IS THE MILNE COORDINATE SYSTEM A GOOD ONE?

1994 ◽  
Vol 09 (01) ◽  
pp. 19-27 ◽  
Author(s):  
R.C. ARCURI ◽  
B.F. SVAITER ◽  
N.F. SVAITER
Keyword(s):  
Field Theory ◽  
Coordinate System ◽  
Gordon Equation ◽  
Fock Space ◽  
Flat Space ◽  
The Other ◽  
Quantum Field ◽  
System A ◽  
Klein Gordon ◽  
Klein Gordon Equation

The upper and lower quadrants of flat space-time can be described using the Milne coordinate system. The Klein-Gordon equation of a scalar field in such a coordinate system admits at least two sets of solutions. Based on the Feynman propagator behavior it is shown that only one of the two sets gives the conventional interpretation of quantum field theory, based on a Fock space. Therefore, discarding the other set, one can still keep the Milne coordinate system.

BILINEAR FORM AND SOLITON SOLUTIONS FOR THE COUPLED NONLINEAR KLEIN–GORDON EQUATIONS

2012 ◽  
Vol 26 (15) ◽  
pp. 1250057
Author(s):  
HE LI ◽  
XIANG-HUA MENG ◽  
BO TIAN
Keyword(s):  
Field Theory ◽  
Bilinear Form ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Soliton Solutions ◽  
Relativistic Quantum Mechanics ◽  
Klein Gordon ◽  
Truncated Painlevé Expansion ◽  
Klein Gordon Equation ◽  
Singular Manifolds

With the coupling of a scalar field, a generalization of the nonlinear Klein–Gordon equation which arises in the relativistic quantum mechanics and field theory, i.e., the coupled nonlinear Klein–Gordon equations, is investigated via the Hirota method. With the truncated Painlevé expansion at the constant level term with two singular manifolds, the coupled nonlinear Klein–Gordon equations are transformed to a bilinear form. Starting from the bilinear form, with symbolic computation, we obtain the N-soliton solutions for the coupled nonlinear Klein–Gordon equations.

scholarly journals Elko and mass dimension one field of spin one-half: Causality and Fermi statistics

2014 ◽  
Vol 23 (14) ◽  
pp. 1430026 ◽  
Author(s):  
Dharam Vir Ahluwalia ◽  
Alekha Chandra Nayak
Keyword(s):  
Gordon Equation ◽  
Quantum Field ◽  
Fermi Statistics ◽  
Mass Dimension ◽  
Klein Gordon ◽  
The Subject ◽  
Expansion Coefficients ◽  
Dimension One ◽  
Complex Valued ◽  
Klein Gordon Equation

We review how Elko arise as an extension of complex-valued four-component Majorana spinors. This is followed by a discussion that constrains certain elements of phase freedom. A proof is reviewed that unambiguously establishes that Elko, and for that matter the indicated Majorana spinors, cannot satisfy Dirac equation. They, however do, as they must, satisfy spinorial Klein–Gordon equation. We then introduce a quantum field with Elko as its expansion coefficients and show that it is causal, satisfies Fermi statistics, and then refer to the existing literature to remind that its mass dimension is one. We conclude by providing an up-to-date bibliography on the subject.

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