Muon decay and equivalence principle

LE~T]~R]~ AL ~UOVO CIMENTO VOL. 9, N. 4 26 Gennaio 1974

Muon Decay and Equivalence Principle.

A. P ~ s

Department o/ Physics, Teehnion.Israel Insti tute o] Technology - Hai]a

(rieevuto il 30 Ottobre 1973)

In a recent paper with the same title as above, SMOI~ODINSKII (1) suggested that the proper t ime for a charged particle in an electromagnetic field is given by

(1) v = f (g~dx~ axa) �89 + f e A = a ~ ,

rather than by just the first term on the r ight-hand side of (1). A consequence of this formula would be that a muon moving in a circular orbit in

a cyclotron, thus enclosing a large amount of magnetic flux, would have a longer life- t ime than a free muon moving with the same speed.

The purpose of this note is to point out that eq. (1) cannot be correct, because it is not gauge invar iant . This is easily seen by performing the gauge transformation

(2) A~,-+ A~, + ~;~/Ox ~ ,

where 2 is an arbitrary function of the co-ordinates. The proper time is then altered by the amount eyd)~.

In Smorodinskii 's paper (1), this difficulty is obviated by tacitly choosing a gauge where A 0 = 0, and taking a closed integration contour in space. These assumptions, however, are quite arbitrary, and i t is clear tha t eq. (t) cannot hold in generul.

(1) YA. S~tORODINSKII: Zurn. Eksp. Teor. Fiz. Pis. Red., 16, 499 (1972) (English translation: J E T P Let&, 16, 356 (1972)).

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