Precanonical quantization of Yang-Mills fields and the functional Schrödinger representation

Kanatchikov, Igor V.

doi:10.1016/s0034-4877(04)90011-0

Cited by 30 publications

(64 citation statements)

References 27 publications

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“…This 21 property can be considered as a consistency test of three different aspects of precanonical quantization playing together: the precanonical representation of quantum operators in terms of Clifford-valued operators, the precanonical Schrödinger equation in (25), and the scalar product for the calculation of expectation values of operators using the Clifford-valued precanonical wave functions in (34).…”

Section: Discussionmentioning

confidence: 99%

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Ehrenfest Theorem in Precanonical Quantization

Kanatchikov

2015

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Abstract.We discuss the precanonical quantization of fields which is based on the De Donder-Weyl (DW) Hamiltonian formulation and treats the space and time variables on an equal footing. Classical field equations in DW Hamiltonian form are derived as the equations for the expectation values of precanonical quantum operators. This field-theoretic generalization of the Ehrenfest theorem demonstrates the consistency of three aspects of precanonical field quantization: (i) the precanonical representation of operators in terms of the Clifford (Dirac) algebra valued partial differential operators, (ii) the Dirac-like precanonical generalization of the Schrödinger equation without the distinguished time dimension, and (iii) the definition of the scalar product for calculation of expectation values of operators using the precanonical wave functions.

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Section: Discussionmentioning

confidence: 99%

“…Precanonical quantization of YM theory, its connection with the functional Schrödinger representation, and a potential application to the mass gap problem have been discussed earlier in [21].…”

Section: Ehrenfest Theorem In Pure Yang-mills Theorymentioning

confidence: 99%

Ehrenfest Theorem in Precanonical Quantization

Kanatchikov

2015

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“…In such cases, one can define G abµν and its inverse G abµν by introducing a gauge fixing term or by using other tricks [8,28,29].…”

Section: Generalizationsmentioning

confidence: 99%

Covariant canonical quantization of fields and Bohmian mechanics

Nikolić

2005

Eur. Phys. J. C

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We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space and time arguments of fields are treated on an equal footing. To achieve both covariance and consistency with standard noncovariant canonical quantization of fields in Minkowski spacetime, it is necessary to adopt a covariant Bohmian formulation of quantum field theory. A preferred foliation of spacetime emerges dynamically owing to a purely quantum effect. The application to a simple time-reparametrization invariant system and quantum gravity is discussed and compared with the conventional noncovariant WheelerDeWitt approach.

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“…As a consequence, the theories which are regular from the point of view of the DW formalism can be irregular from the point of view of the standard Hamiltonian formalism and vice versa. This work is motivated by the project of manifestly space-time symmetric precanonical quantization of field theory [8][9][10][11] based on the DW Hamiltonian formalism, which requires a well understood formalism for degenerate theories on the classical level.…”

Section: Introductionmentioning

confidence: 99%