Canonical Quantization: Explaining the Covariance Paradox

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Canonical quantization is not relativistically covariant because it involves selecting a specific time direction when introducing the Hamiltonian, which disrupts Lorentz invariance. While the mathematical framework may initially appear Lorentz invariant, the process of quantization inherently relies on a preferred time slicing. This preference leads to a breakdown of covariance in the theory. The discussion highlights the tension between canonical quantization methods and the principles of relativity. Understanding this paradox is crucial for deeper insights into Quantum Field Theory.
shereen1
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Hi all
I am studying Quantum Field Theory. I read the following statement :"Canonical quantisation is intrinsically not relativistically covariant. Can anyone explain why?. Although everything we did from the beginning was lorentz invariant!
Thank you .
 
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You are singling out a particular time direction when you introduce the Hamiltonian. This breaks Lorentz covariance.
 
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