Gaussian approximation of the Gross-Neveu model in the functional Schrödinger picture

Kim, SK; Yang, Jie; Soh, Kwang–Sup; Jh, Yee

doi:10.1103/physrevd.40.2647

Cited by 24 publications

(9 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To solve our coupled equations for h and G we continue to use the Pauli basis and the Dirac representation for the α and β matrices featured in the section on the free Dirac theory, and which are described in more detail in the appendix. In agreement with Yee and collaborators [17,18], we find that necessarily Gi = 0 for both the i = 1 and i = 2 matrix components of G in the Pauli basis. Only G3 is non-zero, and we are led to the final form for h and G…”

Section: Gap Equation and Effective Potentialsupporting

confidence: 92%

“…Several groups have applied variational methods to the study of the Gross-Neveu model, including Latorre and Soto [14] and Kovner and Rosenstein [15], as well as J.H. Yee and collaborators [16,17,18], who utilize the Jackiw-Floreanini formalism. The main results of this section and the next are intended as a brief review of these variational methods, and the reader is referred to the literature just cited for more details.…”

Section: Formalismmentioning

confidence: 99%

“…Yee and collaborators [16,17,18] have developed a method for obtaining all of the solutions to the above matrix equations, which we now describe. We will consider the first of the pair of variational equations for G, Eqn.…”

Section: Free Dirac Fieldmentioning

confidence: 99%

“…Unlike the situation with scalar fields, we cannot introduce a variational parameter into the Gaussian variational wavefunctional which is the expectation of a single fermion field and still be consistent with Lorentz invariance. Instead, following the original treatment of Gross and Neveu [10] and within the variational framework discussed by Yee and collaborators [17,18], we introduce a constraint that allows us to consider the expectation value of a fermion bilinear term. We define the auxiliary field σ by…”

Section: Gap Equation and Effective Potentialmentioning

confidence: 99%

See 3 more Smart Citations

Entanglement Entropy of the Gross-Neveu Model

Cotler,

Mueller

2015

Preprint

View full text Add to dashboard Cite

We compute a variational approximation to the entanglement entropy for states of the Gross-Neveu model. Further, we examine the functional dependence of the entanglement entropy on the coupling and number of colors in the theory. Our results display non-peturbative behavior. It is shown that the entanglement entropy is monotonically decreasing and convex with respect to the coupling. We also show how the behavior of the entanglement entropy under renormalization group transformations is related to the beta function of the Gross-Neveu model, and compare these renormalization group results to our previous work on interacting scalar field theories.

show abstract

Section: Gap Equation and Effective Potentialsupporting

confidence: 92%

Section: Formalismmentioning

confidence: 99%

Section: Free Dirac Fieldmentioning

confidence: 99%

Section: Gap Equation and Effective Potentialmentioning

confidence: 99%

See 2 more Smart Citations

Entanglement Entropy of the Gross-Neveu Model

Cotler,

Mueller

2015

Preprint

View full text Add to dashboard Cite

show abstract

“…Our results are nonperturbative and reasonable, though the degree of approximation of the variational approach is difficult to estimate. The earlier investigation by Stevenson [4] and the researches for the bound state [5, 8,9] show that the GWF result is qualitatively correct at least. We hope that the GWF approach can be extended to practical scattering processes such as hydron scattering, etc., which are helpful for the development of quantum field theory.…”

mentioning

confidence: 55%

Variational calculation of the phase shifts in theλφ4model

Lü

Zhang

1994

Phys. Rev. D

View full text Add to dashboard Cite

In this paper, we develop Schiffs discretization procedure for calculating the phase shifts in the hq54 model in (D + 1 )-dimensional space-time (D > 0) with the Gaussian wave-functional approach. In 1 + 1 and 2+ 1 dimensions, the phase shifts are negative, which indicates the interaction between two pions is repulsive. In 3+ 1 dimensions, the phase shifts vanish. We also discuss the dependences of the phase shifts upon the scattering energy in detail.PACS number(s): 11.80.Fv, 11.80.EtThe scattering process serves as a major source of information about the properties of various elementary particles, while the phase shift is a crucial quantity characterizing this process. Traditionally, the scattering problem is coped with mainly by the covariant perturbation technique. Recently, however, the development of the Gaussian wave-functional (GWF) approach has hinted that it is possible to analytically calculate the phase shift in quantum field theory. In the last decade, the Gaussian wave-functional approach in the Schrodinger picture field theory which was gradually developed by Schiff [I], Rosen [2], Barnes and Ghandour [3], etc., has become a powerful tool for investigating the vacuum structure [4-101 as well as searching for the bound states in quantum field theory [5,11,12]. Being explicitly computed, the two-particle state energy may be analyzed to extract knowledge on the phase shift. As an attempt, we have investigated the scattering state in the sinh-Gordon and the sine-Gordon models with this approach [13,14]. In this Brief Report, we continue to study the simplest selfcoupling model, the h44 model, with the same approach.The model was originally introduced into quantum field theory to describe the pion-pion interaction [1,1S]. By now it has become an important model in quantum field theory (including gauge theory), finite-temperature field theory, quantum cosmology, and condensed-matter physics. This model is also an ideal theoretical laboratory for various new methods. Since being advocated [16], the Gaussian wave-functional approach has been used for many problems in ~4~ theory, such as spontaneous symConsider a scalar field 4(x)=4, [ x = ( x l , x 2 , . . . ,x,)is the coordinate in D-dimensional space] described by the Hamiltonian where J x = Jdx = Jdx l d~Z . . dxD and V is the gradient operator in D-dimensional space. m and h are the bare mass and coupling parameters, respectively.From [3,4], the Gaussian vacuum state is where y,z = I dy dz = I d y ,dy2 -. dyDdz ,dz2 . . dz,,

show abstract

Functional Schrödinger picture approach to a dilute bose gas and fluctuation correction to the ground state energy density

et al. 2000

View full text Add to dashboard Cite

A many‐body theoretical scheme based on the functional Schrödinger picture method is formulated for the study of a dilute Bose gas system. The standard ground state properties are obtained by solving the infinite dimensional Schr�dinger equation variationally with a Gaussian trial wavefunctional. It is shown that a shifted Gaussian trial functional enables us to calculate a higher order correction of order na3, which corresponds to the fluctuation constribution from the condensate.

show abstract

Gaussian approximation of the Gross-Neveu model in the functional Schrödinger picture

Cited by 24 publications

References 17 publications

Entanglement Entropy of the Gross-Neveu Model

Entanglement Entropy of the Gross-Neveu Model

Variational calculation of the phase shifts in theλφ4model

Functional Schrödinger picture approach to a dilute bose gas and fluctuation correction to the ground state energy density

Contact Info

Product

Resources

About