Forms of relativistic dynamics with World Line Condition and separability

E. C. G. Sudarshan; N. Mukunda

doi:10.1007/bf01906186

Descriptions of Relativistic Dynamics with World Line Condition

Quantum Reports ◽

10.3390/quantum1020016 ◽

2019 ◽

Vol 1 (2) ◽

pp. 181-192 ◽

Cited By ~ 2

Author(s):

Florio Maria Ciaglia ◽

Fabio Di Cosmo ◽

Alberto Ibort ◽

Giuseppe Marmo

Keyword(s):

Tangent Bundle ◽

Vector Fields ◽

World Line ◽

Poisson Brackets ◽

Relativistic Dynamics ◽

Geometrical Analysis ◽

Poincaré Algebra ◽

Algebra Versus ◽

Line Condition

In this paper, a generalized form of relativistic dynamics is presented. A realization of the Poincaré algebra is provided in terms of vector fields on the tangent bundle of a simultaneity surface in R 4 . The construction of this realization is explicitly shown to clarify the role of the commutation relations of the Poincaré algebra versus their description in terms of Poisson brackets in the no-interaction theorem. Moreover, a geometrical analysis of the “eleventh generator” formalism introduced by Sudarshan and Mukunda is outlined, this formalism being at the basis of many proposals which evaded the no-interaction theorem.

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The variational equation of relativistic dynamics

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100017370 ◽

1940 ◽

Vol 36 (3) ◽

pp. 331-350 ◽

Cited By ~ 40

Author(s):

Myron Mathisson

Keyword(s):

Physical System ◽

Energy Equation ◽

Variational Equation ◽

World Line ◽

Essential Feature ◽

Energy Tensor ◽

Integration Path ◽

Relativistic Dynamics ◽

Linear Integral ◽

Image Position

If Tαβ is the energy-tensor, then, for any vector field ξα, the equationfollows from the energy equationSuppose first that the physical system considered is complete, i.e. that the energytensor vanishes beyond some world tube Z. Let L be a time-like world line running inside the tube. We integrate both sides of (a) over a portion of Z, and we transform an integral over a four-dimensional region into a linear integral over L. We obtain the variational equationin which the m's are tensors characteristic of the physical system. An essential feature of the m's is that they are symmetrical in their two last superscripts. Equation (c) has to be satisfied by every field ξα, provided that the ξ's vanish, with all their derivatives, at the ends of the integration path.

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World-line condition and the noninteraction theorem

Physical Review D ◽

10.1103/physrevd.31.314 ◽

1985 ◽

Vol 31 (2) ◽

pp. 314-318 ◽

Cited By ~ 4

Author(s):

F. Marquès ◽

V. Iranzo ◽

A. Molina ◽

A. Montoto ◽

J. Llosa

Keyword(s):

World Line ◽

Line Condition

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World-line condition for a spinning particle in superspace

Il Nuovo Cimento B ◽

10.1007/bf02723575 ◽

1984 ◽

Vol 82 (1) ◽

pp. 17-28 ◽

Cited By ~ 3

Author(s):

J. Gomis ◽

P. Mato ◽

M. Novell

Keyword(s):

World Line ◽

Spinning Particle ◽

Line Condition

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COVARIANT RELATIVISTIC DYNAMICS AND THE CONCEPT OF TIME

Modern Physics Letters A ◽

10.1142/s0217732311036437 ◽

2011 ◽

Vol 26 (23) ◽

pp. 1681-1696

Author(s):

D. M. LUDWIN ◽

L. P. HORWITZ

Keyword(s):

General Relativity ◽

Wave Function ◽

Quantum Mechanics ◽

World Line ◽

New Physics ◽

Relativistic Dynamics ◽

Newtonian Physics ◽

Covariant Quantum ◽

Spatial Axis

The role of time has changed conceptually moving from classical Newtonian physics to general relativity and is one of the main obstacles avoiding a clear unification between a covariant quantum mechanics theory and a theory of gravity. In quantum mechanics as in Newtonian physics, time is an evolutional causal parameter, while in general relativity, time has become a spatial axis where matter is spread over the whole world line (an unlocalized 4D wave function), and the 4D picture became a static picture where our empirical experience of dynamics is merely an illusion of our minds. Understanding that Newtonian time still exists in parallel to the 4D world, raises the possibility to describe gravity within a manifestly covariant quantum theory. The examples of the use of such a theory raise the possibility of a clear interpretation of recent interference in time experiments, and also raise new physics when dealing with a curved spacetime.

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The kinematics of a point particle

10.1093/oso/9780198786399.003.0020 ◽

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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