Effective Potential for a Renormalized<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-Dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>Field Theory in the Limit<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>→</mml:mo>

Bender, Carl M.; Cooper, Fred; Guralnik, G. S.; Moreno, H.; Roskies, Ralph; Sharp, David H.

doi:10.1103/physrevlett.45.501

Cited by 42 publications

(28 citation statements)

References 7 publications

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“…Weak perturbation theory generally proves to be insufficient to extract all the physics. A well-known case is given by quantum chromodynamics that due to the strength of the coupling constant at low energies, makes useless known perturbation techniques demanding the need for numerical solutions.In the seventies and eighties of the last century a significant attempt to build a perturbation theory for a strongly interacting quantum field theory was proposed [1,2,3,4,5,6,7,8]. In this approach it was stipulated that the perturbation to be considered is the free part of the Lagrangian.…”

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confidence: 99%

Strongly coupled quantum field theory

Frasca¹

2006

Phys. Rev. D

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We analyze numerically a two-dimensional λφ 4 theory showing that in the limit of a strong coupling λ → ∞ just the homogeneous solutions for time evolution are relevant in agreement with the duality principle in perturbation theory as presented in [M.Frasca, Phys. Rev. A 58, 3439 (1998)], being negligible the contribution of the spatial varying parts of the dynamical equations. A consequence is that the Green function method works for this non-linear problem in the large coupling limit as in a linear theory. A numerical proof is given for this. With these results at hand, we built a strongly coupled quantum field theory for a λφ 4 interacting field computing the first order correction to the generating functional. Mass spectrum of the theory is obtained turning out to be that of a harmonic oscillator with no dependence on the dimensionality of spacetime. The agreement with the Lehmann-Källen representation of the perturbation series is then shown at the first order.A lot of problems in physics have such a difficult equations to solve that the most natural approach is a numerical one. Weak perturbation theory generally proves to be insufficient to extract all the physics. A well-known case is given by quantum chromodynamics that due to the strength of the coupling constant at low energies, makes useless known perturbation techniques demanding the need for numerical solutions.In the seventies and eighties of the last century a significant attempt to build a perturbation theory for a strongly interacting quantum field theory was proposed [1,2,3,4,5,6,7,8]. In this approach it was stipulated that the perturbation to be considered is the free part of the Lagrangian. Notwithstanding this approach is still studied today [9] no fruitful results have been obtained so far due to the strongly singular perturbation series that is obtained in this way. Rather, the rationale behind this method is really smart as one recognize that just interchanging the two parts of the Lagrangian one gets different perturbation series.This duality in perturbation theory is a general mathematical property of differential equations as was shown in Ref. [10,11]. What makes duality interesting is the general property of the leading order that, while in the weak perturbation case is just a free linear theory whose solution is generally known, for the dual series that holds in the limit of a strongly coupling, that is a coupling going to infinity, one can prove a theorem showing that the adiabatic approximation applies. We also pointed out in recent works [12,13] that in field theory and general relativity the dual perturbation series at the leading order produces a rather interesting result: in a strongly coupled field theory the leading order is ruled by a homogeneous equation, that is, the spatial variation of the field in the equations of the theory becomes negligible. In general relativity this gives precious informations on the space-time near a singularity where the above behavior was conjectured in [14,15,16] and numerically shown in [17]...

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confidence: 99%

Strongly coupled quantum field theory

Frasca¹

2006

Phys. Rev. D

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“…The limit λ → ∞ has been analyzed in [22,23,24,25,26,27,28,29,30]. These authors showed that when the full kinematical term (∂φ) 2 is taken as a perturbation, a perturbation series is obtained that depends on a regularization parameter a with the interesting limit a → 0 very singular.…”

Section: Infrared Limit Of a Massless Scalar Field Theorymentioning

confidence: 99%

Infrared gluon and ghost propagators

Frasca¹

2008

Physics Letters B

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We derive the form of the infrared gluon propagator by proving a mapping in the infrared of the quantum Yang-Mills and λφ 4 theories. The equivalence is complete at a classical level. But while at a quantum level, the correspondence is spoiled by quantum fluctuations in the ultraviolet limit, we prove that it holds in the infrared where the coupling constant happens to be very large. The infrared propagator is then obtained from the quantum field theory of the scalar field producing a full spectrum. The results are in fully agreement with recent lattice computations. We get a finite propagator at zero momentum, the ghost propagator going to infinity as 1/p 2+2κ with κ = 0.

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“…This is the Landau pole problem and is related to the triviality of the theory. [23] [24]. As is discussed in detail in the appendix, the bare and renormalized couplings are related by the equation:…”

Section: Model and Approximationsmentioning

confidence: 99%

“…al. [24] To make our presentation more clear it may be useful to put together the set of equations we will solve. They arë…”

Section: Initial Conditions and Renormalizationmentioning

confidence: 99%

Quantum evolution of disoriented chiral condensates

et al. 1995

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The nonequilibrium dynamics of the chiral phase transition expected during the expansion of the quark-qluon plasma produced in a high energy hadron or heavy ion collision is studied in the O(4) linear sigma model to leading order in a large N expansion. Starting from an approximate equilibrium configuration at an initial proper time τ in the disordered phase we study the transition to the ordered broken symmetry phase as the system expands and cools. We give results for the proper time evolution of the effective pion mass, the order parameter < σ > as well as for the pion two point correlation function expressed in terms of a time dependent phase space number density and pair correlation density. We determine the phase space of initial conditions that lead to instabilities (exponentially growing long wave length modes) as the system evolves in time. These instabilities are what eventually lead to disoriented chiral condensates. In our simulations,we found that instabilities that are formed during the initial phases of the expansion exist for proper times that are at most 3 f m/c and lead to condensate regions that do not contain large numbers of particles. The damping of instabilities is a consequence of strong coupling.

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Effective Potential for a Renormalizedd-Dimensionalgϕ4Field Theory in the Limitg→

Cited by 42 publications

References 7 publications

Strongly coupled quantum field theory

Strongly coupled quantum field theory

Infrared gluon and ghost propagators

Quantum evolution of disoriented chiral condensates

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