THE SU(2) NONLINEAR σ MODEL IN 2+1 DIMENSIONS: PERTURBATION THEORY IN A POLYNOMIAL FORMULATION

1995 ◽  
Vol 10 (11) ◽  
pp. 1655-1670 ◽  
Author(s):  
C.D. FOSCO ◽  
T. MATSUYAMA
Keyword(s):  
Perturbation Theory ◽  
Vector Field ◽  
Scattering Amplitudes ◽  
Loop Order ◽  
Normal Ordering ◽  
First Order ◽  
Feynman Rules ◽  
Field L ◽  
Polynomial Formulation ◽  
Full Propagator

We construct a perturbation theory for the SU(2) nonlinear σ model in 2+1 dimensions using a polynomial, first-order formulation, where the variables are a non-Abelian vector field Lμ [the left SU(2) current], and a non-Abelian pseudovector field θμ, which imposes the condition Fμv(L)=0. The coordinates on the group do not appear in the Feynman rules, but their scattering amplitudes are easily related to those of the currents. We show that all the infinities affecting physical amplitudes at one-loop order can be cured by normal-ordering, presenting the calculation of the full propagator as an example of an application.

scholarly journals TRANSVERSE WARD–TAKAHASHI RELATION FOR THE FERMION–BOSON VERTEX TO ONE-LOOP ORDER

2006 ◽  
Vol 21 (12) ◽  
pp. 2541-2551 ◽  
Author(s):  
HAN-XIN HE ◽  
F. C. KHANNA
Keyword(s):  
Perturbation Theory ◽  
Gauge Theory ◽  
Loop Order ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Transverse Part ◽  
Feynman Rules ◽  
Covariant Gauge ◽  
The One ◽  
Massless Fermions

In this paper, the transverse Ward–Takahashi relation for the fermion–boson vertex in momentum space is derived in four-dimensional Abelian gauge theory. We show that, by a formal derivation, the transverse Ward–Takahashi relation to one-loop order is satisfied. We also calculate the transverse Ward–Takahashi relation to one-loop order in an arbitrary covariant gauge in the case of massless fermions and find that the result is exactly the same as we obtain in terms of the one-loop fermion–boson vertex calculated in perturbation theory by using Feynman rules. This provides an approach to determine the transverse part of the vertex.

scholarly journals Spurious poles in the scattering of electric and magnetic charges

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
John Terning ◽  
Christopher B. Verhaaren
Keyword(s):  
Perturbation Theory ◽  
Scattering Amplitudes ◽  
Pair Production ◽  
Magnetic Particles ◽  
Single Photon ◽  
Low Energy ◽  
Magnetic Interactions ◽  
Parity Conservation ◽  
Non Local ◽  
The Way

Abstract Theories with both electric and magnetic charges (“mutually non-local” theories) have several major obstacles to calculating scattering amplitudes. Even when the interaction arises through the kinetic mixing of two, otherwise independent, U(1)’s, so that all low-energy interactions are perturbative, difficulties remain: using a self-dual, local formalism leads to spurious poles at any finite order in perturbation theory. Correct calculations must show how the spurious poles cancel in observable scattering amplitudes. Consistency requires that one type of charge is confined as a result of one of the U(1)’s being broken. Here we show how the constraints of confinement and parity conservation on observable processes manages to cancel the spurious poles in scattering and pair production amplitudes, paving the way for systematic studies of the experimental signatures of “dark” electric-magnetic processes. Along the way we demonstrate some novel effects in electric-magnetic interactions, including that the amplitude for single photon production of magnetic particles by electric particles vanishes.

scholarly journals Chiral perturbation theory for GR

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Kirill Krasnov ◽  
Yuri Shtanov
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation ◽  
Perturbative Calculation ◽  
New Formalism ◽  
Yang Mills ◽  
First Order ◽  
Starting Point ◽  
Gauge Fixing ◽  
New Perturbation ◽  
Effective Description

Abstract We describe a new perturbation theory for General Relativity, with the chiral first-order Einstein-Cartan action as the starting point. Our main result is a new gauge-fixing procedure that eliminates the connection-to-connection propagator. All other known first-order formalisms have this propagator non-zero, which significantly increases the combinatorial complexity of any perturbative calculation. In contrast, in the absence of the connection-to-connection propagator, our formalism leads to an effective description in which only the metric (or tetrad) propagates, there are only cubic and quartic vertices, but some vertex legs are special in that they cannot be connected by the propagator. The new formalism is the gravity analog of the well-known and powerful chiral description of Yang-Mills theory.

