Azuma Tanaka

Residual invariance in axial gauge

SummaryThere remains a residual gauge freedom after the axialgauge fixation. We investigate how gauge theories satisfy the residual gauge invariance. It is found that the generator of the residual gauge transformation sandwiched by eigenstates of the total Hamiltonian automatically vanishes. The «constraint» that the generator annihilates physical states does not work.RiassuntoDopo aver fissato la gauge assiale rimane un grado di libertà residuo della gauge. Si studia come le teorie di gauge soddisfano l’invarianza di gauge residua. Si mostra che il generatore della trasformazione di gauge residua intercalata da autostati della hamiltoniana totale si annulla automaticamente. Il vincolo che il generatore annulli stati fisici non funziona.РезюмеПосле фиксирования аксиальной калибровки остается остаточная калибровочная свобода. Мы исследуем, как калибровочные теории удовлетворяют остаточной калибровочной инвариантности. Получается, что генератор остаточного калибровочного преобразования, помещенный между собственными состояниями полного Гамильтониана, автоматически обращается в нуль. «Ограничение», что генератор аннигилирует физические состояния, не работает.

Haag's theorem and dimensional regularization

Abstract It is shown that dimensionally regularized field theories are free from the difficulty in Haags theorem, which states that there exists no relativistic theory with interaction in which the Fock representation is used.

A solvable model for spontaneous symmetry breaking

SummaryA solvable model for the spontaneous symmetry breaking is presented. We explicitly observe the situation in which the symmetry property on the operator side is broken as an inevitable consequence under some condition for the Lagrangian. To do this considerations in the Fock representation are essential.RiassuntoSi presenta un modello risolvibile per la violazione spontanea delia simmetria. Si osserva esplicitamente la situazione in oui la proprietà di simmetria a lato dell’operatore è violata come conseguenza inevitabile sotto certe condizioni per la lagrangiana. Per fare questo sono essenziali considerazioni nello spazio di Fock.