scholarly journals Gauge-Independent Calculation of S-Matrix Elements in Quantum Electrodynamics

1983 ◽  
Vol 69 (4) ◽  
pp. 1225-1235 ◽  
Author(s):  
Y. Kakudo ◽  
Y. Taguchi ◽  
A. Tanaka ◽  
K. Yamamoto
Keyword(s):  
Quantum Electrodynamics ◽  
Matrix Elements ◽  
S Matrix ◽  
Independent Calculation

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).

scholarly journals Discrete phase space - III: The divergence-free S-matrix elements

2010 ◽  
Vol 88 (2) ◽  
pp. 111-130
Author(s):  
A. Das
Keyword(s):  
Phase Space ◽  
Vertex Function ◽  
Quantum Electrodynamics ◽  
Final Section ◽  
Matrix Elements ◽  
S Matrix ◽  
Feynman Rules ◽  
Discrete Phase ◽  
Infrared Divergences ◽  
Special Case

In the arena of the discrete phase space and continuous time, the theory of S-matrix is formulated. In the special case of quantum electrodynamics (QED), the Feynman rules are precisely developed. These rules in the four-momentum turn out to be identical to the usual QED, except for the vertex function. The new vertex function is given by an infinite series that can only be treated in an asymptotic approximation at the present time. Preliminary approximations prove that the second-order self-energies of a fermion and a photon in the discrete model have convergent improper integrals. In the final section, a sharper asymptotic analysis is employed. It is proved that in case where the number of external photon or fermion lines is at least one, then the S-matrix elements converge in all orders. Moreover, there are no infrared divergences in this formulation.

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 Normalizability analysis of the generalized quantum electrodynamics from the causal point of view

2017 ◽  
Vol 32 (27) ◽  
pp. 1750165 ◽  
Author(s):  
R. Bufalo ◽  
B. M. Pimentel ◽  
D. E. Soto
Keyword(s):  
Perturbation Theory ◽  
Physical Model ◽  
Gauge Invariance ◽  
Quantum Electrodynamics ◽  
Lorentz Invariance ◽  
Point Of View ◽  
Inductive Method ◽  
S Matrix ◽  
Causal Approach

The causal perturbation theory is an axiomatic perturbative theory of the S-matrix. This formalism has as its essence the following axioms: causality, Lorentz invariance and asymptotic conditions. Any other property must be showed via the inductive method order-by-order and, of course, it depends on the particular physical model. In this work we shall study the normalizability of the generalized quantum electrodynamics in the framework of the causal approach. Furthermore, we analyze the implication of the gauge invariance onto the model and obtain the respective Ward–Takahashi–Fradkin identities.

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.

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