scholarly journals THE DIRAC FIELD IN TAUB–NUT BACKGROUND

2001 ◽  
Vol 16 (10) ◽  
pp. 1743-1758 ◽  
Author(s):  
ION I. COTĂESCU ◽  
MIHAI VISINESCU
Keyword(s):  
Invariant Theory ◽  
Gordon Equation ◽  
Dirac Field ◽  
Dirac Fermions ◽  
Large Collection ◽  
Scalar Theory ◽  
Gauge Invariant ◽  
Commuting Operators ◽  
Klein Gordon ◽  
Kaluza Klein

We investigate the SO (4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza–Klein monopole, pointing out that the quantum modes can be recovered from a Klein–Gordon equation analogous to the Schrödinger equation in the Taub–NUT background. Moreover, we show that there is a large collection of observables that can be directly derived from those of the scalar theory. These offer many possibilities of choosing complete sets of commuting operators which determine the quantum modes. In addition there are some spin-like and Dirac-type operators involving the covariantly constant Killing–Yano tensors of the hyper-Kähler Taub–NUT space. The energy eigenspinors of the central modes in spherical coordinates are completely evaluated in explicit, closed form.

Mechanics of a charged particle on the Kaluza–Klein background

1995 ◽  
Vol 73 (9-10) ◽  
pp. 602-607 ◽  
Author(s):  
S. R. Vatsya
Keyword(s):  
Electromagnetic Field ◽  
Charged Particle ◽  
Integral Method ◽  
Gordon Equation ◽  
Type Equation ◽  
Fifth Dimension ◽  
Klein Gordon ◽  
Path Integral Method ◽  
Klein Gordon Equation ◽  
Kaluza Klein

The path-integral method is used to derive a generalized Schrödinger-type equation from the Kaluza–Klein Lagrangian for a charged particle in an electromagnetic field. The compactness of the fifth dimension and the properties of the physical paths are used to decompose this equation into its infinite components, one of them being similar to the Klein–Gordon equation.

scholarly journals PROPER TIME FORMALISM AND GAUGE INVARIANCE IN OPEN STRING INTERACTIONS

1994 ◽  
Vol 09 (18) ◽  
pp. 1681-1693
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Sigma Model ◽  
Gordon Equation ◽  
Proper Time ◽  
Open String ◽  
Gauge Invariant ◽  
Point Particles ◽  
Boundary Terms ◽  
Time Formalism ◽  
Klein Gordon ◽  
Model Formalism

The issue of gauge invariances in the sigma model formalism is discussed at the free and interacting level. The problem of deriving gauge invariant interacting equations can be addressed using the proper time formalism. This formalism is discussed, both for point particles and strings. The covariant Klein-Gordon equation arises in a geometric way from the boundary terms. This formalism is similar to the background independent open string formalism introduced by Witten.

QUANTUM CONSISTENCY OF A GAUGE-INVARIANT THEORY OF A MASSIVE SPIN-3/2 PARTICLE INTERACTING WITH EXTERNAL FIELDS

1989 ◽  
Vol 04 (13) ◽  
pp. 1237-1247 ◽  
Author(s):  
SAURABH D. RINDANI
Keyword(s):  
Invariant Theory ◽  
Positive Definite ◽  
External Fields ◽  
Gauge Invariant ◽  
Negative Norm ◽  
Gravitational Fields ◽  
Massive Spin ◽  
Kaluza Klein

A gauge-invariant theory of a massive spin-3/2 particle interacting with external electromagnetic and gravitational fields, obtained earlier by Kaluza-Klein reduction of a massless Rarita-Schwinger theory, is quantized using Dirac’s procedure. The field anticommutators are found to be positive definite. The theory, which was earlier shown to be free from the classical Velo-Zwanziger problem of noncausal propagation modes, is thus also free from the problem of negative-norm states, a longstanding problem associated with massive spin-3/2 theories with external interaction.

scholarly journals A NOTE ON KLEIN–GORDON EQUATION IN A GENERALIZED KALUZA–KLEIN MONOPOLE BACKGROUND

2007 ◽  
Vol 22 (22) ◽  
pp. 1621-1634 ◽  
Author(s):  
EUGEN RADU ◽  
MIHAI VISINESCU
Keyword(s):  
Black Holes ◽  
Gordon Equation ◽  
Asymptotic Structure ◽  
Klein Gordon ◽  
Monopole Solution ◽  
Klein Gordon Equation ◽  
Kaluza Klein

We investigate solutions to the Klein–Gordon equation in a class of five-dimensional geometries presenting the same symmetries and asymptotic structure as the Gross–Perry–Sorkin monopole solution. Apart from globally regular metrics, we consider also squashed Kaluza–Klein black holes backgrounds.

scholarly journals Chiralspin Symmetry and Its Implications for QCD

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 38 ◽  
Author(s):  
Leonid Glozman
Keyword(s):  
Dirac Operator ◽  
Invariant Theory ◽  
Magnetic Interaction ◽  
Kinetic Term ◽  
Dirac Fermions ◽  
Gauge Invariant ◽  
Zero Modes ◽  
Left Handed ◽  
Electric Interaction ◽  
The Right

