References for generalized canonical commutation relations

In summary, generalized canonical commutation relations are mathematical equations that describe the relationship between two physical quantities in quantum mechanics. References are important for providing evidence and support for their validity. These relations were first introduced by Paul Dirac in 1925 and have since been further developed and applied in various areas of quantum mechanics. They are used in research to study quantum systems and in the development of quantum technologies. While widely accepted, there have been debates surrounding their interpretation and application in certain scenarios.
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Ssnow
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Hi to all, I ask if somebody of the Physics community know good references for article where the author works with generalized canonical commutation relations ( I mean that the author works with ##[x,p]=ic\hbar## with ##c## a real constant instead of ##[x,p]=i\hbar##).
Thank you for the answers,
Ssnow
 
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There is a lot of literature with ##c=1/\hbar##, they usually say that they work in units ##\hbar=1##. o0)
 

FAQ: References for generalized canonical commutation relations

What are generalized canonical commutation relations (GCCRs)?

Generalized canonical commutation relations (GCCRs) are mathematical equations that describe the fundamental relationship between two physical quantities, such as position and momentum, in quantum mechanics. They are a generalization of the canonical commutation relations, which only apply to a specific type of system.

Why are GCCRs important in quantum mechanics?

GCCRs are important in quantum mechanics because they provide a framework for understanding the behavior of physical quantities at the quantum level. They allow us to make predictions about the outcomes of measurements and understand the uncertainty inherent in quantum systems.

How are GCCRs derived?

GCCRs are derived using mathematical techniques from quantum mechanics, such as the Heisenberg uncertainty principle and the Schrödinger equation. These equations are used to define the operators for physical quantities, and the GCCRs are then obtained by imposing certain mathematical conditions on these operators.

What are some applications of GCCRs?

GCCRs have many applications in quantum mechanics, including in the study of quantum systems and the development of quantum algorithms for computing. They are also used in the development of new technologies, such as quantum computers and quantum sensors.

Are GCCRs universally applicable?

No, GCCRs are not universally applicable. They are derived for specific types of systems and may not hold true for all physical quantities or in all situations. Additionally, there are alternative theories to quantum mechanics that may have different commutation relations.

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