The Foldy-Wouthuysen Representation for Free Particles

1990 ◽  
pp. 217-231
Author(s):  
Walter Greiner
Keyword(s):  
Free Particles

On the Origin of Four Pi in Physics

2016 ◽  
pp. 3994-4013
Author(s):  
Aaron Hanken
Keyword(s):  
Black Hole ◽  
Surface Area ◽  
Single Particles ◽  
Pythagorean Triples ◽  
Free Particles ◽  
Close Relationship ◽  
Dimensional Parameters ◽  
Gaussian Surface ◽  
Planck Energy ◽  
The Universe

We find the highest symmetry between the fields intrinsic to free particles (free particles having only mass, charge and spin), and show these fields symmetries and their close relationship to force and entropy. The Boltzmann Constant is equal to the natural entropy, in that it is The Planck Energy over The Planck Temperature. This completes a needed symmetry in The Bekenstein-Hawking Entropy. Upon substitution of Planck Units into The Schwarzschild Radius, we find that the mass and radius of any black hole define both the gravitational constant and the natural force. We find that the Gaussian Surface area about a particle is equal to the surface area of an equally massed black hole if we define the gravitational field of that particle to be the quotient of The Planck Force and the particles mass. By these simple substitutions we find that gravity is quantized in units of surface entropy. We also find Pythagorean Triples are resting within the dimensional parameters of Special Relativity, and show this to be the dimensional aspects of single particles observing one another, coupled with the intrinsic Hubble nature of the universe.

The Standard Theory

2017 ◽  
Author(s):  
John Iliopoulos
Keyword(s):  
Gauge Theory ◽  
Invariant Theory ◽  
Standard Theory ◽  
Strong Interactions ◽  
Gauge Invariant ◽  
Electromagnetic Interactions ◽  
Protons And Neutrons ◽  
Free Particles ◽  
Theoretical Predictions ◽  
Theory And Experiment

All ingredients of the previous chapters are combined in order to build a gauge invariant theory of the interactions among the elementary particles. We start with a unified model of the weak and the electromagnetic interactions. The gauge symmetry is spontaneously broken through the BEH mechanism and we identify the resulting BEH boson. Then we describe the theory known as quantum chromodynamics (QCD), a gauge theory of the strong interactions. We present the property of confinement which explains why the quarks and the gluons cannot be extracted out of the protons and neutrons to form free particles. The last section contains a comparison of the theoretical predictions based on this theory with the experimental results. The agreement between theory and experiment is spectacular.

Classical Kinetic Theory

2018 ◽  
Author(s):  
Klaus Morawetz
Keyword(s):  
Kinetic Equation ◽  
Equation Of State ◽  
Mean Field ◽  
Ideal Gas ◽  
Hydrodynamic Equations ◽  
Free Particles ◽  
Internal Mechanism ◽  
The Mean ◽  
Energy Gains ◽  
Non Locality

The classical non-ideal gas shows that the two original concepts of the pressure based of the motion and the forces have eventually developed into drift and dissipation contributions. Collisions of realistic particles are nonlocal and non-instant. A collision delay characterizes the effective duration of collisions, and three displacements, describe its effective non-locality. Consequently, the scattering integral of kinetic equation is nonlocal and non-instant. The non-instant and nonlocal corrections to the scattering integral directly result in the virial corrections to the equation of state. The interaction of particles via long-range potential tails is approximated by a mean field which acts as an external field. The effect of the mean field on free particles is covered by the momentum drift. The effect of the mean field on the colliding pairs causes the momentum and the energy gains which enter the scattering integral and lead to an internal mechanism of energy conversion. The entropy production is shown and the nonequilibrium hydrodynamic equations are derived. Two concepts of quasiparticle, the spectral and the variational one, are explored with the help of the virial of forces.

The stability of a gravitating ring of free particles

1995 ◽  
Vol 7 (4) ◽  
pp. 279-281
Author(s):  
V. A. Antonov ◽  
A. A. Vakhidov
Keyword(s):  
Free Particles ◽  
The Stability

The application of the Whitehead theory of relativity to non-static, spherically symmetrical systems

1954 ◽  
Vol 222 (1151) ◽  
pp. 509-526 ◽  
Keyword(s):  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Current Standard ◽  
World Model ◽  
Basic Principles ◽  
Density Distributions ◽  
Free Particles ◽  
Static Systems ◽  
Solar Field ◽  
Good Agreement

In a recent paper Synge (1952) reformulated in current standard notation the basic principles of the theory of relativity of A. N. Whitehead and investigated the gravitational properties of a spherically symmetrical static distribution of matter. He applied this theory to the solar field and verified the result previously indicated by Whitehead (1922) that the theory is in good agreement with the local tests satisfied by Einstein’s general theory of relativity. The present paper extends the theory of Whitehead to non-static systems whose velocity and density distributions possess complete spherical symmetry about a spatial origin in a Galilean frame of reference. In particular, a uniformly expanding homogeneous world-model is constructed which differs significantly both from Milne’s model and that of special relativity. The motion of free particles and photons in this model is investigated and a formula for the law of red-shifts is derived.

scholarly journals The Confined Atom: James Clerk Maxwell on the Fundamental Particles and the Limits of Scientific Knowledge

2021 ◽  
Vol 29 (2) ◽  
pp. 189-214
Author(s):  
Charis Charalampous
Keyword(s):  
Heat Conduction ◽  
Scientific Knowledge ◽  
Gas Diffusion ◽  
Mathematical Formalism ◽  
James Clerk Maxwell ◽  
Fundamental Particles ◽  
Free Particles ◽  
Gravitational Pull ◽  
Confined Atom

Abstract This paper distinguishes in Maxwell’s thought between “atomic molecules” and “ultimate atoms,” and arrives at a set of properties that characterize each type of atom. It concludes that Maxwell is a mathematical atomist, an approach that entails the notion that although it is impossible to observe the ultimate atoms as free particles, we can nevertheless study them as mathematical observables, on the caveat that mathematical formalism remains tied to phenomenalism and to theoretical interpretations of such phenomena as, for example, mass and force variations, gravitational pull, gas diffusion and viscosity, and heat conduction.

On the pair correlation function for hard spheres at low density and temperature

1968 ◽  
Vol 46 (7) ◽  
pp. 879-888 ◽  
Author(s):  
M. S. Miller ◽  
J. D. Poll
Keyword(s):  
Correlation Function ◽  
Pair Correlation Function ◽  
Hard Spheres ◽  
Pair Correlation ◽  
Quantum Mechanical Calculation ◽  
Quantum Mechanical ◽  
Low Density ◽  
Free Particles ◽  
Low Density Limit ◽  
Hard Sphere Diameters

A quantum-mechanical calculation of the pair correlation function for hard spheres in the low-density limit has been made. This calculation is, therefore, valid at low temperatures, where quantum-mechanical diffraction and symmetry effects are important. Results are given for various temperatures and hard-sphere diameters. The pair correlation function is presented in the form g = gB + gS, where gB is the correlation function for Boltzmann particles and gS describes the symmetry effects. It is found that gS(R) for any value of the separation R is always smaller than the corresponding value for free particles.

Free particles

2016 ◽  
Author(s):  
Mohammad Saleem
Keyword(s):  
Free Particles
Sign in / Sign up

Export Citation Format

Share Document