Rigorous Determination of Bosonic and fermoinic commutation relation

[ClubDogo]

Is there a book that explain in a formal way the deduction of symmetry/antisymmetry of bosonic/fermionic wave equation e/o commutation relation? I've often noticed that some people use examples for the introcution, but is there an axiomatic deduction?

 

[dextercioby]

They follow due to the simple receipt: graded Poisson/Dirac bracket goes to 1/ihbar times graded commutator.

 

[denian]

Yes, there are several books that explain the rigorous determination of bosonic and fermionic commutation relations in a formal way. One example is "Quantum Mechanics: A Modern Development" by Leslie E. Ballentine. This book provides a comprehensive and rigorous treatment of quantum mechanics, including the derivation of the commutation relations for bosonic and fermionic operators.

Other books that cover this topic include "Quantum Field Theory" by Franz Mandl and Graham Shaw, and "Quantum Field Theory for the Gifted Amateur" by Tom Lancaster and Stephen Blundell. These books also provide a rigorous and axiomatic approach to understanding the commutation relations for bosonic and fermionic operators.

It is important to note that while examples can be useful for introducing the concept of commutation relations, a formal and rigorous understanding of these relations requires a mathematical approach. This involves starting from the basic principles of quantum mechanics and using mathematical techniques such as group theory and operator algebra to derive the commutation relations for bosonic and fermionic operators.

In summary, there are several books that provide a formal and rigorous deduction of the symmetry/antisymmetry of bosonic/fermionic wave equations and commutation relations. These books are useful resources for scientists and students who are interested in understanding the underlying principles and mathematical foundations of quantum mechanics.