Cresus F. L. Godinho, Jose Weberszpil, J. A. Helayël Neto
Nowadays, a number of new approaches based on fractional calculus have been presented and discussed in the literature, with the purpose of finding out different perspectives and describing particular phenomena in connection with field theory and gravity at a more fundamental level. On the other hand, procedures related to canonical quantization are really essential in field theory. More recently, the investigation of a wide category of new classical field-theoretic models as well as their respective quantized counterparts have been pursued which yield a very rich scenario, which enables us to connect different areas of physics. For instance, it is not fairly well-known how to deal with dissipative or nonlinear systems; there are many paths of investigation in the literature and none of them present a systematic and general procedure to tackle the problem. Today, it is widely accepted that the fractional formalism may be viewed as a powerful alternative to study dissipative systems. In our present contribution, we propose a pragmatical and detailed way of attacking the question. Using a particular approach to fractional calculus, we build up a consistent extension of the Faddeev- Jackiw (or Symplectic) algorithm to carry out the quantization procedure of nonconservative models in the standard canonical way. In our treatment, we shall adopt the so-called Modified Riemman Liouville (MRL) approach, where the chain rule is so workable as much as it is in its standard form. We believe that by adopting the extended version of Fractional Symplectic Quantization procedure, it shall be possible to analyze more deeply gauge theories embedded in a coarse-grained scenario.
View original:
http://arxiv.org/abs/1208.2266
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