A theory of highly condensed matter

Abstract

To discuss properties of cold, condensed stellar objects such as neutron stars, it is necessary to know the stress tensor T μν , the source in Einstein's field equations, from nuclear matter densities upwards. To overcome some of the difficulties with the conventional many-body approach to this problem, a model relativistic, many-body, quantum field theory composed of a baryon field, a neutral scalar meson field coupled to the scalar density ψψ , and a neutral vector meson field coupled to the conserved baryon current i Ψγλψ is developed. For a uniform system of given baryon density ϱ B , the linearized theory obtained by replacing the scalar and vector fields by their expectation pectation values, φ → φ 0, V λ → iδ λ4 V 0 can be solved exactly. The resulting equation of state for nuclear matter exhibits nuclear saturation, and if the two dimensionless coupling constants in this theory are matched to the binding energy and density of nuclear matter, predictions are obtained for all other systems at all densities. In particular, neutron matter is unbound and the equation of state for neutron matter at all densities is presented; it extrapolates smoothly into the relativistic form P = ϵ. Comparison is made with some conventional many-body calculations. The full field theory is developed by expanding the fields about the condensed values φ 0, V 0, and the unperturbed hamiltonian is shown to correspond to the linearized theory. The energy shift due to these quantum fluctuations in the fields is related to the baryon Green's function. V 0 is related directly to ϱ B ; φ 0, however, must be determined through a self-consistency relation involving the baryon Green's function. The Feynman rules for this theory are developed. Expressions for the lowest-order contributions of the quantum fluctuations to the energy shift and φ 0 are derived. It is shown that the terms q μ q ν in the vector-meson propagator do not contribute to these expressions, and a prescription involving assumptions on the limiting form of the theory as ϱ B → 0 is presented which ensures that these lowest-order quantum fluctuations will yield finite results.