Note on Interference Effects in Two-Step Reaction Processes

1975 ◽  
Vol 53 (23) ◽  
pp. 2590-2592
Author(s):  
J. Cejpek ◽  
J. Dobeš
Keyword(s):  
Perturbation Theory ◽  
Point Of View ◽  
Order Perturbation ◽  
Interference Effects ◽  
Qualitative Explanation ◽  
First Order ◽  
One Step ◽  
Step Transition ◽  
Reaction Processes ◽  
First Order Perturbation

The reaction processes in which a one-step transition is forbidden are analyzed from the point of view of the first order perturbation theory. The interference between two competing two-step reaction paths is found to be always constructive. A qualitative explanation of the experimentally observed reaction intensities is presented.

scholarly journals Quantum many-body effects on Rydberg excitons in cuprous oxide

2021 ◽  
Author(s):  
D. Semkat ◽  
H. Fehske ◽  
H. Stolz
Keyword(s):  
Perturbation Theory ◽  
Oscillator Strength ◽  
Cuprous Oxide ◽  
Many Body ◽  
Electron Hole ◽  
First Order ◽  
Electron Hole Plasma ◽  
Plasma Line ◽  
Many Body Effects ◽  
First Order Perturbation

AbstractWe investigate quantum many-body effects on Rydberg excitons in cuprous oxide induced by the surrounding electron-hole plasma. Line shifts and widths are calculated by full diagonalisation of the plasma Hamiltonian and compared to results in first order perturbation theory, and the oscillator strength of the exciton lines is analysed.

scholarly journals Mikrowellenspektrum, Struktur, Dipolmoment und internes Hinderungspotential von Dimethyldisulfid

1965 ◽  
Vol 20 (12) ◽  
pp. 1676-1681 ◽  
Author(s):  
D. Sutter ◽  
H. Dreizler ◽  
H. D. Rudolph
Keyword(s):  
Perturbation Theory ◽  
Dipole Moment ◽  
Angular Momentum ◽  
Internal Rotation ◽  
Stark Effect ◽  
Order Perturbation ◽  
Frequency Range ◽  
First Order ◽  
Cross Terms ◽  
Second Order Perturbation Theory

The microwave spectra of CD3 —S —S —CD3 and CH3 —S —S—CH3 have been measured in the frequency range from 5.5 to 34 kmc/sec. From the six rotational constants an r0-structure has been calculated. STARK-effect measurements have been made for the 101 —110 and 202—211 rotational transitions of CH3—S—S—CH3. The dipole moment was calculated to be (1.985±0.01) Debye. An approximate value for the barrier to internal rotation of the two methyl tops is given, V3= (1.6±0.1) kcal. The calculation has been based on triplet splittings of the rotational lines using second order perturbation theory in the torsional wavefunctions and neglecting first order and cross terms in angular momentum.

GAUGE INDEPENDENCE OF THE FERMION DAMPING RATE IN A HOT PLASMA - LANDAU GAUGE VS COULOMB GAUGE

1993 ◽  
Vol 08 (08) ◽  
pp. 739-748
Author(s):  
H. NAKKAGAWA ◽  
A. NIÉGAWA ◽  
B. PIRE
Keyword(s):  
Perturbation Theory ◽  
Gluon Propagator ◽  
Landau Gauge ◽  
Coulomb Gauge ◽  
Leading Order ◽  
Loop Order ◽  
Hard Thermal Loop ◽  
Hot Plasma ◽  
Damping Rate

The damping rate of a heavy muon/quark in a hot QED/QCD plasma is calculated in the Landau gauge to the effective one-loop order in the resummed perturbation theory of Braaten and Pisarski. For both a muon/quark at rest and in an energetic case we obtain to leading order the same result as in the Coulomb gauge. Resummation of hard-thermal loop corrections to the photon/gluon propagator is of key importance for this gauge independence.

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