RELATIVISTIC QUANTUM FIELD THEORY FOR CONDENSED SYSTEMS-(III): AN EXPLICIT EXPRESSION OF ATOMIC SCHWINGER–DYSON METHOD

2005 ◽  
Vol 19 (11) ◽  
pp. 1905-1923
Author(s):  
HIROYUKI MATSUURA ◽  
MASAHIRO NAKANO
Keyword(s):  
Relativistic Quantum ◽  
Physical Processes ◽  
Electron Hole ◽  
Consistent System ◽  
Self Energy ◽  
Electron Positron ◽  
Tensor Part ◽  
Condensed Systems ◽  
Quantum Component ◽  
Scalar Part

A new explicit expressions of self-energies Πμν and Σ are introduced for photons and electrons based on the particle-hole-antiparticle representation (PHA) of Atomic Schwinger–Dyson formalism (ASD). The PHA representation describes exactly the physical processes such as particle-hole excitations (electron-hole) and particle-antiparticle excitations (electron-positron). The self-energy Σ includes both the quantum component and the classical component (classical external field and Coulomb's field), which are divided into the scalar part Σs and 4-dimensional vector parts Σ0, Σj. The electron propagators are composed of the particle part, hole part and antiparticle part in PHA representation. The general representation of photon self-energy Πμν with 16 elements is expressed in terms of only two components (transverse and longitudinal) Πt and Πl. The general form of the photon propagators are written in terms of free propagator D0 and two independent propagators Dl and Dt, which include two independent photon self-energies. The tensor part of the electron self-energy does not appear in ASD formalism which makes perfectly the closed self-consistent system, when we take the bare vertex approximation, Γμ→γμ.

scholarly journals Dispersion in a Relativistic Quantum Electron Gas. I. General Distribution Functions

1984 ◽  
Vol 37 (6) ◽  
pp. 615 ◽  
Author(s):  
Leith M Hayes ◽  
DB Melrose
Keyword(s):  
Relativistic Electron ◽  
Occupation Number ◽  
Relativistic Quantum ◽  
Electron Gas ◽  
Distribution Functions ◽  
Quantum Limit ◽  
General Distribution ◽  
Electron Positron ◽  
Quantum Electron ◽  
Plasma Dispersion

The covariant response tensor for a relativistic electron gas is calculated in two ways. One involves introducing a four-dimensional generalization of the electron-positron occupation number, and the other is a covariant generalization of a method due to Harris. The longitudinal and transverse parts are. evaluated for an isotropic electron gas in terms of three plasma dispersion functions, and the contributions from Landau damping and pair creation to the dispersion curve are identified separately. The long-wavelength limit and the non-quantum limit, with first quantum corrections, are found. The plasma dispersion functions are evaluated explicitly for a completely degenerate relativistic electron gas, and a detailed form due to Jancovici is reproduced.

First-Principles Study of Optical Excitations in Alpha Quartz

1999 ◽  
Vol 579 ◽  
Author(s):  
Eric K. Chang ◽  
Michael Rohlfing ◽  
Steven G. Louie
Keyword(s):  
Absorption Spectrum ◽  
First Principles ◽  
Optical Spectrum ◽  
Quantitative Description ◽  
Frequency Range ◽  
Gw Approximation ◽  
Electron Hole ◽  
Self Energy ◽  
Excitonic Effects

ABSTRACTThe properties of silicon dioxide have been studied extensively over the years. However, there still remain major unanswered questions regarding the nature of the optical spectrum and the role of excitonic effects in this technologically important material. In this work, we present an ab initio study of the optical absorption spectrum of alpha-quartz, using a newly developed first-principles method which includes self-energy and electron-hole interaction effects. The quasiparticle band structure is computed within the GW approximation to obtain a quantitative description of the single-particle excitations. The Bethe-Salpeter equation for the electron-hole excitations is solved to obtain the optical spectrum and to understand the spatial extent and physical properties of the excitons. The theoretical absorption spectrum is found to be in excellent agreement with the measured spectrum. We show that excitonic effects are crucial in the frequency range up to 5 eV above the absorption threshold.

