Geodesic
Relativistically Covariant Quantum Field Theory of the Maslov Complex Germ
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 3, pp. 492-512 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider an explicitly covariant formulation of the quantum field theory of the Maslov complex germ (semiclassical field theory) in the example of a scalar field. The main object in the theory is the – semiclassical bundle – whose base is the set of classical states and whose fibers are the spaces of states of the quantum theory in an external field. The respective semiclassical states occurring in the Maslov complex germ theory at a point and in the theory of Lagrangian manifolds with a complex germ are represented by points and surfaces in the “semiclassical bundle” space. We formulate semiclassical analogues of quantum field theory axioms and establish a relation between the covariant semiclassical theory and both the Hamiltonian formulation previously constructed and the axiomatic field theory constructions Schwinger sources, the Bogoliubov $S$-matrix, and the Lehmann–Symanzik–Zimmermann $R$-functions. We propose a new covariant formulation of classical field theory and a scheme of semiclassical quantization of fields that does not involve a postulated replacement of Poisson brackets with commutators.
Keywords: Maslov complex germ, axiomatic quantum field theory, Bogoliubov S-matrix, Lehmann–Symanzik–Zimmermann approach, theory of Schwinger sources, Pierls brackets. 
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     title = {Relativistically {Covariant} {Quantum} {Field} {Theory} of the {Maslov} {Complex} {Germ}},
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O. Yu. Shvedov. Relativistically Covariant Quantum Field Theory of the Maslov Complex Germ. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 3, pp. 492-512. http://geodesic.mathdoc.fr/item/TMF_2005_144_3_a4/

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