In a local gauge-invariant theory with massless Dirac fermions, a symmetry of the Lorentz-invariant fermion charge is larger than a symmetry of the Lagrangian as a whole. While the Dirac Lagrangian exhibits only a chiral symmetry, the fermion charge operator is invariant under a larger symmetry group, S U ( 2 N F ) , that includes chiral transformations as well as S U ( 2 ) C S chiralspin transformations that mix the right- and left-handed components of fermions. Consequently, a symmetry of the electric interaction, which is driven by the charge density, is larger than a symmetry of the magnetic interaction and of the kinetic term. This allows separating in some situations electric and magnetic contributions. In particular, in QCD, the chromo-magnetic interaction contributes only to the near-zero modes of the Dirac operator, while confining chromo-electric interaction contributes to all modes. At high temperatures, above the chiral restoration crossover, QCD exhibits approximate S U ( 2 ) C S and S U ( 2 N F ) symmetries that are incompatible with free deconfined quarks. Consequently, elementary objects in QCD in this regime are quarks with a definite chirality bound by the chromo-electric field, without the chromo-magnetic effects. In this regime, QCD can be described as a stringy fluid.

scholarly journals Proper time and conformal problem in Kaluza–Klein theory

2015 ◽  
Vol 12 (05) ◽  
pp. 1550063
Author(s):  
E. Minguzzi
Keyword(s):  
Scalar Field ◽  
Gordon Equation ◽  
Proper Time ◽  
Inertial Mass ◽  
Scalar Fields ◽  
Conformal Factor ◽  
Klein Theory ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Kaluza Klein

In the traditional Kaluza–Klein theory, the cylinder condition and the constancy of the extra-dimensional radius (scalar field) imply that time-like geodesics on the five-dimensional bundle project to solutions of the Lorentz force equation on spacetime. This property is lost for nonconstant scalar fields, in fact there appears new terms that have been interpreted mainly as new forces or as due to a variable inertial mass and/or charge. Here we prove that the additional terms can be removed if we assume that charged particles are coupled with the same spacetime conformal structure of neutral particles but through a different conformal factor. As a consequence, in Kaluza–Klein theory the proper time of the charged particle might depend on the charge-to-mass ratio and the scalar field. Then we show that the compatibility between the equation of the projected geodesic and the classical limit of the Klein–Gordon equation fixes unambiguously the conformal factor of the coupling metric solving the conformal ambiguity problem of Kaluza–Klein theories. We confirm this result by explicitly constructing the projection of the Klein–Gordon equation and by showing that each Fourier mode, even for a variable scalar field, satisfies the Klein–Gordon equation on the base.

scholarly journals Evolution of Superoscillations in the Dirac Field

2020 ◽  
Vol 50 (11) ◽  
pp. 1356-1375
Author(s):  
Fabrizio Colombo ◽  
Giovanni Valente
Keyword(s):  
Dirac Equation ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Dirac Field ◽  
Field Equations ◽  
Relativistic Quantum Theory ◽  
Dual Purpose ◽  
Klein Gordon ◽  
Superoscillating Functions ◽  
Band Limited

AbstractSuperoscillating functions are band-limited functions that can oscillate faster than their fastest Fourier component. The study of the evolution of superoscillations as initial datum of field equations requires the notion of supershift, which generalizes the concept of superoscillations. The present paper has a dual purpose. The first one is to give an updated and self-contained explanation of the strategy to study the evolution of superoscillations by referring to the quantum-mechanical Schrödinger equation and its variations. The second purpose is to treat the Dirac equation in relativistic quantum theory. The treatment of the evolution of superoscillations for the Dirac equation can be deduced by recent results on the Klein–Gordon equation, but further additional considerations are in order, which are fully described in this paper.

PARTICLE MASSES IN KALUZA–KLEIN–GORDON THEORY AND THE REALITY OF EXTRA DIMENSIONS

1998 ◽  
Vol 13 (33) ◽  
pp. 2689-2694 ◽  
Author(s):  
HONGYA LIU ◽  
PAUL S. WESSON
Keyword(s):  
Wave Function ◽  
Exact Solutions ◽  
Extra Dimension ◽  
Extra Dimensions ◽  
Gordon Equation ◽  
Superstring Theory ◽  
Klein Theory ◽  
Klein Gordon ◽  
Klein Gordon Equation ◽  
Kaluza Klein

To see how the effective 4-D mass of a particle is affected by the geometry of an ND space, we take the Klein–Gordon equation in 5-D and evaluate it in 4-D using two exact solutions of 5-D Kaluza–Klein theory. The mass (squared) turns out to be complex if the theory is independent of the extra coordinate, but can be made real if the wave function depends on an extra dimension which is physical. These results have significant implications for 10-D superstring theory.

The Standard Theory

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Gauge Theory ◽  
Invariant Theory ◽  
Standard Theory ◽  
Strong Interactions ◽  
Gauge Invariant ◽  
Electromagnetic Interactions ◽  
Protons And Neutrons ◽  
Free Particles ◽  
Theoretical Predictions ◽  
Theory And Experiment

All ingredients of the previous chapters are combined in order to build a gauge invariant theory of the interactions among the elementary particles. We start with a unified model of the weak and the electromagnetic interactions. The gauge symmetry is spontaneously broken through the BEH mechanism and we identify the resulting BEH boson. Then we describe the theory known as quantum chromodynamics (QCD), a gauge theory of the strong interactions. We present the property of confinement which explains why the quarks and the gluons cannot be extracted out of the protons and neutrons to form free particles. The last section contains a comparison of the theoretical predictions based on this theory with the experimental results. The agreement between theory and experiment is spectacular.

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