Reggeon field theory: Formulation and use

Abarbanel, Henry D. I.; Bronzan, John D.; Sugar, R.; White, Alan R.

doi:10.1016/0370-1573(75)90034-4

Cited by 158 publications

(70 citation statements)

References 50 publications

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“…This field theory was found to be equivalent (Cardy and Sugar, 1980) to the Reggeon field theory (Abarbanel et al, 1975;Brower et al, 1978), which is a model of scattering elementary particles at high energies and lowmomentum transfers. Perturbative ǫ = 4 − d renormalization group analysis (Bronzan and Dash, 1974;Janssen, 1981) up to twoloop order resulted in estimates for the critical exponents shown in the Table XII.…”

Section: A Directed Percolation Classesmentioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.

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Section: A Directed Percolation Classesmentioning

confidence: 99%

Universality classes in nonequilibrium lattice systems

2004

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“…instead of C P P etc. in (7) to recall that P = P + f andÕ = P + ω but we decided not to do it; we will ignore this formal complication throughout the paper. the contribution of all the diagrams (consisting in n Pomerons and m Odderons) is the following…”

Section: Amplitudesmentioning

confidence: 99%

Eikonalization and unitarity constraints

et al. 2000

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An extensive generalization of the ordinary and quasi-eikonal methods is presented for the pp andpp elastic scattering amplitudes, which takes into account in a phenomenological way all intermediate multiparticle states involving the crossing even and crossing odd combinations of Reggeons. The formalism in this version involves a maximum of three parameters corresponding to the intermediate states which are possible in this configuration. The unitarity restriction is investigated and particular cases are discussed. An interesting result that emerges concerns the Odderon trajectory intercept: we find that unitarity dictates that this quantity must be below or equal unity unless a very peculiar equality exists between the coupling of the particles to the Pomeron and the Odderon.

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“…The Lee model is a cubic interaction and there have been several studies of theories having a cubic interaction multiplied by an imaginary coupling constant and in all these studies it was found that the spectrum is real and positive. In two especially important cases it was noticed that the spectrum of Reggeon field theory is real and positive [10] and that the spectrum of Lee-Yang edge-singularity models is also positive [11].…”

Section: Introduction and Brief Review Of The Lee Modelmentioning

confidence: 99%

Ghost busting:PT-symmetric interpretation of the Lee model

et al. 2005

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The Lee model was introduced in the 1950s as an elementary quantum field theory in which mass, wave function, and charge renormalization could be carried out exactly. In early studies of this model it was found that there is a critical value of g 2 , the square of the renormalized coupling constant, above which g 2 0 , the square of the unrenormalized coupling constant, is negative. Thus, for g 2 larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. It was also discovered that in this non-Hermitian regime a new state appears whose norm is negative. This state is called a ghost state. It has always been assumed that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess PT symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having PT symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a new time-independent operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitary. In this paper the C operator for the Lee model in the ghost regime is constructed in the V /N θ sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum field theory for all values of g 2 .

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Reggeon field theory: Formulation and use

Cited by 158 publications

References 50 publications

Universality classes in nonequilibrium lattice systems

Universality classes in nonequilibrium lattice systems

Eikonalization and unitarity constraints

Ghost busting:PT-symmetric interpretation of the Lee model

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