How to add current user field to view field list, when it has no relation to the content?
This is an answer for Drupal 7.

You can 


use Views template system and rewrite output of the field (will work only for Views) or 
create own formatter for file field (will work everywhere for fields with this formatter) or
alter any file path in hook_file_url_alter (will work everywhere without settings)


I will show how to create field formatter. It will correctly work with standard node rendering, Views, Panels, etc.  

/**
 * Implements hook_field_formatter_info().
 */
function YOURMODULE_field_formatter_info() {
  return array(
    // Our own formatter for 'file' field
    'YOURMODULE_file_link' =&gt; array(
      'label' =&gt; t('Special download link'),
      'field types' =&gt; array('file'),
    ),
  );
}

/**
 * Implements hook_field_formatter_view().
 */
function YOURMODULE_field_formatter_view($entity_type, $entity, $field, $instance, $langcode, $items, $display) {
  global $user;
  // Now just hide field if user not logged in
  if (user_is_anonymous()) {
    return;
  }

  switch ($display['type']) {
    case 'YOURMODULE_file_link':
      foreach ($items as $delta =&gt; $item) {
        // Some title
        $title = isset($item['description']) ? $item['description'] : $item['filename'];
        // Theme link (http://api.drupal.org/api/drupal/includes%21theme.inc/function/theme_link/7)
        $element[$delta] = array(
          '#theme' =&gt; 'link',
          '#text' =&gt; $title,
          '#path' =&gt; 'download.php',
          '#options' =&gt; array(
                        'attributes' =&gt; array(),
                        'html' =&gt; FALSE,
                        'query' =&gt; array('u' =&gt; $user-&gt;uid, 'document-fid' =&gt; $item['fid'])
                      )
        );

      }
      break;

  }
  return $element;
}


Add this code to your module (replace YOURMODULE with your module name), enable module, clear the cache if needed. New formatter will be available in Views field settings and in standard content type display settings.