Functional integral representation of the nuclear many-body grand partition function

Kerman, A.K.; Troudet, T.

doi:10.1016/0003-4916(84)90159-3

Cited by 22 publications

(19 citation statements)

References 15 publications

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“…There is a completely general formalism of a many-body system using grand partition function [25] where the transformation (2) plays an important role in linearizing the two-body part of the Hamiltonian. We do not discuss this aspect of many-body theory here as it is outside the scope of the present article.…”

Section: Asmentioning

confidence: 99%

Non-Linear Transformations and Their Applications in Many-Body Physics

Ullah

1994

Fortschr. Phys.

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The transformations of the type which convert an exponential into a Gaussian and vice-versa and their applications in various areas of many-body physics are discussed. A new and general method of obtaining such transformations is given using the method of moments. It is compared with other methods which could be employed to obtain such transformations. In atomic physics, we have shown how such transformations can be used to obtain electron interaction energy for the ground state of Helium and Wigner transform for the ground state of H atom. It is shown how to bring angular momentum operators to linear form so that one can use the usual property of rotation operator to calculate their matrix elements. A new way of calculating the approximate eigenvalues of a Hamiltonian is given which combines the variational principles with the principle of maximum entropy. The anharmonic oscillator Hamiltonian is used to illustrate this new method. An interesting aspect of these transformations is that one could combine them with other transformations like Grassmann integration to calculate quantities of physical interest in closed form. A general matrix element of the harmonic oscillator is given which can be used to calculate usual quantities like the trace and density matrix. Some future applications are also discussed.

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Section: Asmentioning

confidence: 99%

Non-Linear Transformations and Their Applications in Many-Body Physics

Ullah

1994

Fortschr. Phys.

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“…We use a formulation [9] which is very close to the standard language of non-relativistic, extended mean field approaches of the Hartree-Fock-Bogolyubov type, which can on the other hand be directly related to the methods adopted in connection with the Schro dinger representation of quantum field theory [10]. Although for simplicity we restrict ourselves to the case of uniform systems, extending the formulation to finite, inhomogeneous systems such as those actually realized in the recent alkeli atom experiments is completely straightforward [8] using well known many-body techniques [12]. The inclusion of finite temperature effects is also straightforward in the formulation we use, so that thermodynamic properties can be studied rather easily.…”

Section: Introductionmentioning

confidence: 99%

Non-ideal Boson System in the Gaussian Approximation

Tommasini

Piza

1997

Annals of Physics

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We investigate ground-state and thermal properties of a system of non-relativistic bosons interacting through repulsive, two-body interactions in a self-consistent Gaussian mean-field approximation which consists in writing the variationally determined density operator as the most general Gaussian functional of the quantized field operators. Finite temperature results are obtained in a grand canonical framework. Contact is made with the results of Lee, Yang, and Huang in terms of particular truncations of the Gaussian approximation. The full Gaussian approximation supports a free phase or a thermodynamically unstable phase when contact forces and a standard renormalization scheme are used. When applied to a Hamiltonian with zero range forces interpreted as an effective theory with a high momentum cutoff, the full Gaussian approximation generates a quasi-particle spectrum having an energy gap, in conflict with perturbation theory results. Academic Press

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“…aproximação gaussiana. Além disto, a e.xpansão conserva a energia: no caso de sistemas fechados, ordem a ordem [261. [,sta t,écnica foi recentemente aplicada, no contexto de urna Teoria Quântíca de Campos: a teoria bosônica autointera~ gente >"4>4 em (1 + 1) dimensões [2,5]. Lin e Toledo Piza [25] obtiveram que a aproximação gaussiana falha tanto qualitativamente como quantitativamente na descrição de certos oh serváveis.…”

Section: Capítulounclassified

“…Com o objetivo de renormalizar a teoria, consideremos as soluções estacionárias para o vácuo das eqs. (5.18)1 (5.21) (4)))] ,ín I'kl., = O (5,27) [k' + (m -g (4)ll,,),Q"] (5,28) cot 21',1., = -[iÚ (m g (4)11.,)J[kloos7,1., …”

Section: Renorrnalizaçãounclassified

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Extensão da Aproximação de Campo Médio para a Evolução de Sistemas Férmion-Bóson

Natti¹,

Regina²

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Functional integral representation of the nuclear many-body grand partition function

Cited by 22 publications

References 15 publications

Non-Linear Transformations and Their Applications in Many-Body Physics

Non-Linear Transformations and Their Applications in Many-Body Physics

Non-ideal Boson System in the Gaussian Approximation

Extensão da Aproximação de Campo Médio para a Evolução de Sistemas Férmion-Bóson

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