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.

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 Exact Solutions of the Mass-Dependent Klein-Gordon Equation with the Vector Quark-Antiquark Interaction and Harmonic Oscillator Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. K. Bahar ◽  
F. Yasuk
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Oscillator Potential ◽  
Ansatz Method ◽  
Harmonic Oscillator Potential ◽  
Klein Gordon ◽  
Dependent Mass ◽  
Mass Dependent ◽  
Klein Gordon Equation

Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

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.

EXACT SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE ROSEN–MORSE TYPE POTENTIALS VIA NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 23 (35) ◽  
pp. 3005-3013 ◽  
Author(s):  
A. REZAEI AKBARIEH ◽  
H. MOTAVALI
Keyword(s):  
Exact Solutions ◽  
Gordon Equation ◽  
Bound State ◽  
S Wave ◽  
Vector Potentials ◽  
Klein Gordon ◽  
The One ◽  
Uvarov Method ◽  
Equal Scalar ◽  
Klein Gordon Equation

The exact solutions of the one-dimensional Klein–Gordon equation for the Rosen–Morse type potential with equal scalar and vector potentials are presented. First, we briefly review Nikiforov–Uvarov mathematical method. Using this method, wave functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen–Morse type potentials reduce to the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

scholarly journals ON THE CREATION OF SCALAR PARTICLES IN A FLAT ROBERTSON–WALKER SPACETIME

2011 ◽  
Vol 26 (35) ◽  
pp. 2639-2651 ◽  
Author(s):  
S. HAOUAT ◽  
R. CHEKIREB
Keyword(s):  
Exact Solutions ◽  
Effective Action ◽  
Gordon Equation ◽  
Transition Probability ◽  
Particle Creation ◽  
Pair Creation ◽  
Bogoliubov Transformation ◽  
Scalar Particles ◽  
Klein Gordon ◽  
Klein Gordon Equation

The problem of particle creation from vacuum in a flat Robertson–Walker spacetime is studied. Two sets of exact solutions for the Klein–Gordon equation are given when the scale factor is a2(η) = a+b tanh(λη)+c tanh2 (λη). Then the canonical method based on Bogoliubov transformation is applied to calculate the pair creation probability and the density number of created particles. Some particular cosmological models such as radiation dominated universe and Milne universe are discussed. For both cases the vacuum to vacuum transition probability is calculated and the imaginary part of the effective action is extracted.

scholarly journals A New Approach to Numerical Solution of Nonlinear Klein-Gordon Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Berna Bülbül ◽  
Mehmet Sezer
Keyword(s):  
Exact Solutions ◽  
Numerical Solution ◽  
Numerical Method ◽  
Error Estimation ◽  
Matrix Method ◽  
Gordon Equation ◽  
New Approach ◽  
Collocation Points ◽  
Klein Gordon ◽  
Klein Gordon Equation

A numerical method based on collocation points is developed to solve the nonlinear Klein-Gordon equations by using the Taylor matrix method. The method is applied to some test examples and the numerical results are compared with the exact solutions. The results reveal that the method is very effective, simple, and convenient. In addition, an error estimation of proposed method is presented.

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