"phenomenology side of the high energy physics study" basically means that when this student uploads their article to arXiv, they will, in principle, **choose hep-ph as the primary archive**. This background also indicates that this student has, in general, already learned at least

a. Undergraduate level physics classes;

b. QFT from the first half of Peskin and Schroeder's classical textbook, or, maybe, Greiner's *Field Quantization*;

c. Complex analysis like those covered in the first five chapters of Conway's *Functions of One Complex Variable I*;

d. Some basic knowledge about special functions, like Laguerre Polynomials;

e. Elementary set theory;

f. General topology like those covered in Amstrong's *Basic Topology*;

g. Elementary vector space theory with no details about the operator algebra;

h. Some elementary conclusions from group theory, with a focus on the Lie group and Lorentz group;

i. Enough particle physics so that they is able to understand what the summary tables of the PDG are talking about, or they at least knows how to find the definition of some of those unknown symbols.

"more mathematically rigorous study of quantum field theory" may have different meanings for different people. Just to give an example, Prof. Tachikawa from IPMU had a talk titled "Mathematics of QFT, by QFT, for QFT" on his website (https://member.ipmu.jp/yuji.tachikawa/transp/qft-tsukuba.pdf), which the OP find really tasteful, of course, from a rather personal point of view. One may agree that all those studies covered there may be considered mathematically rigorous studies of quantum field theory. Or, one may agree on only part of them. Or, maybe the answerer thinks that some other researches also count. That is all OK. But, please **specify your altitude before elaborating your answer**. The answerer may also want to **specify explicitly for which subfield** they is recommending references. In the OP's understanding, "more mathematically rigorous study of quantum field theory" basically covers those topics

a. Algebraic/Axiomatic QFT, Constructive QFT or the Yang-Mills millennium problem, which tries to provide a mathematically sounding foundation of QFT.

b. Topological QFT or Cconformal QFT, which utilizes some fancy mathematical techniques to study QFT.

c. Even some math fields stemming from QFT like those fields-awarding work done by Witten.