Thomas Aquinas

“ Further, a man is apparently a schismatic if he disobeys the Church. But every sin makes a man disobey the commandments of the Church, because sin, according to Ambrose (De Parad. viii) "is disobedience against the heavenly commandments." Therefore every sin is a schism.
Objection 3: Further, heresy also divides a man from the unity of faith. If, therefore, the word schism denotes a division, it would seem not to differ, as a special sin, from the sin of unbelief. ”

“ We command that persons consecrated by bishops who were themselves consecrated according to the Catholic rite, but have separated themselves by schism from the Roman Church, should be received mercifully and that their Orders should be acknowledged, when they return to the unity of the Church, provided they be of commendable life and knowledge. ”

“ For in the moral, as in the physical order, the species is not constituted by that which is accidental. Now, in the moral order, the essential is that which is intended, and that which results beside the intention, is, as it were, accidental. ”

“ Consequently such a power as this remains, as to its essence, in the man who has received it by consecration, as long as he lives, even if he fall into schism or heresy: and this is proved from the fact that if he come back to the Church, he is not consecrated anew. Since, however, the lower power ought not to exercise its act, except in so far as it is moved by the higher power, as may be seen also in the physical order, it follows that such persons lose the use of their power, so that it is not lawful for them to use it. ”

“ The punishments of the present life are medicinal, and therefore when one punishment does not suffice to compel a man, another is added: just as physicians employ several body medicines when one has no effect. In like manner the Church, when excommunication does not sufficiently restrain certain men, employs the compulsion of the secular arm. If, however, one punishment suffices, another should not be employed. ”

“ Accordingly when it is said that such like persons have no spiritual power, it is to be understood as referring either to the second power, or if it be referred to the first power, not as referring to the essence of the power, but to its lawful use. ”

“ Accordingly schismatics properly so called are those who, wilfully and intentionally separate themselves from the unity of the Church; for this is the chief unity, and the particular unity of several individuals among themselves is subordinate to the unity of the Church, even as the mutual adaptation of each member of a natural body is subordinate to the unity of the whole body. ”

“ Yet if they use it, this power has its effect in sacramental acts, because therein man acts only as God's instrument, so that sacramental effects are not precluded on account of any fault whatever in the person who confers the sacrament. ”

“ Secondly, they refuse submission to the head of the Church, wherefore, since they are unwilling to be controlled by the Church's spiritual power, it is just that they should be compelled by the secular power. ”