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Boundary dependence of the coupling constant and the mass in the vector N-component $(λϕ^{4})_{D}$ theory

A. P. C. Malbouisson·J. M. C. Malbouisson
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Abstract

Using the Matsubara formalism, we consider the massive $(λϕ^{4})_{D}$ vector $N$-component model in the large $N$ limit, the system being confined between two infinite paralell planes. We investigate the behavior of the coupling constant as a function of the separation $L$ between the planes. For the Wick-ordered model in $D = 3$ we are able to give an exact formula to the $L$-dependence of the coupling constant. For the non-Wick-ordered model we indicate how expressions for the coupling constant and the mass can be obtained for arbitrary dimension $D$ in the small-$L$ regime. Closed exact formulas for the $L$-dependent renormalized coupling constant and mass are obtained in $D = 3$ and their behaviors as functions of $L$ are displayed. We are also able to obtainn in generic dimension $D$, an equation for the critical value of $L$ corresponding to a second order phase transition in terms of the Riemann $zeta$-function. In $D = 3$ a renormalization is done and an explicit formula for the critical $L$ is given.

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BibTeXRIS

A. P. C. Malbouisson, J. M. C. Malbouisson. 2001-09-14. Boundary dependence of the coupling constant and the mass in the vector N-component $(λϕ^{4})_{D}$ theory. https://doi.org/10.1088/0305-4470%2F35%2F9%2F315

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