Abstract:
We extend a recent chiral approach to nuclear matter of Lutz et al. [Phys. Lett. B474 (2000) 7] by calculating the underlying (complex-valued) single-particle potential U(p,k_f) + i W(p,k_f). The potential for a nucleon at the bottom of the Fermi-sea, U(0,k_{f0})= - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi-surface. Also, the imaginary single-particle potential, W(0,k_{f0}) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear matter equation of state can be obtained if the short range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1pi-exchange). We also consider the equation of state of pure neutron matter $bar E_n(k_n)$ and the asymmetry energy A(k_f) in that approach. The downward bending of these quantities above nuclear matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics.

Abstract:
In this proceeding we summarize results for baryonic contact terms derived within SU(3) chiral effective field theory. The four-baryon contact terms, necessary for the description of the hyperon-nucleon interaction, include SU(3) symmetric and explicit chiral symmetry breaking terms. They also include four-baryon contact terms involving pseudoscalar mesons, which become important for three-body forces. Furthermore we derive the leading order six-baryon contact terms in the non-relativistic limit and study their contribution to the $\Lambda NN$ three-body contact interaction. These results could play an important role in studies of hypernuclei or hyperons in nuclear matter.

Abstract:
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.

Abstract:
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.

Abstract:
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.

Abstract:
The contribution of nucleons to the quark condensate in nuclear matter includes a piece of first order in $m_\pi$, arising from the contribution of low-momentum virtual pions to the $\pi N$ sigma commutator. Chiral symmetry requires that no term of this order appears in the $NN$ interaction. The mass of a nucleon in matter thus cannot depend in any simple way on the quark condensate alone. More generally, pieces of the quark condensate that arise from low-momentum pions should not be associated with partial restoration of chiral symmetry.

Abstract:
We extend an effective Lagrangian embodying broken scale and chiral symmetry to include explicit chiral symmetry breaking and an additional chiral invariant term which allows for an axial coupling constant greater than unity. We also include a chiral Lagrangian for the isotriplet vector mesons which leads to a renormalization of the pion field. The properties of nuclear matter and nuclei, low energy $\pi N$ scattering and the behavior of quantities such as the pion mass and axial coupling at finite density are discussed.

Abstract:
We discuss the possible influence of fundamental QCD properties such as spontaneous chiral symmetry breaking and nucleon substructure on nuclear matter properties. We propose a chiral version of the relativistic $\sigma-\omega$ model in which the attractive background scalar field is associated with the chiral invariant field governing the radial fluctuations of the quark condensate. Nuclear matter stability is ensured once the scalar response of the nucleon depending on the quark confinement mechanism is properly incorporated. The needed parameters are estimated from lattice results and a satisfactory description of bulk properties follows, the only really free parameter being the $\omega NN$ coupling constant. Pion loops can be also incorporated to obtain in a consistent way the finite density chiral susceptibilities. A good description of the asymmetry energy is obtained once the full rho meson exchange and Fock terms are included.

Abstract:
We derive the short-range contributions and the leading relativistic corrections to the three-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion.

Abstract:
We derive the long-range contributions to the tree-nucleon force at next-to-next-to-next-to-leading order in the chiral expansion. We give both momentum and coordinate space representations.