On the particle-antiparticle conjugation

ON THE

PARTX~~~AR'I'ICLE

CONJUGATION

Sincetheesrfy~otl;lFof~~f13JawiBarsmannand~~ocr13jan~g emp~hnsktaplaoduponthtrrIatiortskrwccn~rrpracot;uionsofthe~ Poiac& group 9’: (or its aaivasal covaiag group 9:). considcrcd as the kiaunatical symrrttry gtcmp of the pbysicai spacq the dunmary pa&k aad the iaxkaat equatioas 2ssociatcd with them, These kariaat aquatioas ate coasidered as the coaditiioas which detcrmiae the Hilbcrt space X support of a rqrcseatation of 3.. which of course is Educibk bazausc of the cxistcna of sohioru of positive (p” > 0) and negative @O< 0) c;?ergy. Oa the other haad, the rparr of positive awgy solutioas provides the support of an irrcdua%le unitary rqr~~Mc3 Or9:; the spa- of &SC solutiom is c&d oneparride spaceP aad it is cm by the same indias which label the corres~ndiig irrcdua%lc rqfcscatation of 3: (q&+,, for iastan~ for the m # 0 caW wbuz m~mayt=tpin,~dthesignirthatoftheeoe%r). The rciatcrprctatioa of the acgatk eacrgy solutions (which arc aIs0 support of atz itxzducible unitary representation of3:) kads to &c concept of aatipartkk; this tia.mpretation is made by means of the parti&-aatipaz~cle (charge) coajugation Y. 7%~ formalism of chw conjugation ms tlrs contrmpiatcd ia the thirties by Hdxakrg (1% [6D and Kramcn m when the compfetc inmriancc d quantum dcctrodyaamics under the

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We co&da first the easiest spin zero cas the ttnity,a~d the rrprrttntation titk~~ tbef~m

md tl. BOYA

In it the Q f2cton jt~&:l write U

w++(P) - =P h-P V(d(d”)P). Let 0s prove !a

tile following

of

(1.1) are raiucd to heaafortb)

for U(u.Aj

0-U

3

4

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nm

PART?cxsANrIPARTxLE

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