According to Calvinists, what does "looking back" refer to in Luke 9:62?

One possibility:Jesus lived in a culture that was aware of rural activities e.g. ploughing. I have done some ploughing using a tractor but the principles are probably the same with an animal. In order to plough well one has to constantly look ahead to keep the furrows parallel. Worry that what one is doing, leading to looking round to see if ones fears are justified, just about guarantees that one will fail to keep a good line over the next few yards. The tractor/animal moves on unstopping, it is not good to stop its flow. The past will be less than perfect but the best way to look after the future is to give it ones full attention. As a Christian there is nothing to do but forget about fears of the result of ones past actions inhibiting one from making good decisions regarding the future. Whether I am a Calvinist, or whoever, the wisdom that Jesus is giving here, I imagine, is relevant to many walks of life. Jesus' reply to the man who wants to bid farewell may have meant to him, 'be careful to make looking back an exception because the future has so much for you to think about'.

From the Calvinist perspective, there is an emphasis on the "Perseverance of the Saints" the idea that if you are genuinely born again. A.K.A saved by God's sovereign Grace. God will not "fail" in his attempt to save you. He will carry out the act of bringing you through this earthly life, having maintained faith in Christ throughout the whole time.

This idea can be bolstered with scriptures such as these

Romans 8:29-30 29 For whom He foreknew, He also predestined to be conformed to the image of His Son, that He might be the firstborn among many brethren. 30 Moreover whom He predestined, these He also called; whom He called, these He also justified; and whom He justified, these He also glorified.

The idea that God from the beginning is the "Author and Finisher of our Faith" (Heb 12:2)

jude 24 KNJV - Now to Him who is able to keep you from stumbling, And to present you faultless Before the presence of His glory with exceeding joy,

From the earthly perspective, this looks like the individual keeping the faith, but from the Calvinist vantage, it's God who keeps the true Believers.

Now that we have this framework to understand, we can answer the question at hand. What does it mean to "Look back".

The looking back is abandoning the working of the field, which hopefully we can easily see is the mission of spreading the Gospel/Word of God. (John 4:34-38). (Matt 13 parable of sower etc)

Well to look back is to stray away from the faith in some manner. We can see examples of this with Paul in 2 Timothy

2 Tim 4 9 Be diligent to come to me quickly; 10 for Demas has forsaken me, having loved this present world, and has departed for Thessalonica—Crescens for Galatia, Titus for Dalmatia

Here we see an example of one previously called a "Co-worker" in Philemon 24.

So from the Calvinist perspective, one who does not persevere, or who "Looks back" is one who is "Not Fit for the Kingdom of God".

1 John 2:19 speaking of those who "look back".

19 They went out from us, but they were not of us; for if they had been of us, they would have continued with us; but they went out that they might be made manifest, that none of them were of us.

So the Idea being that those who look back, were never fit for the kingdom of God, and their looking back, just reveals that they were not fit from the beginning.

Because if they were fit, they would persevere, by God's grace. And it is God who makes us fit, not ourselves. It is not the looking back that Makes them unfit but rather the looking back which is outward evidence of their being unfit.

Similar to the idea that you will know a tree by its fruit. The tree is the same all along, but when it produces fruit, then you have evidence of what type of tree it was.

John 6:64-65

But there are some of you who do not believe.” For Jesus knew from the beginning who they were who did not believe, and who would betray Him. 65 And He said, “Therefore I have said to you that no one can come to Me unless it has been granted to him by My Father.”