EU2 - Quantum Fields |
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Speaker |
Kanatchikov, Igor |
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| Talk Title |
Ehrenfest theorem in precanonical quantization of fields and gravity. |
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Abstract |
We outline the main conceptual and technical ingredients of the precanonical quantization of fields, which is based on the De Donder-Weyl (polysymplectic) Hamiltonian formulation in classical field theory. This approach does not distinguish space and time variables and it describes fields in terms of the wave functions on the finite dimensional space of field variables and space-time variables. We show that the standard functional Schroedinger representation in QFT can be viewed as a limiting case of precanonical quantization. We also show how the classical field equations are obtained from precanonical quantization as equations on expectation values of corresponding operators obtained from precanonical quantization (Ehrenfest theorem). We consider the Ehrenfest theorem both in flat and curved space-time. We also show how the approach works when applied to the problem of quantization of gravity and how it is consistent with the Einstein equations obtained as the equations for the expectation values calculated according to the principles of precanonical quantization. References: [1] I.V. Kanatchikov, Ehrenfest Theorem in Precanonical Quantization arXiv:1501.00480 [2] I.V. Kanatchikov, On precanonical quantization of gravity, arXiv:1407.3101 [3] I.V. Kanatchikov, De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity, arXiv:1302.2610 [4] I.V. Kanatchikov, On the Ehrenfest Theorem in quantum general relativity. work in progress [5] I.V. Kanatchikov, Precanonical Quantization and the Schroedinger Wave Functional Revisited, Adv. Theor. Math. Phys. 18 (2014) 1249-1265. |
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