## Effective theories

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].

- [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).