Gauge covariance of the fermion Schwinger–Dyson equation in QED

Electroweak SU(2)L × U(1)Y model with strong spontaneously fermion-mass-generating gauge dynamics

Journal of High Energy Physics ◽

10.1007/jhep03(2021)224 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Petr Beneš ◽

Jiří Hošek ◽

Adam Smetana

Keyword(s):

Chiral Symmetry Breaking ◽

Axial Vector ◽

Higgs Sector ◽

Dyson Equation ◽

Mass Splitting ◽

Fermion Mass ◽

Goldstone Bosons ◽

The Standard Model ◽

Exploratory Stage ◽

The Masses

Abstract Higgs sector of the Standard model (SM) is replaced by quantum flavor dynamics (QFD), the gauged flavor SU(3)f symmetry with scale Λ. Anomaly freedom requires addition of three νR. The approximate QFD Schwinger-Dyson equation for the Euclidean infrared fermion self-energies Σf(p2) has the spontaneous-chiral-symmetry-breaking solutions ideal for seesaw: (1) Σf(p2) = $$ {M}_{fR}^2/p $$ M fR 2 / p where three Majorana masses MfR of νfR are of order Λ. (2) Σf(p2) = $$ {m}_f^2/p $$ m f 2 / p where three Dirac masses mf = m(0)1 + m(3)λ3 + m(8)λ8 of SM fermions are exponentially suppressed w.r.t. Λ, and degenerate for all SM fermions in f. (1) MfR break SU(3)f symmetry completely; m(3), m(8) superimpose the tiny breaking to U(1) × U(1). All flavor gluons thus acquire self-consistently the masses ∼ Λ. (2) All mf break the electroweak SU(2)L × U(1)Y to U(1)em. Symmetry partners of the composite Nambu-Goldstone bosons are the genuine Higgs particles: (1) three νR-composed Higgses χi with masses ∼ Λ. (2) Two new SM-fermion-composed Higgses h3, h8 with masses ∼ m(3), m(8), respectively. (3) The SM-like SM-fermion-composed Higgs h with mass ∼ m(0), the effective Fermi scale. Σf(p2)-dependent vertices in the electroweak Ward-Takahashi identities imply: the axial-vector ones give rise to the W and Z masses at Fermi scale. The polar-vector ones give rise to the fermion mass splitting in f. At the present exploratory stage the splitting comes out unrealistic.

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INFRARED DIVERGENCE IN QED3 AT FINITE TEMPERATURE

International Journal of Modern Physics A ◽

10.1142/s0217751x99001421 ◽

1999 ◽

Vol 14 (18) ◽

pp. 2921-2947 ◽

Cited By ~ 6

Author(s):

DOMINIC LEE ◽

GEORGIOS METIKAS

Keyword(s):

Finite Temperature ◽

Statistical Physics ◽

Order Term ◽

Dyson Equation ◽

Infrared Divergence ◽

Fermion Mass ◽

Photon Propagator ◽

Transverse Part ◽

Transverse Photon ◽

Range Of Values

We consider various ways of treating the infrared divergence which appears in the dynamically generated fermion mass, when the transverse part of the photon propagator in N flavour QED 3 at finite temperature is included in the Matsubara formalism. This divergence is likely to be an artifact of taking into account only the leading order term in the [Formula: see text] expansion when we calculate the photon propagator and is handled here phenomenologically by means of an infrared cutoff. Inserting both the longitudinal and the transverse part of the photon propagator in the Schwinger–Dyson equation, we find the dependence of the dynamically generated fermion mass on the temperature and the cutoff parameters. It turns out that consistency with certain statistical physics arguments imposes conditions on the cutoff parameters. For parameters in the allowed range of values we find that the ratio r=2* Mass (T=0)/critical temperature is approximately 6, consistent with previous calculations which neglected the transverse photon contribution.

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Self-consistent Dyson equation and self-energy functionals: An analysis and illustration on the example of the Hubbard atom

Physical Review B ◽

10.1103/physrevb.96.045124 ◽

2017 ◽

Vol 96 (4) ◽

Cited By ~ 22

Author(s):

Walter Tarantino ◽

Pina Romaniello ◽

J. A. Berger ◽

Lucia Reining

Keyword(s):

Dyson Equation ◽

Energy Functionals ◽

Self Energy ◽

Self Consistent

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Target-oriented inversion using the Patched Green′s function method

Geophysics ◽

10.1190/geo2020-0640.1 ◽

2021 ◽

pp. 1-77

Author(s):

Danyelle da Silva ◽

Edwin Fagua Duarte ◽

Wagner Almeida ◽

Mauro Ferreira ◽

Francisco Alirio Moura ◽

...

Keyword(s):

Condensed Matter ◽

Waveform Inversion ◽

Time Lapse ◽

Velocity Model ◽

Dyson Equation ◽

Computational Time ◽

Green Functions ◽

Target Area ◽

Computational Domain ◽

Full Waveform

We have designed a target-oriented methodology to perform Full Waveform Inversion using a frequency-domain wave propagator based on the so-called Patched Greens Function (PGF) technique. Originally developed in condensed matter physics to describe electronic waves in materials, the PGF technique is easily adaptable to the case of wave propagation in a spatially variable media in general. By dividing the entire computational domain into two sections, namely the target area and the outside target area, we calculate the Green Functions related to each section separately. The calculations related to the section outside the target are performed only once at the beginning of inversion, whereas the calculations in the target area are performed repeatedly for each iteration of the inversion process. With the Green Functions of the separate areas, we calculate the Green Functions of the two systems patched together through the application of a Recursive Dyson equation. By performing 2D and time-lapse experiments on the Marmousi model and a Brazilian Pre-salt velocity model, we demonstrate that the target-oriented PGF reduces the computational time of the inversion without compromising accuracy. In fact, when compared with conventional FWI results, the PGF-based calculations are identical but done in a fraction of the time.

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QUARK SPECTRUM ABOVE THE CRITICAL TEMPERATURE FROM SCHWINGER–DYSON EQUATION

International Journal of Modern Physics E ◽

10.1142/s0218301307007817 ◽

2007 ◽

Vol 16 (07n08) ◽

pp. 2282-2288

Author(s):

MASAYASU HARADA ◽

YUKIO NEMOTO ◽

SHUNJI YOSHIMOTO

Keyword(s):

Critical Temperature ◽

Weak Coupling ◽

Gauge Coupling ◽

Dyson Equation ◽

Coupling Region ◽

Chiral Phase ◽

Loop Approximation ◽

Wide Range ◽

Region Temperature ◽

Two Peaks

We investigate a spectrum of a fermion, which we call a quark, above the critical temperature of the chiral phase transition in a gauge theory using the Schwinger–Dyson (SD) equation. The SD equation enables us to study the spectrum over a wide range of the gauge coupling. It is shown that the quark spectrum has two sharp peaks which correspond to the normal quasi-quark and the plasmino and is consistent with that obtained in the hard thermal loop approximation in the weak coupling region, while it has also two peaks but with smaller thermal masses and broader widths in the strong coupling region. Temperature-dependence of the quark spectrum is also discussed.

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