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

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Electromagnetic Fields ◽  
Inertial Frame ◽  
Type A ◽  
Scalar Fields ◽  
Maxwell Theory ◽  
Complex Scalar ◽  
Klein Gordon

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.

Canonical quantization of free fields

2021 ◽  
pp. 70-98
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Quantum Theory ◽  
Electromagnetic Fields ◽  
Classical Theory ◽  
Canonical Quantization ◽  
Classical Mechanics ◽  
Scalar Fields ◽  
Complex Scalar ◽  
Spinor Fields ◽  
Free Fields

This chapter discusses canonical quantization in field theory and shows how the notion of a particle arises within the framework of the concept of a field. Canonical quantization is the process of constructing a quantum theory on the basis of a classical theory. The chapter briefly considers the main elements of this procedure, starting from its simplest version in classical mechanics. It first describes the general principles of canonical quantization and then provides concrete examples. The examples include the canonical quantization of free real scalar fields, free complex scalar fields, free spinor fields and free electromagnetic fields.

scholarly journals Dirac Equation in Cosmological Inertial Frame

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Dirac Equation ◽  
Inertial Frame ◽  
Gordon Equation ◽  
Probability Amplitude ◽  
Function Type ◽  
Klein Gordon ◽  
Klein Gordon Equation

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.

scholarly journals A novel approach to quantum gravity in the presence of matter without the problem of time

2020 ◽  
Vol 35 (04) ◽  
pp. 2050015
Author(s):  
Matej Pavšič
Keyword(s):  
Wave Function ◽  
Time Derivative ◽  
Scalar Fields ◽  
The Novel ◽  
Problem Of Time ◽  
Spinor Fields ◽  
Novel Approach ◽  
Quantization Of Gravity ◽  
Klein Gordon ◽  
Quantum Counterpart

An approach to the quantization of gravity in the presence of matter is examined which starts from the classical Einstein–Hilbert action and matter approximated by “point” particles minimally coupled to the metric. Upon quantization, the Hamilton constraint assumes the form of the Schrödinger equation: it contains the usual Wheeler–DeWitt term and the term with the time derivative of the wave function. In addition, the wave function also satisfies the Klein–Gordon equation, which arises as the quantum counterpart of the constraint among particles’ momenta. Comparison of the novel approach with the usual one in which matter is represented by scalar fields is performed, and shown that those approaches do not exclude, but complement each other. In final discussion it is pointed out that the classical matter could consist of superparticles or spinning particles, described by the commuting and anticommuting Grassmann coordinates, in which case spinor fields would occur after quantization.

scholarly journals Spacelike deformations: higher-helicity fields from scalar fields

2020 ◽  
Vol 110 (8) ◽  
pp. 2019-2038 ◽  
Author(s):  
Vincenzo Morinelli ◽  
Karl-Henning Rehren
Keyword(s):  
Perturbation Theory ◽  
Time Evolution ◽  
Infinite Family ◽  
Scalar Fields ◽  
Quantum Field ◽  
Maxwell Theory ◽  
Hamiltonian Perturbation ◽  
Klein Gordon ◽  
Hamiltonian Perturbation Theory

Abstract In contrast to Hamiltonian perturbation theory which changes the time evolution, “spacelike deformations” proceed by changing the translations (momentum operators). The free Maxwell theory is only the first member of an infinite family of spacelike deformations of the complex massless Klein–Gordon quantum field into fields of higher helicity. A similar but simpler instance of spacelike deformation allows to increase the mass of scalar fields.

scholarly journals EFFECTIVE DYNAMICS FOR SOLITONS IN THE NONLINEAR KLEIN–GORDON–MAXWELL SYSTEM AND THE LORENTZ FORCE LAW

2009 ◽  
Vol 21 (04) ◽  
pp. 459-510 ◽  
Author(s):  
EAMONN LONG ◽  
DAVID STUART
Keyword(s):  
Electromagnetic Field ◽  
Lorentz Force ◽  
Scalar Fields ◽  
Space Time ◽  
Maxwell System ◽  
Complex Scalar ◽  
Effective Dynamics ◽  
Dimensional Minkowski Space ◽  
Klein Gordon ◽  
Lorentz Force Law

