Textbook definition a c-number

In summary, c-number is a term used in quantum field theory that can refer to a classical quantity or a complex number. It is not an operator or spinor, and can also refer to Grassmann numbers used in the functional integral representation of fermionic fields. Some may use the term c-number to refer to Grassmann numbers, but this is not always the case.
  • #1
fliptomato
78
0
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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  • #2
C-number usually refers to "complex" number. At least that is all I have ever seen it used as.
 
  • #4
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.
 

Related to Textbook definition a c-number

What is a c-number?

A c-number, also known as a classical number, is a number that can be represented by a finite sequence of digits or symbols. It is used in classical physics to describe quantities that are continuous and can take on any real value, such as position, velocity, and time.

How is a c-number different from a q-number?

A q-number, or quantum number, is used in quantum mechanics to describe quantities that are discrete and can only take on certain values, such as energy levels. In contrast, a c-number can take on any value within a certain range.

What is the significance of a c-number in physics?

C-numbers are important in classical physics because they allow us to describe and solve mathematical equations that model the behavior of physical systems. They are also used in the transition between classical and quantum mechanics.

Can a c-number be complex?

Yes, a c-number can be complex, meaning it has both a real and an imaginary component. This is often used in physics to model physical quantities that have both magnitude and direction, such as electric and magnetic fields.

How is a c-number represented in mathematical notation?

In mathematical notation, a c-number is represented by a lowercase letter, such as x, y, or t. It can also be represented by a lowercase Greek letter, such as α, β, or γ. These variables can take on any real value within a certain range.

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