The theory of quantum fields is very strange, indeed, I must admit. Usually in books they introduce a quantum field from the standpoint of a vibrating string in one dimension. Along the string are discrete points or masses that when one of which are disturbed a disturbance is created along the length of the string in the from of a wave. As a result, each mass or point is displaced by a certain amount at a specific time, which makes sense. Even when you pass this case into the case of the continuum in which the points are ever so close together it still makes sense. But the problem comes when we try to insist that a point particle can be described by a field which has a value at every space-time point. To make matters worse we are now using Minkowski space which is 4-dimensional and the time and space are mixtures of one another. There is no analogy between the original displacement in the string and a displacement of the field in Minkowski space because each space-time point may not move or be displaced. So how can a particle be described by a field which has infinitely many degrees of freedom? Even if we tried to describe this in the one-dimensional case it still makes no sense.