Abstract
In this work it is proposed a transformation which is useful in order to simplify non-polynomial potentials given in the form of an exponential. As an application, it is shown that the quantum Liouville field theory may be mapped into a field theory with a polynomial interaction between two scalar fields and a massive vector field.
Highlights
The Liouville field theory is actively studied both in physics and mathematics [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
The mapping of Liouville field theory into the two component scalar field theory coupled to a vector field is based in part on known results of the theory of Brownian motion. It is applied the field theoretical representation of the grand canonical partition function of charged particles subjected to a random walk while immersed in a magnetic field. This is not the first time that Liouville field theory has been related to statistical systems
From the above discussion it turns out that Ξ[μ] can be interpreted as the grand canonical partition function of a system of indistinguishable particles which perform a Brownian walk while they are interacting with a massive vector field A
Summary
The Liouville field theory is actively studied both in physics and mathematics [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. The mapping of Liouville field theory into the two component scalar field theory coupled to a vector field is based in part on known results of the theory of Brownian motion It is applied the field theoretical representation of the grand canonical partition function of charged particles subjected to a random walk while immersed in a magnetic field. This is not the first time that Liouville field theory has been related to statistical systems. From the above discussion it turns out that Ξ[μ] can be interpreted as the grand canonical partition function of a system of indistinguishable particles which perform a Brownian walk while they are interacting with a massive vector field A.
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