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SUMMARY:Gabor Balassa (Yonsei U.)\, "Approximating Euclidean path integral
 s with radial basis function neural networks"
DTSTART:20260701T060000Z
DTEND:20260701T070000Z
DTSTAMP:20260715T071700Z
UID:indico-event-1325@indico.ibs.re.kr
DESCRIPTION:In this talk\, I will introduce a lattice-based method to appr
 oximate Euclidean path integrals\, based on a radial basis function (RBF) 
 expansion of the interaction terms that appear in the path integral formal
 ism of quantum field theories. This approach allows numerically efficient 
 determination of both the partition function directly and specific observa
 bles\, which can be used to describe phenomena such as phase transitions\,
  fluctuations\, etc. The method is currently applicable to interacting (re
 al and complex) scalar fields at both zero and non-zero chemical potential
 s\, even in 3+1 dimensions. For real scalar fields in 1+1 dimensions\, the
  phase transition line is approximated at several coupling strengths with 
 very good accuracy\, comparable to previous Monte Carlo lattice calculatio
 ns. As another example\, we will examine complex scalar fields at finite c
 hemical potentials\, which develop a sign problem similar to that of quant
 um chromodynamics at finite densities on the lattice. It will be shown tha
 t by applying the radial basis expansion to the system\, the sign problem 
 can be evaded\, and the phase transition points\, i.e.\, the critical chem
 ical potentials where Bose condensation occurs\, can be determined. Furthe
 rmore\, the silver blaze phenomenon\, which relies on severe cancellations
  in the path integral\, can also be described. At the end I will propose f
 uture directions where the radial basis function approximation could be ad
 vantageous\, such as systems with fermions\, gauge theories\, and possibly
  quantum chromodynamics.\n\nhttps://indico.ibs.re.kr/event/1325/
LOCATION:CTPU Seminar room (Theory Bldg\, 4F)
URL:https://indico.ibs.re.kr/event/1325/
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