scholarly journals On Huygens' principle for Dirac operators associated to electromagnetic fields

2001 ◽  
Vol 73 (4) ◽  
pp. 483-493
Author(s):  
FABIO A.C.C. CHALUB
Keyword(s):  
Electromagnetic Field ◽  
Dirac Equation ◽  
Dirac Operator ◽  
Electromagnetic Fields ◽  
Dirac Operators ◽  
Main Result Theorem ◽  
Dirac Particles ◽  
Result Theorem ◽  
Huygens Principle

We study the behavior of massless Dirac particles, i.e., solutions of the Dirac equation with m = 0 in the presence of an electromagnetic field. Our main result (Theorem 1) is that for purely real or imaginary fields any Huygens type (in Hadamard's sense) Dirac operators is equivalent to the free Dirac operator, equivalence given by changes of variables and multiplication (right and left) by nonzero functions.

SEPARABILITY OF THE MASSIVE DIRAC EQUATION AND HAWKING RADIATION OF DIRAC PARTICLES IN THE CHARGED AdS–KERR–TAUB–NUT BLACK HOLE

2011 ◽  
Vol 26 (20) ◽  
pp. 1509-1520 ◽  
Author(s):  
PU-JIAN MAO ◽  
LIN-YU JIA ◽  
JI-RONG REN
Keyword(s):  
Black Hole ◽  
Dirac Equation ◽  
Dirac Operator ◽  
Thermal Effect ◽  
Hawking Radiation ◽  
Symmetric Operator ◽  
Scalar Particles ◽  
First Order ◽  
Dirac Particles

We investigate the separability of massive Dirac equation in the charged AdS–Kerr–Taub–NUT black hole. It is shown that the Dirac equation can be separated by variables into purely radial and purely angular parts in this background spacetime. From the separated solutions for massive Dirac equation, a first-order symmetric operator that commutes with the Dirac operator is constructed and expressed in terms of Killing–Yano tensor admitted by the charged AdS–Kerr–Taub–NUT spacetime. Then the Hawking radiation of Dirac particles in the background of charged AdS–Kerr–Taub–NUT black hole is investigated via the Damour–Ruffini–Sannan method. It is shown that quantum thermal effect of the Dirac particles in the charged AdS–Kerr–Taub–NUT black hole has the same character with that of the scalar particles.

Time reversal and a stochastic model of the Dirac equation in an electromagnetic field

2004 ◽  
Vol 82 (1) ◽  
pp. 19-27 ◽  
Author(s):  
D.G.C. McKeon ◽  
G N Ord
Keyword(s):  
Electromagnetic Field ◽  
Brownian Motion ◽  
Dirac Equation ◽  
Stochastic Model ◽  
Analytic Continuation ◽  
Time Reversal ◽  
Quantum Interference ◽  
Dirac Particles

We extend a stochastic model underlying the Dirac equation in 1+1 dimensions to include the electromagnetic field. The model obtains the Dirac equation without requiring a formal analytic continuation. The mechanism, which produces quantum behaviour, is the allowed Brownian motion in time. The microscopic time reversals in the Brownian motion are the source of quantum interference. The electromagnetic field is also obtained from a stochastic model and the interaction with Dirac particles is treated as a scattering process.PACS Nos.: 03.65.-w, 03.20.+i, 05.40.+j

scholarly journals The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Higgs Field ◽  
Vacuum State ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

scholarly journals Eigenvalue bounds for non-selfadjoint Dirac operators

2021 ◽  
Author(s):  
Piero D’Ancona ◽  
Luca Fanelli ◽  
Nico Michele Schiavone
Keyword(s):  
Dirac Operator ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Dirac Operators ◽  
Resolvent Estimates ◽  
Eigenvalue Bounds ◽  
Mixed Norms ◽  
Massless Case ◽  
Abstract Version ◽  
Embedded Eigenvalues

AbstractWe prove that the eigenvalues of the n-dimensional massive Dirac operator $${\mathscr {D}}_0 + V$$ D 0 + V , $$n\ge 2$$ n ≥ 2 , perturbed by a potential V, possibly non-Hermitian, are contained in the union of two disjoint disks of the complex plane, provided V is sufficiently small with respect to the mixed norms $$L^1_{x_j} L^\infty _{{\widehat{x}}_j}$$ L x j 1 L x ^ j ∞ , for $$j\in \{1,\dots ,n\}$$ j ∈ { 1 , ⋯ , n } . In the massless case, we prove instead that the discrete spectrum is empty under the same smallness assumption on V, and in particular the spectrum coincides with the spectrum of the unperturbed operator: $$\sigma ({\mathscr {D}}_0+V)=\sigma ({\mathscr {D}}_0)={\mathbb {R}}$$ σ ( D 0 + V ) = σ ( D 0 ) = R . The main tools used are an abstract version of the Birman–Schwinger principle, which allows in particular to control embedded eigenvalues, and suitable resolvent estimates for the Schrödinger operator.

