A derivation of the virial expansion with application to Euclidean quantum field theory

Menikoff, Ralph; Sharp, David H.

doi:10.1063/1.523531

Cited by 17 publications

(4 citation statements)

References 26 publications

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“…We are developing our perturbative expansion around the static ultra-local functional Q 0 (h) [66] [74] [75] [76]. Fields defined in different points of the Euclidean space are decoupled in the ultralocal approximation since the gradient term is dropped.…”

Section: Introductionmentioning

confidence: 99%

The strong-coupling expansion and the ultra-local approximation in field theory

Svaiter

2005

Physica A: Statistical Mechanics and its Applications

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We discuss the strong-coupling expansion in Euclidean field theory. In a formal representation for the Schwinger functional, we treat the off-diagonal terms of the Gaussian factor as a perturbation about the remaining terms of the functional integral. In this way, we develop a perturbative expansion around the ultra-local model, where fields defined at different points of Euclidean space are decoupled. We first study the strong-coupling expansion in the (λϕ 4 ) d theory and also quantum electrodynamics. Assuming the ultra-local approximation, we examine the singularities of these perturbative expansions, analysing the analytic structure of the zerodimensional generating functions in the complex coupling constants plane. Second, we discuss the ultra-local generating functional in two idealized field theory models defined by the following interaction Lagrangians: L II (g 1 , g 2 ; ϕ) = g 1 ϕ p (x) + g 2 ϕ −p (x), and the sinh-Gordon model, i.e., L III (g 3 , g 4 ; ϕ) = g 3 (cosh(g 4 ϕ(x)) − 1). To control the divergences of the strong-coupling pertur-bative expansion two different steps are used throughout the paper. First, we introduce a lattice structure to give meaning to the ultra-local generating functional. Using an analytic regularization procedure we discuss briefly how it is possible to obtain a renormalized Schwinger functional associated with these scalar models, going beyond the ultra-local approximation without using a lattice regularization procedure. Using the strong-coupling perturbative expansion we show how it is possible to compute the renormalized vacuum energy of a self-interacting scalar field, going beyond the one-loop level.

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Section: Introductionmentioning

confidence: 99%

The strong-coupling expansion and the ultra-local approximation in field theory

Svaiter

2005

Physica A: Statistical Mechanics and its Applications

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“…Therefore we are developing our perturbative expansion around the independent-value generating functional Q 0 (h), where different points of the Euclidean space are decoupled [8] [9] [10]. The fundamental problem of the strong-coupling expansion is how to give meaning to the independent-value generating functional.…”

Section: Pos(wc2004)021mentioning

confidence: 99%

The Partition Function for Anharmonic Oscillator in the Strong-Coupling Regime

Svaiter¹

2004

Proceedings of Fourth International Winter Conference on Mathematical Methods in Physics — PoS(WC2004)

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We consider a single anharmonic oscillator with frequency ω and coupling constant λ respectively, in the strong-coupling regime. We are assuming that the system is in thermal equilibrium with a reservoir at temperature β −1 . Using the strong-coupling perturbative expansion, we obtain the partition function for the oscillator in the regime λ >> ω, up to the order 1 √ λ. To obtain this result, we use of a combination of Klauder's independent-value generating functional (Acta Phys. Austr. 41, 237 (1975)), and the spectral zeta function method. The free energy and the mean energy, up to the order 1 √ λ , are also presented.

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“…We study the dominant replica partition function using a representation closely related to the strong-coupling expansion in field theory investigated in Refs. [59][60][61][62]. See also the linked-cluster expansion [63][64][65][66][67].…”

Section: Introductionmentioning

confidence: 99%

Spontaneous symmetry breaking in replica field theory

et al. 2017

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In this paper we discuss a disordered d-dimensional Euclidean λϕ 4 model. The dominant contribution to the average free energy of this system is written as a series of the replica partition functions of the model. In each replica partition function, using the saddle-point equations and imposing the replica symmetric ansatz, we show the presence of a spontaneous symmetry breaking mechanism in the disordered model. Moreover, the leading replica partition function must be described by a large-N Euclidean replica field theory. We discuss finite temperature effects considering periodic boundary condition in Euclidean time and also using the Landau-Ginzburg approach. In the low temperature regime we prove the existence of N instantons in the model.

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A derivation of the virial expansion with application to Euclidean quantum field theory

Cited by 17 publications

References 26 publications

The strong-coupling expansion and the ultra-local approximation in field theory

The strong-coupling expansion and the ultra-local approximation in field theory

The Partition Function for Anharmonic Oscillator in the Strong-Coupling Regime

Spontaneous symmetry breaking in replica field theory

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