Prof. Glazek is interested in the concept of physical theories being effective in the renormalization group sense. One basic question is if an ultimate theory necessarily exists in the form of a distinct structure, asymptotically approachable through research. A different possibility is illustrated by quantum theories that occur in limit cycles [1,2]. The cyclic structure may be more common among quantum theories than one could expect on the basis of experience with fixed point structures that dominate in current considerations of physicists. Moreover, a new renormalization group procedure for studying limit cycles of effective theories with an entire hierarchy of bound states formed at different energy scales, shows that the well-known case of a family of effective theories with asymptotic freedom and bound states formed at one scale of energy in the phenomenon called infrared slavery can be seen as corresponding to just a single cycle [3]. Another study shows that the well-known perturbative increase of the coupling constant at small energies in asymptotically free theories with bound states may be caused by the lack of inclusion in the perturbative calculation of the quantum phenomenon of binding and may be avoided in the new renormalization group approach when its generator includes interactions responsible for the phenomenon of binding [4]. In principle, although effective theories are non-local and their non-locality may always hide layers of unknown substructure, the non-localities implied by any assumed layers can be calculated using the renormalization group procedure for effective particles (RGPEP) [5]. Extension of the RGPEP formalism beyond perturbation theory can be found in [6] and an example of exact solution of RGPEP equations with explicit form of effective-particle quantum field operators is provided in [7]. By the way, the well-known potential one over r squared still awaits analysis using the RGPEP [8]. Elementary outline of the renormalization group procedure for effective particles (RGPEP) is provided in [9]. The wide range of potential applications of the RGPEP to basic Hamiltonians of particle theory is nearly unexplored.

- [1] S. D. Glazek, K. G. Wilson, Phys. Rev. Lett. 89, 230401 (2002).
- [2] S. D. Glazek, K. G. Wilson, Phys. Rev. B 69, 094304 (2004).
- [3] S. D. Glazek, Phys. Rev. D 75, 025005 (2007).
- [4] S. D. Glazek, R. J. Perry, Phys. Rev. D 78, 045011 (2008).
- [5] S. D. Glazek, Acta Phys. Polon. B 41, 1937 (2010).
- [6] S. D. Glazek, Acta Phys. Polon. B 42, 1933 (2011).
- [7] S. D. Glazek, Phys. Rev. D 85, 125018 (2012).
- [8] S. M. Dawid, R. Gonsior, J. Kwapisz, K. Serafin, M. Tobolski, S. D. Glazek, Phys. Lett. B 777, 260 (2018).
- [9] S. D. Glazek, Phys. Rev. D 103, 014021 (2021)