Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-07-20
Mod.Phys.Lett. A20 (2005) 2215-2226
Physics
High Energy Physics
High Energy Physics - Theory
9 pages, considerably expanded form. To be published in Mod. Phys. Lett. A
Scientific paper
10.1142/S0217732305018438
The effective potential $V$ is considered in massless $\lambda\phi^4_4$ theory. The expansion of $V$ in powers of the coupling $\lambda$ and of the logarithm of the background field $\phi$ is reorganized in two ways; first as a series in $\lambda$ alone, then as a series in $\ln\phi$ alone. By applying the renormalization group (RG) equation to $V$, these expansions can be summed. Using the condition $V^\prime(v) = 0$ (where $v$ is the vacuum expectation value of $\phi$) in conjunction with the expansion of $V$ in powers of $\ln\phi$ fixes $V$ provided $v\neq 0$. In this case, the dependence of $V$ on $\phi$ drops out and $V$ is not analytic in $\lambda$. Massless scalar electrodynamics is considered using the same approach.
Brandt Fernando T.
Chishtie Farrukh A.
McKeon Dennis G. C.
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