Since you don't give an example and most people will not have that book available, I think many will be able to answer this. Since this is posted under "Quantum Physics", and linear operators are often used there, without any more information I would suspect something line "adjoint" as in "ad T" is the adjoint of the operator T. Was "ad" used with an operator or just as a word on its own?Jimmy Snyder said:I'm reading QFT: Basics in Mathematics and Physics, by Eberhard Zeidler. Once in a while, in his proofs, I see the word (abbreviation?) Ad. For instance on page 375. The author is German and I suppose this imight be common practice in German texts. Does anyone here know what it means?
I'm sorry, I didn't realize that there were some people that don't have a copy of the book. It must stand for some kind of enumeration like case N, case R, etc. That's how it is used on page 375.my_wan said:I've seen it used as the prefix for an enumeration of the steps in a proof, but don't know what it stands for.
Thanks unusualname.unusualname said:It's an abbreviation for "Ad hoc" which means "for this" (case) as you guessed.
"Ad" is short for "adjoint," which refers to a mathematical operation that is closely related to the concept of a transpose in linear algebra. In the context of Zeidler's proofs, "Ad" is used to denote the adjoint operator in quantum field theory (QFT).
In QFT, the adjoint operator is a fundamental concept that is used to describe the relationship between operators and their corresponding observables. It allows us to formally define the Hermitian conjugate of an operator, which is necessary for calculating physical quantities and making predictions about the behavior of quantum systems.
The "Ad" operation takes an operator and transforms it into its corresponding adjoint operator. In other words, it reflects the operator across the diagonal in a complex vector space. This transformation is essential in QFT because it allows us to define self-adjoint operators, which are crucial for making accurate predictions about quantum systems.
The adjoint operator is closely related to the Hermitian conjugate, but they are not exactly the same thing. While the adjoint operator is a mathematical operation that transforms an operator, the Hermitian conjugate is the actual result of this transformation. In other words, the adjoint operator is a process, while the Hermitian conjugate is the outcome of that process.
Yes, there are several different types of adjoint operators in QFT, including the left adjoint, right adjoint, and adjoint of a chain. Each type of adjoint operator is used to describe a specific relationship between operators and their corresponding observables. These different types of adjoint operators are essential in understanding the complex mathematical structures of QFT.