I am not an expert on either QFT or $C^{*}$-algebras, but I'm trying to learn the basics of QFT. In all books/papers and other materials that I know, QFT is studied mainly using a lot of functional analysis and distribution theory, but I know that some algebraic constructions are also being used, and in this context $C^{*}$-algebras seem to be the most modern tool. So, what should an inexperienced student like me know about these approaches to QFT and statistical mechanics? What's the role of $C^{*}$-algebras and other algebraic methods in those theories? What are the problems they fit better? If I'd like to study QFT, do I have to learn $C^{*}$-algebra? Are there problems in which algebraic methods don't fit well? Are there problems in which either approach is fruitful? What does one lose by not knowing these algebraic constructions?

I am not an expert on either QFT or $C^{*}$-algebras, but I'm trying to learn the basics of QFT. In all books/papers and other materials that I know, QFT is studied mainly using a lot of functional analysis and distribution theory, but I know that some algebraic constructions are also being used, and in this context $C^{*}$-algebras seem to be the most modern tool. So, what should an inexperienced student like me know about these approaches to QFT and statistical mechanics? What's the role of $C^{*}$-algebras and other algebraic methods in those theories? What are the problems they fit better? If I'd like to study QFT, do I have to learn $C^{*}$-algebra? Are there problems in which algebraic methods don't fit well? Are there problems in which either approach is fruitful? What does one lose by not knowing these algebraic constructions?

ADD: I work with rigorous statistical mechanics but I'm trying to learn some QFT because...well, these are two related areas at some level. However, I don't know yet what or how much I need to learn about QFT. I have a background in functional analysis and distribution theory, but not in $C^{*}$-algebra. As an unexperienced student, it will be very useful to get a general picture, i.e. what are the problems one is trying to solve in QFT and where do each of these approaches come into play. I think each of these tools are applicable for different kinds of problems or even different subareas of the theory, but I don't know for sure.

I am not an expert on either QFT or $C^{*}$-algebras but I'm trying to learn the basics on QFT. In all books/papers and other materials that I know, QFT is studied mainly using a lot of functional analysis and distribution theory but I know that some algebraic constructions are also being used and, in this context, $C^{*}$-algebra seems to be the most modern tool. So, what an unexperienced student like me should know about these approaches to QFT and statistical mechanics? What's the role of $C^{*}$-algebras and other algebraic methods in those theories? What are the problems they fit better? If I'd like to study QFT, do I must to learn $C^{*}$-algebra? Are there problems in which algebraic methods doesn't fit well? Are there problems in which either approach is fruitful? What do one lose by not knowing these algebraic constructions?

I am not an expert on either QFT or $C^{*}$-algebras, but I'm trying to learn the basics of QFT. In all books/papers and other materials that I know, QFT is studied mainly using a lot of functional analysis and distribution theory, but I know that some algebraic constructions are also being used, and in this context $C^{*}$-algebras seem to be the most modern tool. So, what should an inexperienced student like me know about these approaches to QFT and statistical mechanics? What's the role of $C^{*}$-algebras and other algebraic methods in those theories? What are the problems they fit better? If I'd like to study QFT, do I have to learn $C^{*}$-algebra? Are there problems in which algebraic methods don't fit well? Are there problems in which either approach is fruitful? What does one lose by not knowing these algebraic constructions?