle of detail equilibrium and so as the charge conjugation. For the light propagation in the vacuum at the microscopically level the geometrical understanding of this manifolds is practical from one and the same nature described by local quantum wave fields which was understanding physically very gut as phenomena but not so gut from the so called pure mathematic point of view. Furthermore following the quantum character of the causality properties of the observed physical quantum entities it is clear that the application of the usual mathematic analysis is not more sufficiently to describe this by the help of the fundamental equations. The generalized functions and more special the tempered distributions make possibly the understanding of the nature by those physical phenomena from the mathematical point of view too, e.g.without to consider the set of the zero measures i.e. by Lebesgue's integrations. The entity of the distributions consist in them that by dropping the knowledge of the function which define the Lebesgue's zero measure it is possibly to define wide class of generalized functions, included different Dirac δ-functions and his derivations.


Tsvetkov T.D.,Institute for Cryobiology and Food Technologies | Petrov G.,Bulgarian Academy of Science
Bulgarian Journal of Agricultural Science | Year: 2014

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.,). © 2014, National Centre for Agrarian Sciences. All rights reserved.

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