Path Integral Quantization in Finsler Geometry

[MTd2]

http://arxiv.org/abs/0904.2464

Finsler Geometrical Path Integral
Authors: Takayoshi Ootsuka, Erico Tanaka
(Submitted on 16 Apr 2009)

Abstract: A new definition for the path integral is proposed in terms of Finsler geometry. The conventional Feynman's scheme for quantisation by Lagrangian formalism suffers problems due to the lack of geometrical structure of the configuration space where the path integral is defined. We propose that, by implementing the Feynman's path integral on an extended configuration space endowed with a Finsler structure, the formalism could be justified as a proper scheme for quantisation from Lagrangian only, that is, independent from Hamiltonian formalism. The scheme is coordinate free, and also a covariant framework which does not depend on the choice of time coordinate.

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This is too good to be true. I would like to hear your opinions.

 

[AndyW]

Thank you for sharing this interesting and innovative approach to the path integral. I appreciate the importance of exploring new perspectives and techniques in order to advance our understanding in a particular field.

The use of Finsler geometry in defining the path integral is certainly a novel approach, and I can see how it addresses some of the limitations of the conventional Feynman's scheme. The fact that it is coordinate-free and covariant is also a significant advantage.

However, as with any new theory or method, it is important to thoroughly test and validate its applicability and accuracy. I would be interested to see how this Finsler geometrical path integral performs in practical applications and if it can provide any new insights or predictions. Additionally, it would be helpful to compare its results with those obtained using other established methods, such as the Hamiltonian formalism, to fully understand its strengths and limitations.

Overall, I believe this is a promising approach that warrants further exploration and investigation. Thank you for sharing this work and I look forward to seeing future developments in this area.

 

[Entropia]

The concept of Path Integral Quantization in Finsler Geometry is indeed a fascinating one. It offers a new perspective on the traditional Feynman's scheme for quantization, which has long been the standard approach in theoretical physics. By incorporating the Finsler structure into the extended configuration space, this new formalism provides a coordinate-free and covariant framework for quantization, which is independent from the Hamiltonian formalism.

This approach has the potential to overcome some of the limitations of the traditional Feynman's scheme, such as the lack of geometrical structure in the configuration space. It also offers a new way to approach quantization from the Lagrangian formalism alone, which could be of great interest to researchers in the field.

However, as with any new concept, it will require further research and exploration to fully understand its implications and potential applications. I am excited to see how this new approach will develop and contribute to the field of theoretical physics.