Exact renormalisation group flow for ultracold Fermi gases in unitary limit

We study the exact renormalisation group flow for ultracold Fermi-gases in unitary regime. We introduce a pairing field to describe the formation of the Cooper pairs, and take a simple ansatz for the effective action. Set of approximate flow equations for the effective couplings including boson and fermionic fluctuations is derived. At some value of the running scale, the system undergoes a phase transition to a gapped phase. The values of the energy density, chemical potential, pairing gap and the corresponding proportionality constants relating the interacting and non-interacting Fermi gases are calculated. Standard mean field results are recovered if we omit the boson loops.Comment: 11 pages, Revtex, misprints corrected, references and comments adde

Toward Chiral Theory of NN interactions in nuclear matter

The effective chiral theory of the in-medium NN interactions is considered. The shallow bound states, which complicate the effective field theory analysis in vacuum do not exist in matter. We show that the next-to-leading order terms in the chiral expansion of the effective Lagrangian can be interpreted as corrections so that the expansion is systematic. The Low Energy Effective Constants of this Lagrangian are found to satisfy the concept of naturalness. The potential energy per particle is calculated. The problems and challenges in constructing the chiral theory of nuclear matter are outlined.Comment: Talk given at International Workshop "Gross properties of Nuclei and Nuclear Exitations", Hirschegg, Austria, 16-22.01.2000, Latex, 6 page

Nonperturbative Renormalisation Group: Applications to the few and many-body systems

We consider the applications of functional renormalisation group to few and many-body systems. As an application to the few-body dynamics we study the ratio between the fermion-fermion scattering length and the dimer-dimer scattering length for systems of few nonrelativistic fermions. We find a strong dependence on the cutoff function used in the renormalisation flow for a two-body truncation of the action. Adding a simple three-body term substantially reduces this dependence. In the context of many-body physics we study the dynamics of both symmetric and asymmetric many-fermion systems using the same functional renormalisation technique. It is demonstrated that functional renormalisation group gives sensible and reliable results and provides a solid theoretical ground for the future studies. Open questions as well as lines of further developments are discussed.Comment: Talk on International IUPAP Conference on Few-Body Problems in Physics, September, 2009, Bonn, German

Chiral NN interaction in nuclear matter

The effective field theory of NN interactions in nuclear matter is considered. Due to the Pauli principle the effective NN amplitude is not affected by the shallow bound states. We show that the next-to-leading order terms in the chiral expansion of the effective NN potential can be interpreted as corrections so the expansion is systematic. The value of potential energy per particle is calculated and some issues concerning the chiral effective theory of nuclear matter are outlined.Comment: 7 pages, Revtex, Talk given on the International Workshop on Hadron Physics "Effective Theories of Low Energy QCD", Coimbra, Portugal, September 10 - 15, 199

Chiral NN interactions in nuclear matter

We consider an effective field theory of NN system in nuclear medium. The shallow bound states, which complicate the effective field theory analysis and lead to the large scattering length in the vacuum case do not exist in matter. We study whether the chiral expansion of the effective potential can be truncated in such situation. The cutoff regularization is used to render the solution of the Bethe-Goldstone equation finite. We show that the next-to-leading order terms in the chiral expansion of the effective NN potential can indeed be interpreted as corrections so that the truncation of the expansion is justified. However, it is pointed out that it is still useful to treat the problem nonperturbatively since it may allow the consideration of the nuclear systems with the density smaller that the normal nuclear matter one. The possible directions of constructing the chiral theory of NN interaction in medium are outlined.Comment: 10 pages, revte

Effective theory of NN interactions in a separable representation

We consider the effective field theory of the NN system in a separable representation. The pionic part of the effective potential is included nonperturbatively and approximated by a separable potential. The use of a separable representation allows for the explicit solution of the Lippmann-Schwinger equation and a consistent renormalization procedure. The phase shifts in the $^1S_0$ channel are calculated to subleading order.Comment: 7 page

Chiral Dynamics of the low-energy Kaon-Baryon interactions

The processes involving $K^{-}p, KN, \Sigma\pi, \Lambda\pi,\Sigma\eta, \Lambda\eta$ coupled channels are studied in the nonperturbative chiral approach. An effective potential is constructed using a chiral meson-baryon Lagrangian at lowest order. This potential is iterated to all orders with the Lippmann-Schwinger equation. A reasonable fit of the experimental data is obtained. It is pointed out, however, that due to a strong sensitivity of the results to the value of the cut-off, such an approach should be viewed as a rather phenomenological way to fit the experimental data since there is no small expansion parameter allowing for truncation of the chiral expansion of the effective potential at some given order. A possible way to construct the consistent chiral expansion is briefly discussedComment: 11 pages, 3 figures, LATE