We consider the nonlinear Klein–Gordon–Maxwell system derived from the Lagrangian [Formula: see text] on four-dimensional Minkowski space-time, where ϕ is a complex scalar field and Fμν = ∂μ𝔸ν - ∂ν𝔸μ is the electromagnetic field. For appropriate nonlinear potentials [Formula: see text], the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons introduced and studied by Lee and collaborators for pure complex scalar fields. In this article, we develop a rigorous dynamical perturbation theory for these solitons in the small e limit, where e is the electromagnetic coupling constant. The main theorems assert the long time stability of the solitons with respect to perturbation by an external electromagnetic field produced by the background current 𝕁B, and compute their effective dynamics to O(e). The effective dynamical equation is the equation of motion for a relativistic particle acted on by the Lorentz force law familiar from classical electrodynamics. The theorems are valid in a scaling regime in which the external electromagnetic fields are O(1), but vary slowly over space-time scales of [Formula: see text], and δ = e1 - k for [Formula: see text] as e → 0. We work entirely in the energy norm, and the approximation is controlled in this norm for times of [Formula: see text].

scholarly journals Schrodinger Equation in Cosmological Inertial Frame

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Inertial Frame ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Klein Gordon

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.

The classical scalar field

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Scalar Field ◽  
Symmetry Breaking ◽  
Free Field ◽  
Scalar Fields ◽  
Global Symmetry ◽  
Lagrange Equations ◽  
Complex Scalar ◽  
Klein Gordon ◽  
Complex Scalar Field ◽  
The Fourier Transform

This chapter explains some of the properties of scalar fields, which are paradigmatic in relativistic field theory. It also shows how a complex scalar field can confer an effective mass to a ‘gauge’ field. The chapter first provides the Klein–Gordon equation derived from the Euler–Lagrange equations outlined in the previous chapter. It then illustrates the Fourier transform of a free field, before embarking on further discussions on complex fields, charge, and symmetry breaking. Finally, this chapter considers that the fact that global symmetry breaking leads to the appearance of a massless, and therefore long-range, scalar field is problematic because such a field is not observed experimentally. It thus takes a look at the BEH mechanism (named after its inventors, Robert Brout, François Englert, and Peter Higgs), which can make it ‘disappear’.

Time evolving potentials for electromagnetic knots

2017 ◽  
Vol 14 (05) ◽  
pp. 1750073 ◽  
Author(s):  
Antonio F. Rañada ◽  
Alfredo Tiemblo ◽  
José L. Trueba
Keyword(s):  
Electromagnetic Fields ◽  
Scalar Fields ◽  
Future Research ◽  
Topological Invariants ◽  
Topological Properties ◽  
Complex Scalar ◽  
Level Curves ◽  
Three Sphere ◽  
Vector Potentials ◽  
And Topology

Electromagnetic knots are electromagnetic fields in which the magnetic and electric lines are level curves of two complex scalar fields. If these scalar fields are chosen so that they can be interpreted as maps between the three-sphere and the two-sphere every time, then the electromagnetic helicity is proportional to the sum of the Hopf indices of both maps, that are topological invariants. An important example of this kind of electromagnetic fields with topological properties is often called the Hopfion. It is an electromagnetic knot in which the scalar fields are built from Hopf maps. In this work, we study the conditions for these electromagnetic fields to be null, i.e. to have both Lorentz invariant quantities [Formula: see text] and [Formula: see text] equal to zero. We derive from these fields explicit vector potentials [Formula: see text] and [Formula: see text] satisfying force-free like conditions for every time. In particular, equations [Formula: see text], [Formula: see text] are derived for them. As a consequence, the energy, which is discretized, is proportional to the electromagnetic helicity. This relation between Physics and Topology is intriguing and worth of future research.

scholarly journals Several Physical Properties of Two Interacting Complex Scalar Fields at Finite Density

2011 ◽  
Vol 21 (1) ◽  
pp. 1
Author(s):  
Tran Huu Phat ◽  
Phan Thi Duyen
Keyword(s):  
Mean Field ◽  
Scalar Fields ◽  
Meissner Effect ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Goldstone Theorem ◽  
Complex Scalar ◽  
Finite Density ◽  
Chemical Potentials ◽  
The Mean

The two interacting complex scalar fields at finite density is considered in the mean field approximation. It is shown that although the symmetry is spontaneously broken for the chemical potentials bigger than the meson masses in vacuum, but the Goldstone theorem is not preserved in broken phase. Then two mesons are condensed and their condensates turn out to be two-gap superconductor which is signaled by the appearance of the Meissner effect as well as the Abrikosov and non-Abrikosov vortices. Finally, there exhibits domain wall which is the plane, where two condensates flowing in opposite directions collide and generate two types of vortices with cores in the wall.

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