Possessive pronouns as subjects

[Abstract Idea]

Dear colleagues

Regarding possessive pronouns, may they play the role of subject on a clause?
See the following examples:
a) The total Lagrangian is now invariant, by virtue of our having introduced a field A, which couples to the currente J. (from a Physics book)
b) Well, if he's respectable, of course I've nothing to say against your knowing him. (from a short story by Thomas Hardy)

I wonder if those are indeed possessive pronouns here and if they are playing a subject role. Are these subordinate clauses? And after such possessive pronoun playing subject roles must one alwasy use the verb in its gerund form?

Thanks in advance

P.S.: Feel free to correct any possible mistakes of mine.

[Soup]

Dear colleagues

Regarding possessive pronouns, may they play the role of subject in a clause? See the following examples:

a) The total Lagrangian is now invariant, by virtue of our having introduced a field A, which couples to the currente J. (from a Physics book)

b) Well, if he's respectable, of course I've nothing to say against your knowing him. (from a short story by Thomas Hardy)

I wonder if those are indeed possessive pronouns here and if they are playing a subject role. Are these subordinate clauses? And after such possessive pronouns playing subject roles must one alwa[ys] use the verb in its gerund form?

Thanks in advance

P.S.: Feel free to correct any possible mistakes of mine.

The following explanation is from this source.
Gerunds preceded by a genitive

Because of its noun properties, the genitive (possessive case) is preferred for a noun or pronoun preceding a gerund.

• We enjoyed their [genitive] singing.

This usage is preferred in formal writing. The objective case is often used in place of the possessive, especially in casual situations:

• I do not see it making any difference.

In some cases, either the possessive or the objective case may be logical:

• The teacher's shouting startled the student. (Shouting is a gerund, and teacher's is a possessive pronoun. The shouting is the subject of the sentence.)
• The teacher shouting startled the student. (Shouting is a participle describing the teacher. This sentence means The teacher who was shouting startled the student. In this sentence, the subject is the teacher herself.)

Either of these sentences could mean that the student was startled because the teacher was shouting.
Using the objective case can be awkward if the gerund is singular but the other noun is plural. It can look like a problem with subject-verb agreement:

• The politicians' debating was interesting.

One might decide to make to be plural so that debating can be a participle.

• The politicians debating were interesting.

[orangutan]

Dear colleagues

Regarding possessive pronouns, may they play the role of subject on a clause?
See the following examples:
a) The total Lagrangian is now invariant, by virtue of our having introduced a field A, which couples to the currente J. (from a Physics book)
b) Well, if he's respectable, of course I've nothing to say against your knowing him. (from a short story by Thomas Hardy)

I wonder if those are indeed possessive pronouns here and if they are playing a subject role.

Yes, this is exactly right.

Are these subordinate clauses?

Yes, though of course nominalized.

And after such possessive pronoun playing subject roles must one alwasy use the verb in its gerund form?

No; one can also talk about Napoleon's invasion of Russia (from "Napoleon invaded Russia). It is a general feature of nominalizations coming from verbs.

Also, it is possible with gerunds (but not other nominalizations) for the subject (and object) to be in their normal non-possessive cases ("Napoleon invading Russia...). The rules governing when this is possible are quite complicated.