# QuantiZing the Foliation in History Generalized Quantum Field Theory of Living Cells

Tsv. D. TSVETKOV, G. PETROV and P. TSVETKOVA

*Institute of Cryobiology and Food Technologies, BG - 1407 Sofia, Bulgaria*

### Abstract

TSVETKOV, Tsv. D., G. PETROV and P. TSVETKOVA, 2008. Quantizing the Foliation in Biological-time Generalized Quantum Field Theory of Leaving Cells. *Bulg. J. Agric. Sci*., 14: 523-527

From the recent consideration of the temporal organization of the leaving cells to discussing the quantization of the foliation in a causality form of generalized quantum field theory, we show how the discussion in (Tsvetkov et al.) of a history arrow version of free, generalized scalar field theory can be augmented in such way as to include the quantization of the non local generalized quantum field, the time-like vector kx^{µ} = |kx|l^{µ} that determines a Lorentzian foliation of Minkowski space-time in the non local sense. It is employed a Hilbert bundle construction for the energy impulse tensor of the vacuum state of the generalized scalar quantum field that is motivated by: 1) discussing the role of the special conform group in the limit of the free massles scalar field on the light cone in the existing temporal organization of the living cells as a local coordinate system (chart) considered at a view of the generalized scalar quantum field theory (Tsvetkov et al., 2004 - 2008); and 2) considering a specific representation of extended history algebra in the sense of the causality group following from the Zeeman’s theorem by the consideration of the energy impulse tensor of the vacuum state in the foliated Minkowski space-time obtained from the multi-symplectic representation of the non local generalized scalar field theory.

*Key words*: causality condition, temporal organization of leaving cells, history time arrow algebra, special conform group, scalar quantum field on the light cone

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