scholarly journals Higher spectral flow and an entire bivariant JLO cocycle

2012 ◽  
Vol 11 (1) ◽  
pp. 183-232 ◽  
Author(s):  
Moulay-Tahar Benameur ◽  
Alan L. Carey
Keyword(s):  
Dirac Operator ◽  
Chern Character ◽  
Dirac Operators ◽  
Cyclic Cohomology ◽  
Closed Manifold ◽  
Spectral Flow ◽  
Smooth Functions ◽  
Base Manifold ◽  
K Theory ◽  
Higher Spectral Flow

AbstractFor a single Dirac operator on a closed manifold the cocycle introduced by Jaffe-Lesniewski-Osterwalder [19] (abbreviated here to JLO), is a representative of Connes' Chern character map from the K-theory of the algebra of smooth functions on the manifold to its entire cyclic cohomology. Given a smooth fibration of closed manifolds and a family of generalized Dirac operators along the fibers, we define in this paper an associated bivariant JLO cocycle. We then prove that, for any l ≥ 0, our bivariant JLO cocycle is entire when we endow smoooth functions on the total manifold with the Cl+1 topology and functions on the base manifold with the Cl topology. As a by-product of our theorem, we deduce that the bivariant JLO cocycle is entire for the Fréchet smooth topologies. We then prove that our JLO bivariant cocycle computes the Chern character of the Dai-Zhang higher spectral flow.

scholarly journals ON EIGENVALUE ESTIMATES FOR THE SUBMANIFOLD DIRAC OPERATOR

2002 ◽  
Vol 13 (05) ◽  
pp. 533-548 ◽  
Author(s):  
NICOLAS GINOUX ◽  
BERTRAND MOREL
Keyword(s):  
Dirac Operator ◽  
Lower Bounds ◽  
Dirac Operators ◽  
Extrinsic Curvature ◽  
Eigenvalue Estimates ◽  
Killing Spinors ◽  
Spinor Fields ◽  
Twisted Dirac Operators

We give lower bounds for the eigenvalues of the submanifold Dirac operator in terms of intrinsic and extrinsic curvature expressions. We also show that the limiting cases give rise to a class of spinor fields generalizing that of Killing spinors. We conclude by translating these results in terms of intrinsic twisted Dirac operators.

Experimental study of the transmission of energy of a microwave electromagnetic field into the oil environment employing a submersible emitter

2021 ◽  
pp. 120-129
Author(s):  
A. F. Sekachev ◽  
V. V. Shalai ◽  
Yu. D. Zemenkov ◽  
A. F. Fitzner ◽  
A. E. Yakovlev
Keyword(s):  
Experimental Study ◽  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Thermal Process ◽  
Oil Industry ◽  
Coaxial Cable ◽  
Transport Systems ◽  
Thermal Imager ◽  
Pipeline Transport ◽  
Optically Transparent

The supply of heat to oil media pumped by pipeline transport systems is one of the main problems in the oil industry. The article describes a method for supplying heat to oil-containing media using the energy of an electromagnetic field. The possibility of releasing surfaces in contact with oil sludge under the influence of electromagnetic fields has been shown by experiment. We describe the design and parameters of a biconical horn radiator of a microwave electromagnetic field operating at a frequency of 2 450 MHz. A method for generating energy and transmitting it to the emitter by means of a coaxial cable is shown. Testing the emitter in oil placed in an optically transparent and radio-tight double-walled tank is presented. The design of the stand allows us to safely examine the thermal process using a thermal imager. The installation made it possible to heat 7 liters of oil at 15 °C in 12 minutes.

scholarly journals INFLUENCE OF GRAVITY ON NONCOMMUTATIVE DIRAC EQUATION

2005 ◽  
Vol 20 (26) ◽  
pp. 1997-2005 ◽  
Author(s):  
SOFIANE BOUROUAINE ◽  
ACHOUR BENSLAMA
Keyword(s):  
Dirac Equation ◽  
Electric Field ◽  
Covariant Derivative ◽  
Strong Electric Field ◽  
Curved Spacetime ◽  
Tetrad Formalism ◽  
Dirac Particles ◽  
Modified Dirac Equation ◽  
New Form

In this paper, we investigate the influence of gravity and noncommutativity on Dirac particles. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved spacetime with an operator which depends on the noncommutative θ-parameter. As an application, we have computed the density number of the created particles in the presence of constant strong electric field in an anisotropic Bianchi universe.

scholarly journals High energy scattering of Dirac particles on smooth potentials

2016 ◽  
Vol 31 (23) ◽  
pp. 1650126 ◽  
Author(s):  
Nguyen Suan Han ◽  
Le Anh Dung ◽  
Nguyen Nhu Xuan ◽  
Vu Toan Thang
Keyword(s):  
Dirac Equation ◽  
Cross Sections ◽  
Differential Cross ◽  
Scattering Amplitude ◽  
High Energy ◽  
Type Representation ◽  
Dirac Particles ◽  
Energy Scattering ◽  
Two Component ◽  
High Energy Scattering

The derivation of the Glauber type representation for the high energy scattering amplitude of particles of spin 1/2 is given within the framework of the Dirac equation in the Foldy–Wouthuysen (FW) representation and two-component formalism. The differential cross-sections on the Yukawa and Gaussian potentials are also considered and discussed.

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