Exact solutions of the Dirac equations in external non-Abel gauge fields

1985 ◽  
Vol 28 (7) ◽  
pp. 564-567 ◽  
Author(s):  
A. S. Vshivtsev ◽  
V. K. Peres-Fernandes ◽  
A. V. Tatarintsev
Keyword(s):  
Exact Solutions ◽  
Gauge Fields ◽  
Dirac Equations

scholarly journals Higher-derivative heterotic Double Field Theory and classical double copy

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Eric Lescano ◽  
Jesús A. Rodríguez
Keyword(s):  
Field Theory ◽  
Exact Solutions ◽  
Maxwell Equations ◽  
Action Principle ◽  
Low Energy ◽  
Gauge Fields ◽  
Metric Tensor ◽  
Higher Derivative ◽  
Double Field Theory ◽  
Double Copy

Abstract The generalized Kerr-Schild ansatz (GKSA) is a powerful tool for constructing exact solutions in Double Field Theory (DFT). In this paper we focus in the heterotic formulation of DFT, considering up to four-derivative terms in the action principle, while the field content is perturbed by the GKSA. We study the inclusion of the generalized version of the Green-Schwarz mechanism to this setup, in order to reproduce the low energy effective heterotic supergravity upon parametrization. This formalism reproduces higher-derivative heterotic background solutions where the metric tensor and Kalb-Ramond field are perturbed by a pair of null vectors. Next we study higher-derivative contributions to the classical double copy structure. After a suitable identification of the null vectors with a pair of U(1) gauge fields, the dynamics is given by a pair of Maxwell equations plus higher derivative corrections in agreement with the KLT relation.

Exact Solutions of Two Body Dirac Equations

1994 ◽  
Vol 49 (10) ◽  
pp. 983-986
Author(s):  
Nivedita Nag ◽  
Rajkumar Roychoudhury
Keyword(s):  
Quantum Mechanics ◽  
Exact Solutions ◽  
Supersymmetric Quantum Mechanics ◽  
Dirac Equations ◽  
Eigen Values

Abstract A set of exact eigen values and eigen functions for the two body Dirac problem described by the Hamiltonian H = (α⃗1 - α⃗2)p⃗ + β1m 1+ β2m2 + ½ (β1 + β2) λrare obtained using the properties of Supersymmetric Quantum Mechanics.

EXACT SOLUTIONS OF THE SELF-DUALITY EQUATIONS ON THE MINKOWSKI SPACE-TIME

2001 ◽  
Vol 12 (06) ◽  
pp. 801-806 ◽  
Author(s):  
V. MANTA ◽  
G. ZET
Keyword(s):  
Gauge Theory ◽  
Exact Solutions ◽  
Minkowski Space ◽  
Space Time ◽  
The Self ◽  
Gauge Fields ◽  
Self Duality ◽  
Minkowski Space Time ◽  
Dynamical Type ◽  
Analytical Program

A SU(2) Gauge Theory with spherical symmetry over the Minkowski space-time is considered. The self-duality equation of the gauge fields are written and their solutions are obtained. Two exact solutions, one of which is statical and another of dynamical type are given. All the calculations are performed using an analytical program written in GRTensor computer algebra package, which runs on the MapleV platform.

scholarly journals The Dirac electron consistent with proper gravitational and electromagnetic field of the Kerr-Newman solution

2020 ◽  
Author(s):  
Александр Буринский
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Exact Solutions ◽  
Coordinate System ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

We consider the Dirac electron as a non-perturbative particle-like solution consistent with its own Kerr-Newman (KN) gravitational field. In our previous works we regularized the model of electron suggested by Israel and Lopez on the base of KN solution. Our model of electron was shaped similar to the bag models - the thin superconducting disk coupled with circular string placed along its perimeter. The specific feature of the KN string was its orientifold (two-faced) structure. In this work we use unique features of the Kerr-Schild coordinate system, which allows us to linearize Dirac equations in KN background, and obtain the exact solutions of the Dirac equations consistent with the KN gravitational and electromagnetic field. We show that the corresponding solution take the form of a massless relativistic string. Strong parallelism with quantum theory, which appears by our treatment, explains remarkable properties of the electron in relativistic scattering processes, which allow us to consider it as a point-like particle.

New exact solutions of the Dirac equations. VI

1977 ◽  
Vol 20 (6) ◽  
pp. 783-790 ◽  
Author(s):  
V. G. Bagrov ◽  
D. M. Gitman ◽  
A. V. Shapovalov ◽  
V. N. Shapovalov
Keyword(s):  
Exact Solutions ◽  
Dirac Equations ◽  
New Exact Solutions

scholarly journals ABOUT SOME EXACT SOLUTIONS FOR 2 + 1 GRAVITY COUPLED TO GAUGE FIELDS

1992 ◽  
Vol 07 (25) ◽  
pp. 2341-2350 ◽  
Author(s):  
IAN I. KOGAN
Keyword(s):  
Black Holes ◽  
Exact Solutions ◽  
Gauge Field ◽  
Three Dimensional ◽  
Einstein Gravity ◽  
Gauge Fields ◽  
Abelian Gauge ◽  
Planck Mass ◽  
Static Solutions

Some exact static solutions for Einstein gravity in 2 + 1 dimensions coupled to Abelian gauge field are discussed, where the invariant interval is of the form: ds2 = N2 (r) dt2 − dr2 − C2 (r) dθ2. Some of these solutions are three-dimensional analogs of the Schwarzschild black holes. The metrics in the regions inside and outside the horizon are connected by the changing of the Planck mass sign.

Supplement to papers ?New exact solutions of dirac equations. II, III?

1977 ◽  
Vol 20 (1) ◽  
pp. 103-104 ◽  
Author(s):  
V. G. Bagrov ◽  
D. M. Gitman ◽  
A. G. Meshkov ◽  
V. N. Shapovalov
Keyword(s):  
Exact Solutions ◽  
Dirac Equations ◽  
New Exact Solutions
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