Lost in Normalization

Abstract

The consequences of the gauge-coupling dependent normalization-factor of $1/g^{\alpha }$ in the transfer-matrix of 2d U(1) lattice gauge theory are explored. It is seen by the $\alpha =1$ choice that the lowest energy develops a minimum at coupling $g_{\ast }=1.125$, leading to a \textit{multi-valued} Gibbs energy similar to the systems with the first-order phase transition. It is argued how the $1/g$ normalization may be regarded as a lost normalization in the commonly used change of variable to the dimensionless angle-variables. Based on the continuum limit at the next-leading order and the Ostrogradsky formulation of higher-order time-derivatives theories, it is argued that the spectrum at continuum is compatible only with the $\alpha =1$ choice.

Comments: v1: LaTeX, 9 pages, 1 fig. v2: the power in E_0 is corrected based on proper normalization; abstract and title are modified. v3: presentation and title are changed (old title: On Significance of Transfer-Matrix Normalization in Lattice Gauge Theories), to appear in EPL