Elastic collisions of classical point particles on a finite frictionless linear track with perfectly reflecting endpoints

2006 ◽  
Vol 27 (2) ◽  
pp. 437-449
Author(s):  
R De Luca
Keyword(s):  
Elastic Collisions ◽  
Point Particles ◽  
Classical Point Particles ◽  
Classical Point

Statistical Mechanics of Classical Particles with Gravitational Interactions: Exactly Solvable (for N≤∞) in d=1 and d>2

1997 ◽  
Vol 11 (01n02) ◽  
pp. 127-131 ◽  
Author(s):  
Michael K.-H. Kiessling
Keyword(s):  
Statistical Mechanics ◽  
Continuum Model ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Point Particles ◽  
Exactly Solvable ◽  
Classical Point Particles ◽  
Classical Particles ◽  
Classical Point ◽  
Liouville’S Equation

This paper is concerned with a curious gap in a string of exactly solvable models, a gap that is suggestively related to a completely integrable nonlinear PDE in d=2 known as Liouville's equation. This PDE emerges in a limit N→∞ from the equilibrium statistical mechanics of classical point particles with gravitational interactions (SMGI) in dimension d=2 which, accordingly, is an exactly solvable continuum model in this limit. Interestingly, in d=1 and all d>2, the SMGI can be, and partly has been, exactly evaluated for all N≤∞. This entitles one to suspect that the SMGI for d=2 is likewise exactly solvable for N>∞, but currently this is an unproven hypothesis. If this conjecture can be answered in the affirmative, spin-offs in various areas associated with Liouville's equation, such as vortex gases, superfluidity, random matrices, and string theory can be expected.

Electromagnetic (self-) interactions in relativistic Schrödinger theory

2001 ◽  
Vol 79 (6) ◽  
pp. 879-906
Author(s):  
M Mattes ◽  
S Rupp ◽  
M Sorg
Keyword(s):  
Gauge Field ◽  
Mathematical Structure ◽  
Point Particle ◽  
Pathological Features ◽  
Fibre Bundles ◽  
Point Particles ◽  
Self Energy ◽  
Electromagnetic Interactions ◽  
Classical Point Particles ◽  
Classical Point

The Relativistic Schrödinger Theory (RST) is applied to a system of N particles with electromagnetic interactions. The gauge group is U(1) × U(1)... × U(1). By exploiting the mathematical structure of fibre bundles, the energy-momentum content of the gauge field can be defined in such a way that no infinite self-energy of point charges can arise. However, the picture of classical point particles becomes insufficient in any case in view of the exchange and overlap effects occurring in RST. The presence of overlap currents seems to be necessary to remedy certain pathological features of the classical point-particle theories. PACS Nos.: 03.65Pm, 03.65Ge, 03.65Ta

scholarly journals OPERATIONAL GEOMETRY ON DE SITTER SPACETIME

2012 ◽  
Vol 27 (23) ◽  
pp. 1250130 ◽  
Author(s):  
P. AGUILAR ◽  
Y. BONDER ◽  
C. CHRYSSOMALAKOS ◽  
D. SUDARSKY
Keyword(s):  
Quantum Theory ◽  
Operational Definition ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Spacetime Geometry ◽  
Point Particles ◽  
Sitter Spacetime ◽  
Classical Point Particles ◽  
Definition Of ◽  
Classical Point

Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though, leading us to consider the implications of using realistic probes in defining an effective spacetime geometry. As an example, we consider de Sitter spacetime and employ the centroid of various composite probes to obtain its effective sectional curvature, which is found to depend on the probe's internal energy, spatial extension, and spin. Possible refinements of our approach are pointed out and remarks are made on the relevance of our results to the quest for a quantum theory of gravity.

scholarly journals Finite Self-Energy of Classical Point Particles

1960 ◽  
Vol 4 (7) ◽  
pp. 375-377 ◽  
Author(s):  
R. Arnowitt ◽  
S. Deser ◽  
C. W. Misner
Keyword(s):  
Point Particles ◽  
Self Energy ◽  
Classical Point Particles ◽  
Classical Point

Maximum number of collisions of elastic particles

1972 ◽  
Vol 331 (1584) ◽  
pp. 1-18 ◽  
Keyword(s):  
Kinetic Theory ◽  
Degrees Of Freedom ◽  
Elastic Collisions ◽  
Two Degrees Of Freedom ◽  
Point Particles ◽  
Elastic Particles

Consider n point-particles, all of the same mass, moving freely in space and interacting only by elastic collisions. There are two degrees of freedom in the outcome of any collision. Let C(n) be the maximum number of collisions possible under Newtonian laws and C*(n) the maximum number possible in relativistic mechanics. This paper is directed towards finding those two functions but is far from achieving that. The following results are established: C(n) ≥1/2n ( n — 1), (C*(n) ≥ 1/2n( n — 1); C(3) = C*(3) = 3; C(4) = 6 (but only for a certain collision-topology) and C*(4)≥ 7. The problem of finding C(n) and C*(n) is of interest in kinetic theory and elsewhere.

scholarly journals Acceleration-Induced Nonlocality

2017 ◽  
Author(s):  
Bahram Mashhoon
Keyword(s):  
World Line ◽  
Integral Relation ◽  
Field Measurements ◽  
Physical Principle ◽  
Relativity Theory ◽  
General Integral ◽  
Electric And Magnetic Fields ◽  
The Status ◽  
Classical Point Particles ◽  
Classical Point

The locality postulate of the standard relativity theory is exact when dealing with phenomena involving classical point particles and rays of radiation, but breaks down for electromagnetic fields, as field properties cannot be measured instantaneously. Furthermore, Bohr and Rosenfeld pointed out in 1933 that only spacetime averages of the classical electric and magnetic fields have immediate physical significance. This assertion acquires the status of a physical principle when the intrinsic acceleration scales of observers are taken into account. To incorporate acceleration-induced nonlocality into relativity theory, a general integral relation is postulated between the field as measured by an accelerated observer and the instantaneous field measurements of the momentarily comoving inertial observers along the past world line of the observer. This nonlocal ansatz involves an acceleration kernel and leads to nonlocal special relativity once the kernel is determined.

The kinematics of a point particle

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Internal Structure ◽  
Proper Time ◽  
World Line ◽  
Point Particle ◽  
Material Point ◽  
Spatial Extent ◽  
Geometric Representation ◽  
Mathematical Result ◽  
Point Particles ◽  
The World

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.

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