scholarly journals The Dirac–Hamiltonian in an Aharonov–Bohm Gauge Field and its Self-Adjoint Extensions

1997 ◽  
Vol 12 (05) ◽  
pp. 337-345 ◽  
Author(s):  
Kazuhiko Odaka ◽  
Kazuya Satoh
Keyword(s):  
Gauge Field ◽  
The Self ◽  
Unitary Matrix ◽  
Spherical Coordinates ◽  
Angular Part ◽  
Aharonov Bohm ◽  
Dirac Hamiltonian

By using the spherical coordinates in (3+1) dimensions we study the self-adjointness of the Dirac–Hamiltonian in an Aharonov–Bohm gauge field of an infinitely thin magnetic fluxtube. It is shown that the angular part of the Dirac–Hamiltonian requires self-adjoint extensions. These self-adjoint extensions are parametrized by a 2×2 unitary matrix.

scholarly journals Five-brane current algebras in type II string theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Machiko Hatsuda ◽  
Shin Sasaki ◽  
Masaya Yata
Keyword(s):  
Poisson Bracket ◽  
Gauge Field ◽  
The Self ◽  
Dirac Bracket ◽  
Type Ii ◽  
Gauge Transformations ◽  
Transition Rules ◽  
Superstring Theories ◽  
Kaluza Klein ◽  
Current Algebras

Abstract We study the current algebras of the NS5-branes, the Kaluza-Klein (KK) five-branes and the exotic $$ {5}_2^2 $$ 5 2 2 -branes in type IIA/IIB superstring theories. Their worldvolume theories are governed by the six-dimensional $$ \mathcal{N} $$ N = (2, 0) tensor and the $$ \mathcal{N} $$ N = (1, 1) vector multiplets. We show that the current algebras are determined through the S- and T-dualities. The algebras of the $$ \mathcal{N} $$ N = (2, 0) theories are characterized by the Dirac bracket caused by the self-dual gauge field in the five-brane worldvolumes, while those of the $$ \mathcal{N} $$ N = (1, 1) theories are given by the Poisson bracket. By the use of these algebras, we examine extended spaces in terms of tensor coordinates which are the representation of ten-dimensional supersymmetry. We also examine the transition rules of the currents in the type IIA/IIB supersymmetry algebras in ten dimensions. Based on the algebras, we write down the section conditions in the extended spaces and gauge transformations of the supergravity fields.

scholarly journals Synthesis and observation of non-Abelian gauge fields in real space

Science ◽  
2019 ◽  
Vol 365 (6457) ◽  
pp. 1021-1025 ◽  
Author(s):  
Yi Yang ◽  
Chao Peng ◽  
Di Zhu ◽  
Hrvoje Buljan ◽  
John D. Joannopoulos ◽  
...  
Keyword(s):  
Gauge Field ◽  
Building Blocks ◽  
Real Space ◽  
Gauge Fields ◽  
Final States ◽  
Abelian Gauge ◽  
Classical Waves ◽  
Break Time ◽  
Bohm Effect ◽  
Aharonov Bohm

Particles placed inside an Abelian (commutative) gauge field can acquire different phases when traveling along the same path in opposite directions, as is evident from the Aharonov-Bohm effect. Such behaviors can get significantly enriched for a non-Abelian gauge field, where even the ordering of different paths cannot be switched. So far, real-space realizations of gauge fields have been limited to Abelian ones. We report an experimental synthesis of non-Abelian gauge fields in real space and the observation of the non-Abelian Aharonov-Bohm effect with classical waves and classical fluxes. On the basis of optical mode degeneracy, we break time-reversal symmetry in different manners, via temporal modulation and the Faraday effect, to synthesize tunable non-Abelian gauge fields. The Sagnac interference of two final states, obtained by reversely ordered path integrals, demonstrates the noncommutativity of the gauge fields. Our work introduces real-space building blocks for non-Abelian gauge fields, relevant for classical and quantum exotic topological phenomena.

scholarly journals Self-Dual Chern–Simons Solitons in the Planar CP(1) Model

1997 ◽  
Vol 12 (40) ◽  
pp. 3169-3176 ◽  
Author(s):  
Yoonbai Kim ◽  
Phillial Oh ◽  
Chaiho Rim
Keyword(s):  
Gauge Field ◽  
Spin System ◽  
Soliton Solutions ◽  
The Self ◽  
Charge Densities ◽  
Rotationally Symmetric ◽  
Uniform Background ◽  
Background Charge ◽  
Chern Simons

We consider a nonrelativistic CP (1) system coupled minimally to an Abelian Chern–Simons gauge field and study the self-dual solitons which saturate the Bogomol'nyi bound. We find a rich structure of rotationally symmetric static soliton solutions for various uniform background charge densities. Possible application to spin system is mentioned.

EQUIVALENCE OF THE QUADRATIC LAGRANGIANS FOR CHIRAL BOSONS

1992 ◽  
Vol 07 (20) ◽  
pp. 4965-4979
Author(s):  
AHMED ABOUELSAOOD
Keyword(s):  
Gauge Field ◽  
Canonical Quantization ◽  
The Self ◽  
Kinetic Term ◽  
Schwinger Model ◽  
Zero Modes ◽  
Self Duality ◽  
Compact Case ◽  
Chiral Bosons ◽  
Proper Account

Canonical quantization of both the Labastida-Pernici quadratic Lagrangian for two chiral bosons and the simplest chiral boson quadratic Lagrangian where the self-duality is imposed using a Lagrange-multiplier term is performed taking a proper account of the zero modes in the compact case, showing that they are exactly equivalent. The result is extended to the case of the bosonized chiral Schwinger model where no kinetic term for the gauge field is present, showing that a Wess-Zumino term does not affect the physics of the model.

Solution to the self-dual SU(2) gauge field in Yang'sKgauge

1978 ◽  
Vol 18 (8) ◽  
pp. 3035-3036 ◽  
Author(s):  
Zenaida E. S. Uy
Keyword(s):  
Gauge Field ◽  
The Self

BOUND FERMION STATES IN A VECTOR 1/r AND AHARONOV–BOHM POTENTIAL IN (2+1) DIMENSIONS

2011 ◽  
Vol 26 (12) ◽  
pp. 865-883 ◽  
Author(s):  
V. R. KHALILOV ◽  
K. E. LEE
Keyword(s):  
Magnetic Flux ◽  
Boundary Conditions ◽  
Effective Charge ◽  
The Self ◽  
Critical Charge ◽  
Spin Particle ◽  
Bohm Potential ◽  
Aharonov Bohm

We construct systematically all the self-adjoint Dirac Hamiltonians with a vector 1/r and Aharonov–Bohm potential in (2+1) dimensions with taking into account the fermion spin. Then we find spectra of these self-adjoint Dirac Hamiltonians. There are one-parameter families of the self-adjoint Dirac Hamiltonians selected by physically acceptable boundary conditions. Equations determining spectra of the self-adjoint radial Dirac Hamiltonians are derived for various values of parameters. We show that the lowest fermion state in the considered potential becomes unstable when the effective charge is greater than the so-called critical charge, and that the effective charge is influenced by the magnetic flux and spin particle.

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