A single Lanczos propagation method for calculating transition amplitudes. III. S-matrix elements with a complex-symmetric Hamiltonian

2001 ◽  
Vol 115 (21) ◽  
pp. 9637-9643 ◽  
Author(s):  
Shenmin Li ◽  
Guohui Li ◽  
Hua Guo
Keyword(s):  
Matrix Elements ◽  
S Matrix ◽  
Complex Symmetric ◽  
Transition Amplitudes

Functional Solution Scheme for Relativistic Strong Coupling Theor

1964 ◽  
Vol 19 (7-8) ◽  
pp. 828-834
Author(s):  
G. Heber ◽  
H. J. Kaiser
Keyword(s):  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Functional Integral ◽  
The Self ◽  
Matrix Elements ◽  
Point Function ◽  
Expectation Value ◽  
Lattice Space ◽  
S Matrix ◽  
Functional Solution

The vacuum expectation value of the S-matrix is represented, following HORI, as a functional integral and separated according to Svac=exp( — i W) ∫ D φ exp( —i ∫ dx Lw). Now, the functional integral involves only the part Lw of the Lagrangian without derivatives and can be easily calculated in lattice space. We propose a graphical scheme which formalizes the action of the operator W = f dx dy δ (x—y) (δ/δ(y))⬜x(δ/δ(x)) . The scheme is worked out in some detail for the calculation of the two-point-function of neutral BOSE fields with the self-interaction λ φM for even M. A method is proposed which under certain convergence assumptions should yield in a finite number of steps the lowest mass eigenvalues and the related matrix elements. The method exhibits characteristic differences between renormalizable and nonrenormalizable theories.

scholarly journals ELECTROWEAK THEORY WITHOUT HIGGS BOSONS

2000 ◽  
Vol 15 (10) ◽  
pp. 1497-1519
Author(s):  
ANGUS F. NICHOLSON ◽  
DALLAS C. KENNEDY
Keyword(s):  
Higgs Bosons ◽  
Gauge Parameter ◽  
Electroweak Theory ◽  
Matrix Elements ◽  
S Matrix ◽  
Novel Method ◽  
The Masses

A perturbative SU (2)L× U (1)Y electroweak theory containing W, Z, photon, ghost, lepton and quark fields, but no Higgs or other fields, gives masses to W, Z and the nonneutrino fermions by means of an unconventional choice for the unperturbed Lagrangian and a novel method of renormalization. The renormalization extends to all orders. The masses emerge on renormalization to one loop. To one loop the neutrinos are massless, the A↔Z transition drops out of the theory, the d quark is unstable and S matrix elements are independent of the gauge parameter ξ.

Dimensional reduction and background field quantization

1982 ◽  
Vol 60 (10) ◽  
pp. 1429-1430
Author(s):  
Gerry McKeon
Keyword(s):  
Dimensional Reduction ◽  
Background Field ◽  
Matrix Elements ◽  
S Matrix ◽  
Considerable Simplification ◽  
Field Quantization

It is pointed out that if one uses dimensional reduction to regularize integrals that arise when one evaluates S-matrix elements defined by background field quantization, a considerable simplification occurs.

scholarly journals A New Family of Interactions between Clothed Particles in QED

2021 ◽  
Vol 66 (10) ◽  
pp. 833
Author(s):  
A. Arslanaliev ◽  
Y. Kostylenko ◽  
O. Shebeko
Keyword(s):  
Perturbation Theory ◽  
Compton Scattering ◽  
Quantum Electrodynamics ◽  
Matrix Elements ◽  
Energy Shell ◽  
New Family ◽  
Shell Matrix ◽  
Electron Positron ◽  
S Matrix ◽  
Novel Interactions

The method of unitary clothing transformations (UCTs) has been applied to the quantum electrodynamics (QED) by using the clothed particle representation (CPR). Within CPR, the Hamiltonian for interacting electromagnetic and electron-positron fields takes the form in which the interaction operators responsible for such two-particle processes as e−e− → e−e−, e+e+ → e+e+, e−e+ → e−e+, e−e+ → yy, yy → e−e+, ye− → ye−, and ye+ → ye+ are obtained on the same physical footing. These novel interactions include the off-energy-shell and recoil effects (the latter without any expansion in (v/c)2-series) and their on-energy shell matrix elements reproduce the well-known results derived within the perturbation theory based on the Dyson expansion for the S-matrix (in particular, the Møller formula for the e−e−-scattering, the Bhabha formula for e−e+-scattering, and the Klein–Nishina one for the Compton scattering).

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