Lehmann-Symanzik-Zimmermann Formalism in the Lee Model

Maxon, M. Stephen; Curtis, Richard B.

doi:10.1103/physrev.137.b996

Cited by 29 publications

(8 citation statements)

References 4 publications

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“…8 of [55]. 2 These four functions are analogous to the fourτ functions in [56]. since |k↓ and |↑ are eigenstates of H 0 .…”

Section: Definitionsmentioning

confidence: 96%

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Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides

Kocabaş

2016

Phys. Rev. A

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We study one-and two-photon scattering from a qubit embedded in a one-dimensional waveguide in the presence of modal dispersion. We use a resolvent based analysis and utilize techniques borrowed from the Lee model studies. Modal dispersion leads to atom-photon bound states which necessitate the use of multichannel scattering theory. We present multichannel scattering matrix elements in terms of the solution of a Fredholm integral equation of the second kind. Through the use of the Lippmann-Schwinger equation, we derive an infinite series of Feynman diagrams that represent the solution to the integral equation. We use the Feynman diagrams as vertex correction terms to come up with closed form formulas that successfully predict the trapping rate of a photon in the atom-photon bound state. We verify our formalism through Krylov-subspace based numerical studies with pulsed excitations. Our results provide the tools to calculate the complex correlations between scattered photons in a dispersive environment.

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“…8 of [55]. 2 These four functions are analogous to the fourτ functions in [56]. since |k↓ and |↑ are eigenstates of H 0 .…”

Section: Definitionsmentioning

confidence: 96%

“…ONE-PHOTON SCATTERING, BOUND STATES, FEYNMAN DIAGRAM REPRESENTATION We will first start by calculations in the one-photon sector. The notation we use is borrowed from [56] in which the Lee model is solved in its lowest excitation sector. There are four relevant matrix elements of G(z) 2…”

Section: Definitionsmentioning

confidence: 99%

Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides

Kocabaş

2016

Phys. Rev. A

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“…We mention that the computational procedure of solving such equations is well known, so we do not insist here on a detailed discussion. where the operators "in" and "out" are defined in the sense of LSZ as weak limits of the HEISENBERG fields a t t 3 00 (see e. g. [15]). At this point we must notice that since the physical and bare states for the N and 8 particles are equi-valent, the asymptotic conditions are well defined.…”

Section: Dk-(w)mentioning

confidence: 99%

Lehmann‐Symanzik‐Zimmermann Formalism in the (n, 2) Sector of the Lee Model

Uliu

1970

Annalen der Physik

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In this work the LE~NN-SYMANZIK-ZIMMERMANN treatment of the (n, 2) sector of the LEE model is given. All physical quantities are expressed by means of the ?-functions.It is found that the solutions of two singular integral equations solve the entire seotor. IntroductionModel field theories have been developed in order to get some insight into several problems which are also encountered in the relativistic quantum field theory. For example, the LEE model [l, 21 and its generalizations have proved to be useful in renormalization theory [3], the description of unstable particles in field theory [4-61, the effects of resonant final -state interactions on scattering and production amplitudes [ 71, the study of elementarity and compositiveness [8-lo], the meaning of the bootstrap mechanism [ll, 121, and others.In the last 15 years the LEE model has been investigated by various techniques: the dispersional approach [13,14], the LSZ formalism [15-201, the

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“…The dispersion theory technique based on the LEHMANN SYMANZIK--ZIMMERMAN~ formalism [2] has been used by TREIMAr~ and GOLDRERGER [3] to calculate NO scattering in the V-sector of the LEE model. MAXON and CURTIS [5] have first used the LSZ-formalism to evaluate all processes simultaneously including the eigenvalue problem in a sector. All such ealculations were restricted to a particular process in one sector of the LEE model.…”

Section: Introductionmentioning

confidence: 99%

“…All such ealculations were restricted to a particular process in one sector of the LEE model. In V-and VNsectors the solutions can be obtained in a straightforward manner as shown by MAXON and CURTIS [5] and SCARFONE [7]. The basic idea behind their computation was to get linear differential equations for the z-functions that appear in the S-matrix, which are called MATTHEWS SALAM [6] equations.…”

Section: Introductionmentioning

confidence: 99%

Multichannel processes inV- andVΘ i -sectors in an extended Lee model

Choudhury

1974

Acta Physica

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The LEHMANN--SYMANZIK--ZIMMEIIM&NN (LSZ) formalism is used in a multi-O extended LEE model to calculate the relevant multichannel scattering and production amplitudes. The extended rr/ulti-O LEE model introduces nO particles in addition to heavy recoi]less V and N particles of the normal LEE mode]. The processes allowed ate V ~~_ NOi, for i = = 1,2 ..... n. In the V-and VOi-sectors, a]l the T-functions are obtained by solving the MATTHEWS--SALAM equations for the T-functions. The multichanne] seattering and production amplitudes ate also evaluated.

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Lehmann-Symanzik-Zimmermann Formalism in the Lee Model

Cited by 29 publications

References 4 publications

Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides

Effects of modal dispersion on few-photon–qubit scattering in one-dimensional waveguides

Lehmann‐Symanzik‐Zimmermann Formalism in the (n, 2) Sector of the Lee Model

Multichannel processes inV- andVΘ i -sectors in an extended Lee model

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