Particle spectrum in model field theories from semiclassical functional integral techniques

Dashen, Roger; Hasslacher, Brosl; Neveu, A.

doi:10.1103/physrevd.11.3424

Cited by 674 publications

(496 citation statements)

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“…The particles with mass M s = Ms = 8 √ α 0 /β 2 are single solitons and antisolitons, which masses do not contain quantum corrections [19]. The single solitons and antisolitons are described by (1.6).…”

Section: Particle Mass Spectramentioning

confidence: 99%

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Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Faber

Ivanov²

2003

J. Phys. A: Math. Gen.

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We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088Rev. D 11, (1975. According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants β 2 > 8π. The consequence of this theorem would be the non-existence of the quantum ground state of the sineGordon model for β 2 > 8π. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for β 2 > 8π. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model. *

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Section: Particle Mass Spectramentioning

confidence: 99%

“…Breathers describe soliton-antisoliton bound states [19]. In the rest frame the classical solution corresponding to the nth quantum state reads [17,19] …”

Section: Particle Mass Spectramentioning

confidence: 99%

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Faber

Ivanov²

2003

J. Phys. A: Math. Gen.

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“…Provided that a specific counterterm which depends on the field is added to the Lagrangian, the S-matrix is also factorisable at one-loop level. In their following paper [11] they used the inverse scattering method to obtain the classical two-soliton solution and the spectrum of states using the semi-classical methods by Dashen, Hasslacher and Neveu [12,13].…”

Section: Quantum Complex Sine-gordon Theory In the Bulkmentioning

confidence: 99%

“…The fact that the model possesses exact periodic solutions bound to the boundary makes the stationary-phase method a suitable candidate for their quantisation. The method is based on the work of Dashen, Hasslacher and Neveu [12,13] for the semi-classical quantisation of the sine-Gordon model. In this case it appears as a generalised version of the Bohr-Sommerfeld quantisation rule…”

Section: Semi-classical Quantisationmentioning

confidence: 99%

Quantum complex sine-Gordon model on a half line

Bowcock

Tzamtzis

2007

J. High Energy Phys.

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In this paper, we examine the quantum complex sine-Gordon model on a half line. We obtain the quantum spectrum of boundary bound states using the the semiclassical method of Dashen, Hasslacher and Neveu. The results are compared and found to agree with the bootstrap programme. A particle/soliton reflection factor is conjectured, which is consistent with unitary, crossing and our semi-classical results.

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“…The traditional bound-state picture 56 ) typically involves the ladder approximation for a scattering amplitude. The semi-classical approaches 57 ) …”

Section: Asymptotic Freedom I)mentioning

confidence: 99%

Asymptotic Behaviour in Quantum Field Theory

Crewther¹

1976

Weak and Electromagnetic Interactions at High Energies

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Convergence is tested by applying power-counting arguments 10 • 11 ). Imagine that a subset S = {p~, ... , p~} of the loop momenta {p 1 , ••• , p£} is scaled to infinity [all p~ = O(n) with n ~ 00 ] with all other momenta held fixed*). The exponent c(r) for its asymptotic behaviour as p 1 , ••• , p£ become large is reduced by at least 1, while no increase occurs in the other c(S). Therefore, if a/aq.1.is applied a sufficient number of times tor, the result is completely convergent.Since rd. (the divergent part of r) is annihilated by these differentiations, it lV must be a polynomial of degree~ d(r) in q 1 , ••• , qL-l. In diagrammatic language ( Fig. 1), this means that rd. is a local vertex produced by shrinking the blob r lV to a point.An £-loop divergence of this type is easily cancelled by including a counterterm ~ff£ in the Lagrangian ;t with bare vertex equal to -rdiv' However, many lPI graphs do not possess this property of being "primitively divergent"~<*). An arbitrary £-loop lPI graph may contain divergent £ 1 -loop lPI subgraphs (£ 1 < £) which must first be made convergent by including suitable counterterms ~ff£' in ff; i.e., it will be necessary to include internal counterterm vertices in the blob in Fig. 1. So we try the following prescription 10 • 12 ): *) **)More precisely, write pj = nrj and let n tend to 00 , keeping all rj, Pi ('any pj), and qi fixed and not allowing any partial sum L' r of the rj to vanish.Tfle latter condition ensures that a p 1 -dependent propagator (which carries momentum n l' r + ~p1p' p + f 1 q) has the expected asymptotic dependence on n. The special directions l r = 0 are covered by looking at appropriate su b sets s' of s .A primitively divergent graph becomes convergent if any internal line is cut.-3 -i) Start with !t 0 , a Lagrangian from which propagators and vertices can be constructed.ii) Construct counterterms 62? 1 which remove all divergences in 1-loop lPI graphs generated by 21 0 • iii) Use a new Lagrangian 'l! 1 = :t + 6 'l! to generate 2-loop graphs and construct , a , 16 '/! 2 to get rid of the resulting lPI divergences, and so on, to any finite number of loops and vertices 13 ):J,1 = ii-I + ~£1.Obviously, we obtain finite results for diagrams in which, for each pair of divergent lPI subgraphs, one subgraph is entirely contained within the other ("nested" divergences) or the two subgraphs are disjoint. The difficult step in the proof 12 )of convergence is to disentangle overlapping divergences (sets of divergent lPI graphs which are neither disjoint nor nested). The result, valid for all polynomial interactions (renormalizable or otherwise), is that the above procedure renders all subintegrations convergent by power-counting*). In other words, the Given the constraint (1.6), the rule for renormalization counterterms ~Q generated by lPI diagrams with a single Q-insertion is simply dim(Q) (1. 8) For example, consider = I 2. d);i., 2m1(1. 9)as a trial Lagrangian. Only the two-and four-legged lPI amplitudes r( 2 ),r ( 4 ) are superficially divergent. Accor...

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Particle spectrum in model field theories from semiclassical functional integral techniques

Cited by 674 publications

References 23 publications

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Quantum complex sine-Gordon model on a half line

Asymptotic Behaviour in Quantum Field Theory

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Particle spectrum in model field theories from semiclassical functional integral techniques

Cited by 674 publications

References 23 publications

Is the energy density of the ground state of the sine-Gordon model unbounded from below for 2> 8 ?

Is the energy density of the ground state of the sine-Gordon model unbounded from below for 2> 8 ?

Quantum complex sine-Gordon model on a half line

Asymptotic Behaviour in Quantum Field Theory

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Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?

Is the energy density of the ground state of the sine-Gordon model unbounded from below for ²> 8 ?