scholarly journals CAUSALITY VERSUS WARD IDENTITY IN DISORDERED ELECTRON SYSTEMS

2004 ◽  
Vol 18 (19n20) ◽  
pp. 1051-1058 ◽  
Author(s):  
V. JANIŠ ◽  
J. KOLORENČ
Keyword(s):  
Ward Identity ◽  
The Self ◽  
Diffusive Transport ◽  
Electron Systems ◽  
Electron Hole ◽  
Consistency Conditions ◽  
Self Energy ◽  
Disordered Electron Systems ◽  
Symmetric Theory ◽  
Diffusion Pole

We address the problem of fulfilling consistency conditions in solutions for disordered noninteracting electrons. We prove that if we assume the existence of the diffusion pole in an electron–hole symmetric theory we cannot achieve a solution with a causal self-energy that would fully fit the Ward identity. Since the self-energy must be causal, we conclude that the Ward identity is partly violated in the diffusive transport regime of disordered electrons. We explain this violation in physical terms and discuss its consequences.

Towards numerical implementation of the relativistically covariant many-body perturbation theoryThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at University of Windsor, Windsor, Ontario, Canada on 21–26 July 2008.

2009 ◽  
Vol 87 (7) ◽  
pp. 817-824 ◽  
Author(s):  
Daniel Hedendahl ◽  
Ingvar Lindgren ◽  
Sten Salomonson
Keyword(s):  
Standard Procedure ◽  
Operator Method ◽  
Vertex Correction ◽  
Many Body ◽  
Atomic Systems ◽  
Self Energy ◽  
Electron Positron ◽  
Many Body Perturbation Theory ◽  
Qed Effects ◽  
First Time

The standard procedure for relativistic many-body perturbation theory (RMBPT) is not relativistically covariant, and the effects of retardation, virtual-electron-positron-pair, and radiative effects (self-energy, vacuum polarisation, and vertex correction) — the so-called QED effects — are left out. The energy contribution from the QED effects can be evaluated by the covariant evolution operator method, which has a structure that is similar to that of RMBPT, and it can serve as a merger between QED and RMBPT. The new procedure makes it, in principle, possible for the first time to evaluate QED effects together with correlation to high order. The procedure is now being implemented, and it has been shown that the effect of electron correlation on first-order QED for He-like neon dominates heavily over second-order QED effects.

RELATIVISTIC QUANTUM FIELD THEORY FOR CONDENSED SYSTEMS (II): RENORMALIZATION PROCEDURE

2003 ◽  
Vol 17 (30) ◽  
pp. 5713-5723 ◽  
Author(s):  
HIROYUKI MATSUURA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Electric Charge ◽  
Relativistic Quantum ◽  
Free Field ◽  
Mass Shift ◽  
Quantum Field ◽  
Relativistic Quantum Field Theory ◽  
Self Energy ◽  
Physical Mass

We proposed Atomic Schwinger–Dyson method (ASD method) in previous paper, which was a nonperturbative and relativistic quantum field theory for a finite baryon density. We think it is important to show the significance of renormarization in order to get real physical predictions. Moreover, the real value of physical mass, electric charge and wave function are completely different from those of the non-renormalized electron and photon in mean field theory, since there are many of the particle-antiparticle creations and annihilations, particle-hole excitation, and Pauli blocking, which give an effect on bare mass, electric charge, polarization of vacuum, and self-energy. In this paper, we shows that ASD method is renormalizable theory, and that photon condensation of ASD method gave rise to Coulomb's potential and the mass shift of electron. The interacting photon and electron fields, which have physical mass and electric charge, are expressed as generalized free field equations by using the mass shift and the self-energy of those particles. We obtain the expression of an exact solution of these particles on the basis of the Green functional method.

