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

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

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.

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 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.

Phenomena and devices at the quantum scale and the mesoscale

2017 ◽  
Author(s):  
Sandip Tiwari
Keyword(s):  
Coulomb Blockade ◽  
Secure Communication ◽  
Quantum Hall ◽  
Nanoscale Device ◽  
Self Energy ◽  
Stability Diagrams ◽  
Charge Stability ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Non Locality

Unique nanoscale phenomena arise in quantum and mesoscale properties and there are additional intriguing twists from effects that are classical in origin. In this chapter, these are brought forth through an exploration of quantum computation with the important notions of superposition, entanglement, non-locality, cryptography and secure communication. The quantum mesoscale and implications of nonlocality of potential are discussed through Aharonov-Bohm effect, the quantum Hall effect in its various forms including spin, and these are unified through a topological discussion. Single electron effect as a classical phenomenon with Coulomb blockade including in multiple dot systems where charge stability diagrams may be drawn as phase diagram is discussed, and is also extended to explore the even-odd and Kondo consequences for quantum-dot transport. This brings up the self-energy discussion important to nanoscale device understanding.

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