Dirac Equation in Cosmological Inertial Frame

Dirac equation is a one order-wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Dirac Equation from wave function, Type A in cosmological inertial frame.The Dirac equation satisfy Klein-Gordon equation in cosmological inertial frame.

Quantization of Klein-Gordon Scalar Field in Cosmological Inertial Frame

In the Cosmological Special Theory of Relativity, we quantized Klein-Gordon scalar field. We treatLagrangian density and Hamiltonian in quantized Klein-Gordon scalar field in the Cosmological SpecialTheory of Relativity

Schrodinger Equation in Cosmological Inertial Frame

Schrodinger equation is a wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Schrodinger equation from Klein-Gordon free particle’s wave function in cosmological special theory of relativity.

Yukawa Potential in Klein-Gordon Equation in Cosmological Inertial Frame

We study Yukawa potential dependent about time in cosmological inertial frame. If we solve Klein-Gordon equation, we obtain Yukawa potential dependent about time in cosmological inertial frame.

Interaction of Complex Scalar Fields and Electromagnetic Fields in Klein-Gordon-Maxwell Theory in Cosmological Inertial Frame

We found equations of complex scalar fields and electromagnetic fields on interaction of complexscalar fields and electromagnetic fields in Klein-Gordon-Maxwell theory from Type A of wave function andType B of expanded distance in cosmological inertial frame.

Quantization of Electromagnetic Field and Potential in Rindler Space-Time

The article treats quantization of electromagnetic field that is defined in Rindler space-time. Likely the electromagnetic field, the potential did quantizated in inertial frame, the electromagnetic field, the potential can quantizate by the transformation of electromagnetic field or the transformation of the potential in the accelerated frame. We treat Lorentz gauge condition in quantization of electromagnetic potential.

Electromagnetic Wave Function and Equation, Lorentz Force in Rindler Spacetime

In the general relativity theory, we find the electro-magnetic wave function and equation in Rindlerspace-time. Specially, this article is that electromagnetic wave equation is corrected by the gauge fixingequation in Rindler space-time. We define the force in Rindler space-time We find Lorentz force(electromagnetic force) by electro-magnetic field transformations in Rindler space-time. In the inertial frame, Lorentz force is defined as 4-dimensional force. Hence, we had to obtain 4-dimensional force in Rindler space-time. We define energy-momentum in Rindler space-time.

Dragging of inertial frames by matter and waves

In this paper, we review and analyze four specific general-relativistic problems in which gravitomagnetism plays an important role: the dragging of magnetic fields around rotating black holes, dragging inside a collapsing slowly rotating spherical shell of dust, compared with the dragging by rotating gravitational waves. We demonstrate how the quantum detection of inertial frame dragging can be accomplished by using the Unruh–DeWitt detectors. Finally, we shall briefly show how “instantaneous Machian gauges” can be useful in the cosmological perturbation theory.

Terminology and notation

Notation and sign conventions adopted for the rest of the book are explained. The book employs index notation, but not abstract index notation. The metric signature for GR is taken as (-1,1,1,1). Terminology such as “local inertial frame” and “Rieman normal coordinates” is explained.

Further useful ideas

The chapter discusses several further aspects of the physics and mathematics that prove very useful in practice. First we define 4-velocity, 4-momentum and 4-acceleration. Then we introduce the tetrad and show how it can be used to relate a given 4-momentum to the energy and momentum observed in a LIF (local inertial frame). Then we define covariant version of the vector operators div, grad, curl, and obtain simplified expressions for the divergence of a vector and an antisymmetric tensor. The generalized Gauss divergence theorem is then presented.