Padmanabhan, T.
(1994)
*Path intergral for the relativistic particle and harmonic oscillator*
Foundations of Physics, 24
(11).
pp. 1543-1562.
ISSN 0015-9018

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Official URL: http://www.springerlink.com/content/t2jj281516h073...

Related URL: http://dx.doi.org/10.1007/BF02054782

## Abstract

The action for a massive particle in special relativity can be expressed as the invariant proper length between the end points. In principle, one should be able to construct the quantum theory for such a system by the path integral approach using this action. On the other hand, it is well known that the dynamics of a free, relativistic, spinless massive particle is best described by a scalar field which is equivalent to an infinite number of harmonic oscillators. We clarify the connection between these two - apparently dissimilar - approaches by obtaining the Green function for the system of oscillators from that of the relativistic particle. This is achieved through defining the path integral for a relativistic particle rigorously by two separate approaches. This analysis also shows a connection between square root Lagrangians and the system of harmonic oscillators which is likely to be of value in more general context.

Item Type: | Article |
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Source: | Copyright of this article belongs to Springer. |

ID Code: | 72483 |

Deposited On: | 29 Nov 2011 05:30 |

Last Modified: | 29 Nov 2011 05:30 |

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