Influence of Electron-Electron Correlations and Lattice Effects on Positron-Electron Enhancement Factors

2010 ◽  
Vol 666 ◽  
pp. 5-9 ◽  
Author(s):  
Edward Boroński
Keyword(s):  
Electron Gas ◽  
Momentum Density ◽  
Many Body ◽  
Fermi Sphere ◽  
Self Energy ◽  
Density Distributions ◽  
Lattice Effects ◽  
Electron Positron ◽  
Enhancement Factors ◽  
Momentum Distributions

We present an approach taking into account the effect of electron-electron (e-e) correlations on electron-positron (e-p) momentum density distributions. The approach bases on the modification of the Bethe-Goldstone (B-G) equation for the positron in the electron gas due to self-energy effects. The example calculations have been performed for selected parameters corresponding to simple metals. The calculated dependencies exhibit the increase of the e-p enhancement factors below Fermi momentum, like Kahana enhancements, and a decrease above the Fermi sphere, leading to a many-body “tail” in the e-p momentum density distributions. Moreover, the influence of lattice effects on enhancement factors (EF) is taken into account. This decreases by a few percent the absolute values of the e-p momentum distributions and the corresponding annihilation rates and for real metals such as Mg or Cu evidently improve the agreement with experiment.

scholarly journals The Electron-Positron Cauldron and the Formation of the Hard Radiation of Quasars and AGN

1986 ◽  
Vol 119 ◽  
pp. 383-393
Author(s):  
N.S. Kardashev ◽  
I.D. Novikov ◽  
B.E. Stern
Keyword(s):  
Active Galactic Nuclei ◽  
Galactic Nuclei ◽  
Physical Parameters ◽  
Physical Processes ◽  
Physical Conditions ◽  
Electron Positron ◽  
Hard Radiation ◽  
The Universe

Active Galactic Nuclei (AGN) and quasars have unique physical parameters among all the objects in the Universe. Undoubtedly it is the uniqueness of the physical conditions in these systems that gives rise to the peculiar physical processes in them.

scholarly journals NONEQUILIBRIUM THERMO FIELD DYNAMICS FOR RELATIVISTIC COMPLEX SCALAR AND DIRAC FIELDS

2012 ◽  
Vol 27 (14) ◽  
pp. 1250078 ◽  
Author(s):  
YUICHI MIZUTANI ◽  
TOMOHIRO INAGAKI
Keyword(s):  
Chemical Potential ◽  
Relativistic Quantum ◽  
The Self ◽  
Quantum Field Theories ◽  
Renormalization Condition ◽  
Complex Scalar ◽  
Dirac Fields ◽  
Self Energy ◽  
Thermo Field Dynamics ◽  
Self Consistency

Relativistic quantum field theories for complex scalar and Dirac fields are investigated in nonequilibrium thermo field dynamics. The thermal vacuum is defined by the Bogoliubov transformed creation and annihilation operators. Two independent Bogoliubov parameters are introduced for a charged field. Its difference naturally induces the chemical potential. Time-dependent thermal Bogoliubov transformation generates the thermal counterterms. We fix the terms by the self-consistency renormalization condition. Evaluating the thermal self-energy under the self-consistency renormalization condition, we derive the quantum Boltzmann equations for the relativistic fields.

scholarly journals Topological Quantum Interplay between Magnetic Flux and Mass in an Electron

2019 ◽  
Author(s):  
Vincenzo Vinciguerra
Keyword(s):  
Magnetic Flux ◽  
Wilson Loop ◽  
Energy Scale ◽  
Phase Factor ◽  
Electroweak Theory ◽  
Gauge Invariant ◽  
Self Energy ◽  
Topological Quantum ◽  
Electron Positron ◽  
Electron Positron Pair

A topological quantum interplay between the magnetic flux and the mass has been investigated, for the case of an electron, by evaluating a gauge-invariant phase factor (a Wilson loop) linked to the electromagnetic gauge field of the particle. In particular, from this phase factor and the quantization of the magnetic flux variations, a relationship between the mass at rest of the electron and its self-energy , arising from radiative corrections, has been obtained also within a QED approach. Besides, a formulation of an energy scale comparable to the energy at rest of an electron-positron pair is proposed. Remarkably, a reckoning of the Bohr energy of a W+ W- pair is compatible with constants and parameters usually employed within the electroweak theory and comparable to the energy at rest of an electron-positron pair.

Sign in / Sign up

Export Citation Format

Share Document