Canonical Quantization: Explaining the Covariance Paradox

In summary, canonical quantization is a mathematical procedure used in quantum mechanics to describe physical systems by converting classical variables into quantum operators. The covariance paradox refers to the fact that this process does not preserve the covariance of classical equations of motion, but it is resolved by considering quantum commutation relations between operators. This paradox is important in highlighting the differences between classical and quantum theories and has applications in other areas of physics.
  • #1
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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  • #2
You are singling out a particular time direction when you introduce the Hamiltonian. This breaks Lorentz covariance.
 
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1. What is canonical quantization?

Canonical quantization is a mathematical procedure used in quantum mechanics to describe the behavior of physical systems. It involves converting classical variables, such as position and momentum, into quantum operators that represent the measurable quantities of a system.

2. What is the covariance paradox in canonical quantization?

The covariance paradox refers to the fact that the mathematical process of canonical quantization does not preserve the covariance of the classical equations of motion. This means that the quantum equations of motion do not have the same form as the classical equations, even though they should be equivalent in the classical limit.

3. How is the covariance paradox resolved?

The covariance paradox is resolved by taking into account the quantum commutation relations between operators. These relations dictate how the operators representing different physical quantities should behave, and when properly accounted for, they lead to equations of motion that are consistent with the classical ones.

4. What is the importance of the covariance paradox in quantum mechanics?

The covariance paradox is important because it highlights the differences between classical and quantum theories. It also helps us better understand the limitations of classical mechanics and the need for a more accurate description of the behavior of physical systems at the quantum level.

5. How does canonical quantization relate to other areas of physics?

Canonical quantization is a fundamental concept in quantum mechanics, but it also has applications in other areas of physics such as quantum field theory and general relativity. It provides a way to understand the behavior of physical systems at a microscopic level and has led to many important discoveries in modern physics.

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