Restoration and breakdown of the ϕ→-ϕ symmetry in the (1+1)-dimensional massive sine-Gordon field theory by quantum and finite-temperature effects

Lü, Wei

doi:10.1088/0954-3899/26/8/307

Cited by 5 publications

(1 citation statement)

References 74 publications

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“…On the other hand, we have explicitly shown that, in the case of (1 + 1) dimensional λψ 4 (which is non-integrable), it is not possible to solve in general the recurrence relation establishing the non-linear to linear mapping, except for a restricted class of solutions for f . Other interesting aspects of the sine-Gordon model for which the present approach could be useful are the finite temperature behavior [70] and the duality with the Thirring model both at zero [36] and finite temperature [71].…”

Section: Discussionmentioning

confidence: 99%

Topological Defects as Inhomogeneous Condensates in Quantum Field Theory: Kinks in (1+1) Dimensional λψ4 Theory

Blasone

Jizba²

2002

Annals of Physics

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We study topological defects as inhomogeneous (localized) condensates of particles in quantum field theory. In the framework of the closed-time-path formalism, we consider explicitly a (1 + 1) dimensional λψ 4 model and construct the Heisenberg picture field operator ψ in the presence of kinks. We show how the classical kink solutions emerge from the vacuum expectation value of such an operator in the Born approximation and/or λ → 0 limit. The presented method is general in the sense that it applies also to the case of finite temperature and to non-equilibrium; it also allows for the determination of Green's functions in the presence of topological defects. We discuss the classical kink solutions at T = 0 in the high temperature limit. We conclude with some speculations on the possible relevance of our method for the description of the defect formation during symmetry-breaking phase transitions. C 2002 Elsevier Science (USA)

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Section: Discussionmentioning

confidence: 99%

Topological Defects as Inhomogeneous Condensates in Quantum Field Theory: Kinks in (1+1) Dimensional λψ4 Theory

Blasone

Jizba²

2002

Annals of Physics

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On the renormalization of the bosonized multi-flavor Schwinger model

Nándori

2008

Physics Letters B

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The phase structure of the bosonized multi-flavor Schwinger model is investigated by means of the differential renormalization group (RG) method. In the limit of small fermion mass the linearized RG flow is sufficient to determine the low-energy behavior of the N-flavor model, if it has been rotated by a suitable rotation in the internal space. For large fermion mass, the exact RG flow has been solved numerically. The low-energy behavior of the multi-flavor model is rather different depending on whether N=1 or N>1, where N is the number of flavors. For N>1 the reflection symmetry always suffers breakdown in both the weak and strong coupling regimes, in contrary to the N=1 case, where it remains unbroken in the strong coupling phase.Comment: 13 pages, 2 figures, final version, published in Physics Letters

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Gaussian effective potential and Coleman's normal-ordering prescription: the functional integral formalism

Lü¹,

Kim²

2002

J. Phys. A: Math. Gen.

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For a class of system, the potential of whose Bosonic Hamiltonian has a Fourier representation in the sense of tempered distributions, we calculate the Gaussian effective potential within the framework of functional integral formalism. We show that the Coleman's normal-ordering prescription can be formally generalized to the functional integral formalism.Recently, one of the authors, Lu, with his other collaborators obtained formulae of the Gaussian effective potential (GEP) [1] for a relatively general scalar field theory (see Eq.(1)) in the functional Schrödinger picture [2]. There, the Coleman's normal-ordering prescription [3] was used, and accordingly these formulae have no divergences in low dimensions. Employing these formulae, one can obtain the GEP of any system in a certain class of models, which will be specified below, by carrying out ordinary integrations without performing functional integrations. In this paper, we demonstrate that the same formulae of the GEP can also be obtained within the functional integral formalism. In doing so, we also show that, although quantities in the functional integral formalism are not operators, the Coleman's normal-ordering prescription can be formally used for renormalizing the GEP in the cases of low dimensions. We believe that our simple work is interesting and useful, since the functional integral formalism is importmant in quantum field theory, nuclear and condensed matter physics [4], and can be used for performing some variational perturbation schemes [5,6].In this paper, we first generalize the Coleman's normal-ordering prescription to the functional integral formalism. This formal generalization will be realized by borrowing the normal-ordered Hamiltonian expression in the functional Schrödinger picture because the Euclidean action for a system has the same form with the corresponding classical Hamiltonian in the Minkowski space. Then, following the procedure in Ref.[6], we calculate the GEP for a class of systems. Finishing the above generalization, as an explicit illustration, we will perform a model calculation for the λφ 4 field theory. Consider a class of systems, scalar field systems or Fermi field systems which can be bosonized, with the Lagrangian densitywhere the subscript x represents, x = ( x, t), the coordinates in a (D + 1)-dimensional Minkowski space, ∂ µ and ∂ µ are the corresponding covariant derivatives, and φ x the scalar field at x. In Eq.(1), the potential V (φ x ) has a Fourier reprensentation in a sense of tempered distributions [7]. Speaking roughly, this requires that the integral2 dα with a positive constant C is finite. Obviously, quite a number of model potentials, such as polynomial models, sine-Gordon and sinh-Gordon models, possess this property.For the system, Eq.(1), the conjugate field momentum is expressed as Π x ≡ ∂L ∂(∂tφx) = ∂ t φ x , and the Hamiltonian density is given byIn a time-fixed functional Schrödinger picture at t = 0, one can normal-order the Hamiltonian density H x with respect to any given mass-dimension co...

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Restoration and breakdown of the ϕ→-ϕ symmetry in the (1+1)-dimensional massive sine-Gordon field theory by quantum and finite-temperature effects

Cited by 5 publications

References 74 publications

Topological Defects as Inhomogeneous Condensates in Quantum Field Theory: Kinks in (1+1) Dimensional λψ4 Theory

Topological Defects as Inhomogeneous Condensates in Quantum Field Theory: Kinks in (1+1) Dimensional λψ4 Theory

On the renormalization of the bosonized multi-flavor Schwinger model

Gaussian effective potential and Coleman's normal-ordering prescription: the functional integral formalism

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