KLEIN-GORDON-LANGEVIN QUANTUM GEOMETRY

Equivalence of the Klein-Gordon random field and the complex Klein-Gordon quantum field

The difference between a Klein-Gordon random field and the complex Klein-Gordon quantum field is characterized, explicitly comparing the roles played by negative frequency modes of test functions in creation and annihilation operator presentations of the two theories. The random field and the complex quantum field can both be constructed from the same creation and annihilation operator algebra,...

Quantum Mechanics of Klein-Gordon-Type Fields and Quantum Cosmology

With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂2 t +D)ψ(t) = 0, where t ∈ R and D is a positive-definite operator acting in a Hilbert space H̃. In particular, we determine all the positive-definite inner products on the space H of the solutions of such an equation and establish t...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Nonlinear Klein-Gordon Equation

An extended ( ′ G )–expansion method is obtained by improving the form of solution in ( G′ G )– expansion method which is proposed in recent years. By using the extended ( ′ G )–expansion method and with the aid of homogeneous balance principle, many explicit and exact travelling wave solutions with two arbitrary parameters to the Klein-Gordon equation are presented, including the hyperbolic so...

Relativistic Klein-Gordon-Maxwell multistream model for quantum plasmas.

A multistream model for spinless electrons in a relativistic quantum plasma is introduced by means of a suitable fluidlike version of the Klein-Gordon-Maxwell system. The one- and two-stream cases are treated in detail. A new linear instability condition for two-stream quantum plasmas is obtained, generalizing the previously known nonrelativistic results. In both the one- and two-stream cases, ...