Relativistic Many-body Theory Research Articles

Elementary-particle symmetries in relativistic many-body theory at finite temperature and density

The consequences of a phase transition associated with symmetry restoration to SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) in nuclear matter are investigated. The changes in the mass spectrum due to the phase transition (a) at zero temperature and high nuclear density, and (b) at high temperature with zero nuclear chemical potential are evaluated in the $\ensuremath{\sigma}$ model of particle physics. The experimentally observable effects necessitate the measurement of current correlation functions. In this paper we consider the vector-vector-axial-vector ($\mathrm{VVA}$) and the vector-vector-pseudoscalar ($\mathrm{VVP}$) current correlation functions. The relation between the $\mathrm{VVA}$ and $\mathrm{VVP}$ correlation functions is obtained and it is shown that the Adler-Bell-Jackiw anomaly in the divergence of the axial-vector current remains unaltered in the nuclear medium, even though the $\mathrm{VVA}$ and the $\mathrm{VVP}$ correlation functions have additional contributions from processes specific to the many-particle system. The $\mathrm{VVP}$ correlation function is related to the neutral-pion decay amplitude. The changes in the decay rate of ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ in the nuclear medium are evaluated by including the effects of changes in the mass spectrum of particles, and by using the cutting rules of many-body field theory for the real and imaginary parts of the amplitude. The photon in the nuclear medium is dressed by polarization effects and propagates as a plasmon. This effect is taken into account by evaluating the plasmon frequency or the plasmon mass. The changes in the mass spectrum due to symmetry restoration affect the decay rate of ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ by at least 2 orders of magnitude and these results are tabulated. It is suggested that the Primakoff effect might provide the signal for the presence of the "abnormal nuclear matter" phase.

Correlation corrections to the mean-field theory of nuclear matter

To investigate high-density nuclear matter, a relativistic many-body field theory has been proposed and discussed in the mean-field approximation. A criticism of this approximation is the neglect of two-body correlation effects, which are investigated here.

A relativistic many-body theory of high density matter

A fully relativistic quantum many-body theory is applied to the study of high-density matter. The latter is identified with the zero-temperature ground state of a system of interacting baryons. In accordance with the observed short-range repulsive and long-range attractive character of the nucleon-nucleon force, baryons are described as interacting with each other via a massive scalar and a massive vector meson exchange. In the Hartree approximation, the theory yields the same result as the mean-field theory, but with additional vacuum fluctuation corrections. The resultant equation of state for neutron matter is used to determine properties of neutron stars. The relativistic exchange energy, its corresponding single-particle excitation spectrum, and its effect on the neutron matter equation of state, are calculated. The correlation energy from summing the set of ring diagrams is derived directly from the energy-momentum tensor, with renormalization carried out by adding counterterms to the original Lagrangian and subtracting purely vacuum expectation values. Terms of order g4lng2 are explicitly given. Effects of scalarvector mixing are discussed. Collective modes corresponding to macroscopic density fluctuation are investigated. Two basic modes are found, a plasma-like mode and zero sound, with the latter dominant at high density. The stability and damping of these modes are studied. Last, the effect of vacuum polarization in high-density matter is examined.

A relativistic many-body theory of high-density matter: S. A. Chin. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

A relativistic many-body theory of high-density matter: S. A. Chin. Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

Relativistic many-body studies of high density matter

A fully relativistic quantum many-body theory is applied to the study of a model high-density matter which qualitatively describes known nuclear matter. Results pertaining to the equation of state of neutron matter, neutron star mass, vacuum fluctuation corrections, collective modes, exchange energies, and correlation energies are reported.

Relativistic Baryon Effective Masses and Thresholds for Strongly Interacting Superdense Matter

The relativistic effective mass of a baryon from the first SU(3)-symmetric octet is discussed. The calculation is based on a fully relativistic many-body theory for strongly interacting superdense matter. The dependence on interaction parameters is discussed. The resulting effective mass for high density becomes ${m}_{\mathrm{eff}}\ensuremath{\sim}{({a}^{2}\ensuremath{-}1)}^{\frac{1}{2}}{q}_{F}$. The density-independent coefficient $a$ contains the baryon mass, exchanged pseudoscalar-meson mass, and coupling constant. The discussion employs analytic expressions which fit the results of numerical calculation to better than 10% over a density range ${10}^{13}<{\ensuremath{\rho}}_{0}<{10}^{21}$ g/${\mathrm{cm}}^{3}$. The reduction in pressure of asymptotic superdense matter and the effect of increased thresholds for particle production are discussed. Finally we mention the possible importance of density-dependent effective coupling constants.

Relativistic Quantum Many-Body Theory in Riemannian Space-Time

A relativistic quantum many-body theory, which includes the strong interactions between elementary particles in curved space-time, is constructed. Using a generalized statisticaldensity operator, which incorporates the effects of gravitation as given by Einstein's field equations, as well as observables constructed from a generally covariant Lagrangian for matter fields, the definition of an $N$-point function of second-quantized matter fields is presented. The Yukawa coupling of a spinor field is then introduced. Coupled integral equations for the fermion and boson two-point functions in terms of the vertex function are given, which contain density and temperature effects in curved space-time; they are coupled to Einstein's equations through the expectation value of the energy-momentum density operator. Renormalization to effective masses and charge, as well as regularization, are discussed. The curved-space-time statistical-density operator is examined in the flat-space-time limit, and also in the nonrelativistic limit. The former agrees with previous work in relativistic statistical mechanics. The introduction of temperature and density as boundary conditions on flat-space-time $N$-point functions is carried out yielding a relativistic formalism, which may be applied to the calculation of such quantities as the equation of state of a superdense system of strongly interacting baryons. The nonrelativistic limit suggests a new approach to the statistical mechanics of Newtonian gravitation, in which such parameters as temperature become functions of coordinates. The relativistic flat-space-time limit is applicable to neutron stars at densities $\ensuremath{\rho}>{10}^{15}$ g/${\mathrm{cm}}^{3}$ consisting of strongly interacting matter.

Asymptotic Limit for the Speed of Sound in a System of Relativistically Interacting Particles

A relativistic many-body theory is used to evaluate the equation of state to lowest order in the weak coupling constant for a dense system of electrons and neutrinos interacting through the universal Fermi interaction. The asymptotic limit for the speed of sound ${v}_{s}l~\frac{c}{\sqrt{3}}$ is obtained; it is conjectured that a large class of relativistic interactions leads to the same limit.