Straight-line motion of classical point particles in a three-dimensional lattice

2016 ◽  
Vol 37 (4) ◽  
pp. 045802
Author(s):  
R De Luca
Keyword(s):  
Three Dimensional ◽  
Dimensional Lattice ◽  
Point Particles ◽  
Straight Line ◽  
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

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

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