9 papers
Geometric (pre)quantization in the polysymplectic approach to field theory
I. V. Kanatchikov
The prequantization map for a Poisson-Gerstenhaber algebra of dynamical variables represented by differential forms within the polysymplectic formulation of the De Donder--Weyl cov…
Covariant Geometric Prequantization of Fields
I. V. Kanatchikov
A geometric prequantization formula for the Poisson-Gerstenhaber bracket of forms found within the DeDonder-Weyl Hamiltonian formalism earlier is presented. The related aspects of…
Quantization of Gravity: Yet Another Way
I. V. Kanatchikov
Recently proposed quantization in field theory based on an analogue of Hamiltonian formulation which treats space and time on equal footing (the so-called De Donder-Weyl theory) is…
Towards a "pre-canonical" quantization of gravity without the space+time decomposition
I. V. Kanatchikov
Quantization of gravity is discussed in the context of field quantization based on an analogue of canonical formalism (the De Donder-Weyl canonical theory) which does not require t…
From the DeDonder-Weyl Hamiltonian formalism to quantization of Gravity
I. V. Kanatchikov
An approach to quantization of fields and gravity based on the De Donder-Weyl covariant Hamiltonian formalism is outlined. It leads to a hypercomplex extension of quantum mechanics…
Towards the Born-Weyl Quantization of Fields
Igor V. Kanatchikov
Elements of the quantization in field theory based on the covariant polymomentum Hamiltonian formalism (the De Donder-Weyl theory), a possibility of which was originally discussed…