Grassman number in functional quantization?

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SUMMARY

The discussion centers on the properties of Grassman numbers in the context of functional quantization, particularly regarding their complex conjugation and Hermitian properties. It is established that when calculating with Grassman numbers without altering their order, they behave similarly to ordinary numbers. However, the treatment of the complex conjugation of Grassman number products, which involves reversing the order, raises questions about consistency with Hermitian conjugation of operators. The consensus indicates that while individual Grassman field operators are not Hermitian, their products can exhibit Hermitian characteristics under certain conditions.

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ndung200790
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Please teach me this:
When calculating something with Grassman numbers without changing order of the numbers,then there are nothing different from ordinary numbers.So I think it would be contrary if we define the complex conjugation of a product of two Grassman numbers to reverse the order of products,just like Hermitian conjugation of operators.But in some books,they do that(they treat the quantization Dirac fields using functional method)
Thank you very much in advanced.
 
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It seem to me that despite field operators is not Hermitian,but the product of the two operators could be Hermitian.So product of two complex Grassman numbers that represent the Fermi fields must be like Hermitian operators.But saying that product of two operators of the field be hermitian is correct or not?
 

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