Momentum projection and relativistic boost of solitons: Coherent states and projection

Abstract

We present a method for calculating center-of-mass corrections to hadron properties in soliton models and we apply the method to the soliton bag model. A coherent state is used to provide a quantum wave function corresponding to the mean-field approximation. This state is projected onto a zero-momentum eigenstate. States of nonzero momentum can be constructed from this with a Lorentz boost operator. Hence center-of-mass corrections can be made in a properly relativistic way. The energy of the projected zero-momentum state is the hadron mass with spurious center-ofmass energy removed. We apply a variational principle to our projected state and use three "virial theorems" to test our approximate solution. We also study projection of general one-mode states. Projection reduces the nucleon energy by up to 25%. Variation after projection gives a further reduction of less than 20%. Somewhat larger reductions in the energy are found for meson states.

Quantum liquids resulting from quark systems with four-quark interaction

“…We are also able to estimate the compression coefficient of the quark matter K , which occurs significantly larger than the nuclear one. Actually, we see a quite smooth analogy between the results obtained and the results of the bag soliton model [60][61][62][63]. The thermodynamic treatment developed in the present paper allows us to formulate the adequate boundary conditions for the bag in physical vacuum and to diminish considerably the uncertainties in searching the true soliton Lagrangian.…”

Medium modifications of baryon properties in nuclear matter and hypernuclei

“…In our previous work [37], we used two approaches for the center-of-mass correction. The first one is based on the relativistic energy-momentum relation [27] and the second one is the Peierls-Yoccoz projection technique [28]. For simplicity, in this work we take only the first approach for the center-of-mass correction that has been extensively discussed in Refs.…”

“…There are several methods for the removal of the center-of-mass motion in the FL model [27][28][29]. In our previous work [37], we used two approaches for the center-of-mass correction.…”

“…Also, it could be used to investigate the deconfinement phase transition at high densities and/or temperatures based on its dynamical formation of solitons. In past decades, the FL model has been extensively used to study the properties of hadrons in free space [26][27][28][29][30][31][32][33][34]. It has also been applied to study the medium modifications of the nucleon [4,35] and dense-matter properties [6,36].…”

Analytic structure of meson propagators in the proper-time regularized Nambu-Jona-Lasinio model

“…The mean field approximation used in soliton calculations does not separate the center-of-mass coordinates from intrinsic coordinates. This notorious problem of projecting out the center-of-mass motion of solitons has attracted a lot of attention [31][32][33][34][35][36][37][38] and numerical estimates give a negative contribution of the order of 300…”