A reader writes:
I have heard you and others say it is not written that holding hands is part of the proper way to say the Lords Prayer during the Liturgy. I have looked in the GIRM. No instructions are given as to posture, sitting, standing or holding hands. Is there another reference I can read about the church's instructions?
The posture for this point in the liturgy is standing. This actually is found in the GIRM, but it isn't as explicit as one might want. Here is the reference:
43. The faithful should stand from the beginning of the Entrance chant, or while the priest approaches the altar, until the end of the Collect; for the Alleluia chant before the Gospel; while the Gospel itself is proclaimed; during the Profession of Faith and the Prayer of the Faithful; from the invitation, Orate, fraters (Pray, brethren), before the prayer over the offerings until the end of Mass, except at the places indicated below.
They should, however, sit while the readings before the Gospel and the responsorial Psalm are proclaimed and for the homily and while the Preparation of the Gifts at the Offertory is taking place; and, as circumstances allow, they may sit or kneel while the period of sacred silence after Communion is observed.
In the dioceses of the United States of America, they should kneel beginning after the singing or recitation of the Sanctus until after the Amen of the Eucharistic Prayer, except when prevented on occasion by reasons of health, lack of space, the large number of people present, or some other good reason. Those who do not kneel ought to make a profound bow when the priest genuflects after the consecration. The faithful kneel after the Agnus Dei unless the Diocesan Bishop determines otherwise.
With a view to a uniformity in gestures and postures during one and the same celebration, the faithful should follow the directions which the deacon, lay minister, or priest gives according to whatever is indicated in the Missal.
The part in blue is what governs the posture during the Lord's Prayer. Since this occurs after the Orate, Fratres ("Pray, Bretheren") it is in the part of Mass where standing is the default posture. There is no exception carved out for it in what follows, so standing is what is supposed to be happening for the Lord's Prayer.
Standing means standing without doing anything fancy with your arms. It is distinct, for example, from the orans posture, which the priest uses when he stands and prays with arms outstretched. It is also distinct from the hand-holding posture.
The latter is not expressly forbidden in liturgical law because it is one of those "Please don't eat the daisies" situations. The legislator (the pope) did not envision that anybody would try to alter the standing posture in this way. As a result, the practice is not expressly forbidden, the same way that standing on one foot and hopping up and down as an effort to get closer to God in heaven is not expressly forbidden.
In general what liturgical documents do is to say what people should be doing and not focus on what they should not be doing (though there are exceptions). To prevent "Please don't eat the daisies" situations, what the law does is prohibit things that aren't mentioned in the liturgical books. Here's the basic rule:
Can. 846 §1. In celebrating the sacraments the liturgical books approved by competent authority are to be observed faithfully; accordingly, no one is to add, omit, or alter anything in them on one’s own authority.
Changing from standing to hand holding during the Lord's Prayer would be an alteration or addition of something provided for in the liturgical books and thus would be at variance with the law.
The reader also writes:
I have also heard the term "the rubrics of the Mass". Is this a separate document? If so, where do I find it at?
The rubrics aren't found in a separate book. They're little instructions written into the Sacramentary itself. For example, they tell the priest when to perform certain actions with respect to the prayers that he is saying. To set them off from the text of the prayers (which are printed in black ink), these instructions are printed in red ink. The Latin word for red is "ruber," and so the little red instructions in book came to be called "rubrics."
If you'd like to see them, just look in a normal Sacramentary. (Though they won't address hand holding either.)