An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the $ϕ^4$ theory in 1+1 dimensions. We show that standard RPA approach leads to an instability which can be removed when going to a superior version,i.e. the renormalized RPA. We present a method based on the so-called charging formula of the many electron problem to calculate the correlation energy and the RPA effective potential.An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the $ϕ^4$ theory in 1+1 dimensions. We show that standard RPA approach leads to an instability which can be removed when going to a superior version,i.e. the renormalized RPA. We present a method based on the so-called charging formula of the many electron problem to calculate the correlation energy and the RPA effective potential.

arXiv:hep-ph/0201279Jan 30, 20020 citations

Extension of the second random-phase approximation

D. Gambacurta, M. Grasso, F. Catara +1 more

The second random-phase approximation (SRPA) is the simplest and most natural extension of the RPA. It enlarges the space of the elementary modes introduced to describe the collective states by adding 2 particle -2 hole excitations to the 1 particle -1 hole ones of the RPA. In deriving the SRPA equations, use is made, as in the RPA, of the so-called quasi-boson approximation (QBA) where expectation values in the ground state of the system are approximated by their values in the uncorrelated reference state. This, however, has been shown to imply a degree of approximation worse than that in the RPA. It is, therefore, necessary to improve the QBA by considering a reference state which contains some correlations. Having in mind to perform such calculations for realistic systems, we consider a simple extension of the SRPA in which the reference state contains 2 particle - 2 hole correlations. The quality of such an extension is tested by applying it to a solvable three-level model and found to be good.The second random-phase approximation (SRPA) is the simplest and most natural extension of the RPA. It enlarges the space of the elementary modes introduced to describe the collective states by adding 2 particle -2 hole excitations to the 1 particle -1 hole ones of the RPA. In deriving the SRPA equations, use is made, as in the RPA, of the so-called quasi-boson approximation (QBA) where expectation values in the ground state of the system are approximated by their values in the uncorrelated reference state. This, however, has been shown to imply a degree of approximation worse than that in the RPA. It is, therefore, necessary to improve the QBA by considering a reference state which contains some correlations. Having in mind to perform such calculations for realistic systems, we consider a simple extension of the SRPA in which the reference state contains 2 particle - 2 hole correlations. The quality of such an extension is tested by applying it to a solvable three-level model and found to be good.

Physical Review CFeb 28, 200621 citations

Study of random matrix ensembles for bosonic systems

N. D. Chavda

Oct 31, 20041 citation

Random Phase Approximation (RPA)

Lukong Cornelius Fai

This chapter examines different problems that apply the field theory in condensed matter physics. It considers bosonic as well as fermionic systems and applies the techniques of the quantum field theory. The chapter provides a model describing electrons in a metal known as the electron gas model that considers a system of electrons interacting with each other via the instantaneous Coulomb force e2r. The electron gas model provides a framework from which introduces standard many-body approaches such as the Gell-Mann-Bruckner theory or random phase approximation and show how they are formulated within diagrammatic or functional integral techniques. The chapter also considers a quantum three-dimensional coulomb gas and apply the field-theoretic techniques to systems of interacting electrons. The terminology of the order parameter for the field ϕ is to indicate the treatment of the Coulomb interaction within a mean-field theory with the inclusion of Gaussian fluctuations around the mean-field value of the order parameter.This chapter examines different problems that apply the field theory in condensed matter physics. It considers bosonic as well as fermionic systems and applies the techniques of the quantum field theory. The chapter provides a model describing electrons in a metal known as the electron gas model that considers a system of electrons interacting with each other via the instantaneous Coulomb force e2r. The electron gas model provides a framework from which introduces standard many-body approaches such as the Gell-Mann-Bruckner theory or random phase approximation and show how they are formulated within diagrammatic or functional integral techniques. The chapter also considers a quantum three-dimensional coulomb gas and apply the field-theoretic techniques to systems of interacting electrons. The terminology of the order parameter for the field ϕ is to indicate the treatment of the Coulomb interaction within a mean-field theory with the inclusion of Gaussian fluctuations around the mean-field value of the order parameter.

CRC Press eBooksJun 20, 20190 citations

ϕ^4

theory in 1+1 dimensions. We show that standard RPA approach leads to an instability which can be removed when going to a superior version,i.e. the renormalized RPA. We present a method based on the so-called charging formula of the many electron problem to calculate the correlation energy and the RPA effective potential.