This can be achieved by simply creating 3 fields.
First field: For others.
Computed. HideWhen: @Ismember(@Name[CN];@USername);ThirdField)
Default formulae: SecondFieldName
SecondField: For only Author to edit.
Editable. HideWhen: !@Ismember(@Name[CN];@USername);ThirdField)
You can place the First and Second field one below the other.
Third Field: To store Author name
ComputedWhenComposed. You can hide it for all.
Formulae:
@Name([CN];@Username)
When Author opens the document in Edit mode, Author will see second field in Edit mode, while others will see the First field (in read/edit mode).
Hope it helps.