POSSIBLE CONFINEMENT MECHANISMS FOR NONRELATIVISTIC PARTICLES ON A LINE

The gauge model of nonrelativistic particles on a line interacting with nonstandard gravitational fields5 is supplemented by the addition of a (non)-Abelian gauge interaction. Solving for the gauge fields we obtain equations, in closed form, for a classical two-particle system. The corresponding Schrödinger equation, obtained by the Moyal quantization procedure, is solved analytically. Its solutions exhibit two different confinement mechanisms — dependent on the sign of the coupling λ to the nonstandard gravitational fields. For λ >0 confinement is due to a rising potential, whereas for λ<0 it is due to the dynamical (geometric) bag formation. Numerical results for the corresponding energy spectra are given. For a particular relation between two coupling constants, the model fits into the scheme of supersymmetrical quantum mechanics.

Download Full-text

MASS GENERATION FOR NON-ABELIAN GAUGE FIELDS WITHOUT SCALARS

International Journal of Modern Physics A ◽

10.1142/s0217751x95001698 ◽

1995 ◽

Vol 10 (25) ◽

pp. 3581-3592

Author(s):

DIDIER CAENEPEEL ◽

MARTIN LEBLANC

Keyword(s):

Type Theory ◽

Functional Integration ◽

Higgs Mechanism ◽

Coupling Constants ◽

Fine Tuning ◽

Effective Theory ◽

Gauge Fields ◽

Mass Generation ◽

Abelian Gauge

We present an alternative to the Higgs mechanism for generating masses for non-Abelian gauge fields in 3+1 dimensions. The initial Lagrangian is composed of a fermion with current-current and dipole-dipole type self-interactions minimally coupled to non-Abelian gauge fields. The mass generation occurs when we perform a fermionic functional integration. We show that by fine-tuning the coupling constants, the effective theory may be written as a BΛF type theory describing massive non-Abelian gauge fields.

Download Full-text

Classical and quantum mechanics of non-abelian gauge fields

Nuclear Physics B ◽

10.1016/0550-3213(84)90298-0 ◽

1984 ◽

Vol 246 (2) ◽

pp. 302-334 ◽

Cited By ~ 121

Author(s):

G.K. Savvidy

Keyword(s):

Quantum Mechanics ◽

Gauge Fields ◽

Abelian Gauge ◽

Classical And Quantum Mechanics

Download Full-text

One-dimensional soliton system of gauged kink and Q-ball

The European Physical Journal C ◽

10.1140/epjc/s10052-019-7302-6 ◽

2019 ◽

Vol 79 (9) ◽

Cited By ~ 1

Author(s):

A. Yu. Loginov ◽

V. V. Gauzshtein

Keyword(s):

Electric Field ◽

Gauge Coupling ◽

Scalar Fields ◽

Coupling Constants ◽

Gauge Model ◽

Complex Scalar ◽

Abelian Gauge ◽

Small Perturbations ◽

One Dimensional ◽

Dimensional Soliton

Abstract In the present paper, we consider a $$(1 + 1)$$(1+1)-dimensional gauge model consisting of two complex scalar fields interacting with each other through an Abelian gauge field. When the model’s gauge coupling constants are set to zero, the model possesses non-gauged Q-ball and kink solutions that do not interact with each other. It is shown here that for nonzero gauge coupling constants, the model has a soliton solution describing the system that consists of interacting Q-ball and kink components. These two components of the kink-Q-ball system have opposite electric charges, meaning that the total electric charge of the system vanishes. The properties of the kink-Q-ball system are studied both analytically and numerically. In particular, it was found that the system possesses a nonzero electric field and is unstable with respect to small perturbations in the fields.

Download Full-text

NON-LOCALITY OF QUANTUM MECHANICS AND THE LOCALITY OF GENERAL RELATIVITY

Modern Physics Letters A ◽

10.1142/s0217732302007661 ◽

2002 ◽

Vol 17 (15n17) ◽

pp. 1097-1106 ◽

Cited By ~ 1

Author(s):

JEEVA ANANDAN

Keyword(s):

General Relativity ◽

Quantum Mechanics ◽

Gauge Fields ◽

Abelian Gauge ◽

Non Local ◽

Frame Work ◽

Time Description ◽

Aharonov Bohm ◽

Space Description ◽

Non Locality

The conflict between the locality of general relativity, reflected in its space-time description, and the non-locality of quantum mechanics, contained in its Hilbert space description, is discussed. Gauge covariant non-local observables that depend on gauge fields and gravity as well as the wave function are used in order to try to understand and minimize this conflict within the frame-work of these two theories. Applications are made to the Aharonov-Bohm effect and its generalizations to non Abelian gauge fields and gravity.

Download Full-text

Dilatonic dyon black hole solutions in the model with two Abelian gauge fields

EPJ Web of Conferences ◽

10.1051/epjconf/201816809004 ◽

2018 ◽

Vol 168 ◽

pp. 09004

Author(s):

Medeu Abishev ◽

Dmitry Ivashchuk ◽

Kuantay Boshkayev ◽

Algys Malybayev

Keyword(s):

Black Hole ◽

Scalar Field ◽

Coupling Constants ◽

Gravitational Mass ◽

Kinetic Term ◽

Gauge Fields ◽

Abelian Gauge ◽

Dilatonic Black Hole ◽

Ghost Scalar Field ◽

Black Hole Solutions

Dilatonic black hole dyon-like solutions in the gravitational 4d model with a scalar field, two 2-forms, two dilatonic coupling constants λi ≠ 0, i = 1,2, obeying λ1 ≠ − λ2 and sign parameter ε = ±1 for scalar field kinetic term are considered. Here ε = −1 corresponds to ghost scalar field. These solutions are defined up to solutions of two master equations for two moduli functions, when λi2 ≠ 1/2 for ε = −1. A set of bounds on gravitational mass and scalar charge are presented by using a certain conjecture on parameters of solutions, when 1 + 2λi2ε > 0, i = 1, 2.

Download Full-text

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

Risalah Fisika ◽

10.35895/rf.v2i2.117 ◽

2018 ◽

Vol 2 (2) ◽

pp. 43-47

Author(s):

A. Suparmi, C. Cari, Ina Nurhidayati

Keyword(s):

Wave Function ◽

Quantum Mechanics ◽

Schrödinger Equation ◽

Coulomb Potential ◽

Schrodinger Equation ◽

Minimal Length ◽

Energy Spectra ◽

Atomic Particle ◽

Approximate Analytical Solutions ◽

Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

Download Full-text

Non-Abelian generalizations of the Hofstadter model: spin–orbit-coupled butterfly pairs

Light Science & Applications ◽

10.1038/s41377-020-00384-7 ◽

2020 ◽

Vol 9 (1) ◽

Cited By ~ 1

Author(s):

Yi Yang ◽

Bo Zhen ◽

John D. Joannopoulos ◽

Marin Soljačić

Keyword(s):

Quantum Hall ◽

Building Blocks ◽

Real Space ◽

Gauge Fields ◽

Spin Orbit ◽

Abelian Gauge ◽

Experimental Realization ◽

Integer Quantum Hall Effect ◽

Integer Quantum ◽

Necessary And Sufficient

Abstract The Hofstadter model, well known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum Hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment, we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin–orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to topological insulators. We conclude by discussing possible schemes for experimental realization of the models on photonic platforms.

Download Full-text