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.

scholarly journals Feynman Rules for Magnetised Spin-O Bosons

1991 ◽  
Vol 44 (4) ◽  
pp. 335
Author(s):  
ET Rowe
Keyword(s):  
Vertex Function ◽  
Gordon Equation ◽  
Feynman Diagrams ◽  
New Class ◽  
Two Photon ◽  
S Matrix ◽  
Matrix Expansion ◽  
Feynman Rules ◽  
Klein Gordon ◽  
Klein Gordon Equation

Solutions of the Klein-Gordon equation are given in the Landau and cylindrical gauges and these are used to calculate explicit forms of the vertex function. From an S-matrix expansion analogous to the spin-i case we obtain the Feynman rules for magnetised spin-O particles: the major differences between the spin-i and spin-O cases are the explicit forms of the respective vertex functions and the addition of a two-photon vertex in the spin-O case. This additional vertex makes possible a whole new class of Feynman diagrams.

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 Infrared-safe scattering without photon vacuum transitions and time-dependent decoherence

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Dominik Neuenfeld
Keyword(s):  
Low Energy ◽  
Time Dependent ◽  
Matrix Elements ◽  
Scattering Process ◽  
Zero Energy ◽  
Ir Radiation ◽  
S Matrix ◽  
Inequivalent Representations ◽  
Infrared Divergences ◽  
Over Time

Abstract Scattering in 3 + 1-dimensional QED is believed to give rise to transitions between different photon vacua. We show that these transitions can be removed by taking into account off-shell modes which correspond to Liénard-Wiechert fields of asymptotic states. This makes it possible to formulate scattering in 3 + 1-dimensional QED on a Hilbert space which furnishes a single representation of the canonical commutation relations (CCR). Different QED selection sectors correspond to inequivalent representations of the photon CCR and are stable under the action of an IR finite, unitary S-matrix. Infrared divergences are cancelled by IR radiation. Using this formalism, we discuss the time-dependence of decoherence and phases of out-going density matrix elements in the presence of classical currents. The results demonstrate that although no information about a scattering process is stored in strictly zero-energy modes of the photon field, entanglement between charged matter and low energy modes increases over time.

scholarly journals Discrete phase space, relativistic quantum electrodynamics, and a non-singular Coulomb potential

2020 ◽  
Vol 35 (24) ◽  
pp. 2050199
Author(s):  
Anadijiban Das ◽  
Rupak Chatterjee ◽  
Ting Yu
Keyword(s):  
Phase Space ◽  
Coulomb Potential ◽  
Quantum Electrodynamics ◽  
Relativistic Quantum ◽  
Mathematical Formulation ◽  
Dirac Field ◽  
Field Equations ◽  
Partial Difference ◽  
Moller Scattering ◽  
Discrete Phase

This paper deals with the relativistic, quantized electromagnetic and Dirac field equations in the arena of discrete phase space and continuous time. The mathematical formulation involves partial difference equations. In the consequent relativistic quantum electrodynamics, the corresponding Feynman diagrams and [Formula: see text]-matrix elements are derived. In the special case of electron–electron scattering (Møller scattering), the explicit second-order element [Formula: see text] is deduced. Moreover, assuming the slow motions for two external electrons, the approximation of [Formula: see text] yields a divergence-free Coulomb potential.

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 Discrete phase space - I: Variational formalism for classical relativistic wave fields

2010 ◽  
Vol 88 (2) ◽  
pp. 73-91 ◽  
Author(s):  
A. Das
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Wave Equations ◽  
Relativistic Wave ◽  
Lagrange Equations ◽  
Partial Difference ◽  
S Matrix ◽  
Discrete Phase ◽  
Space Formulation ◽  
The Difference

This is the first in a series of papers dealing with a discrete phase space formulation for classical and quantum fields. This formulation leads to a representation of quantum field theory that is covariant and possesses singularity free S-matrix. In this paper, the classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and continuous time. The relativistic invariance and covariance of the equations in both versions are established. The partial difference and difference-differential equations are derived as the Euler–Lagrange equations from the variational principle. The difference and difference-differential conservation equations are derived. Finally, the total momentum, energy, and charge of the relativistic classical fields satisfying difference-differential equations are computed.

scholarly journals Classical black hole scattering from a worldline quantum field theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gustav Mogull ◽  
Jan Plefka ◽  
Jan Steinhoff
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Quantum Field ◽  
Expectation Values ◽  
Path Integral Representation ◽  
S Matrix ◽  
Feynman Rules ◽  
Definition Of ◽  
Three Body

Abstract A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field hμν(x) and position $$ {x}_i^{\mu}\left({\tau}_i\right) $$ x i μ τ i of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈hμv(k)〉 and 2PM two-body deflection $$ \Delta {p}_i^{\mu } $$ Δ p i μ from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2 → 2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.

scholarly journals ON CANONICAL QUANTIZATION OF THE GAUGED WZW MODEL WITH PERMUTATION BRANES

2011 ◽  
Vol 26 (26) ◽  
pp. 4647-4660
Author(s):  
GOR SARKISSIAN
Keyword(s):  
Riemann Surface ◽  
Phase Space ◽  
Boundary Conditions ◽  
Canonical Quantization ◽  
Simons Theory ◽  
Gauge Fields ◽  
Time Line ◽  
Chern Simons ◽  
Special Case ◽  
Chern Simons Theory

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the N-fold product of the gauged WZW model G/H on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern–Simons theory on a sphere with N holes times the time-line with G and H gauge fields both coupled to two Wilson lines. For the special case of the topological coset G/G we arrive at the conclusion that the phase space of the N-fold product of the topological coset G/G on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern–Simons theory on a Riemann surface of the genus N-1 times the time-line with four Wilson lines.

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