What Is a C-Number in Quantum Field Theory?

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Discussion Overview

The discussion centers around the definition and interpretation of the term "c-number" in the context of quantum field theory. Participants explore its meaning, potential equivalences to other concepts, and its application in various contexts, including the distinction between classical and quantum quantities.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks a textbook definition of c-number, questioning whether it refers to a commuting number or a classical quantity, and notes a potential confusion in sources.
  • Another participant suggests that c-number typically refers to "complex" number based on their experience.
  • A different participant asserts that c-number is defined as a classical number and emphasizes that it is not an operator or spinor.
  • One participant introduces the concept of Grassmann numbers as anticommuting numbers used in fermionic field representations, noting that they are often not referred to as c-numbers.

Areas of Agreement / Disagreement

Participants express differing interpretations of what constitutes a c-number, with no consensus reached on its definition or its relationship to other types of numbers such as Grassmann numbers.

Contextual Notes

There are unresolved distinctions regarding the definitions of c-numbers, commuting numbers, and classical quantities, as well as the relationship between c-numbers and Grassmann numbers.

fliptomato
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Hello everyone--I was hoping someone could give (or refer to) a textbook definition of a [tex]c[/tex]-number, as used in the context of quantum field theory.

Does this refer to a commuting number? I've also read it referring to a classical quantity. classical quantity, from a not-very-reputable source. (Though are these the same?)

If the 'c' refers to commuting, when I read something like "...spinors are anti-commuting (c-numbers)." (Bailin and Love, SUSY book) Does this mean that spinors are anti-commuting objects composed of commuting numbers? (It certainly doesn't mean that the spinors themselves are commuting...)

Thanks,
Flip
 
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C-number usually refers to "complex" number. At least that is all I have ever seen it used as.
 
c-number is really defined as a classical number. it is not an operator or
spinor.!

anticommuting number is Grassmann number used in the functional integral
representation of fermionic field.

Often the Grassman number is not called c-number, maybe someone can call
Grassmann number as c-number.
 

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