Can you pick up and move a gate?

Question

The gate spell creates a 5-20 ft. hoop that connects 2 locations.

Can I simply pick up the hoop and carry it with me?

Answer 1

No. The rules state:

The gate itself is a circular hoop or disk from 5 to 20 feet in diameter (caster’s choice), oriented in the direction you desire when it comes into existence (typically vertical and facing you). It is a two-dimensional window looking into the plane you specified when casting the spell, and anyone or anything that moves through is shunted instantly to the other side.

A gate has a front and a back. Creatures moving through the gate from the front are transported to the other plane; creatures moving through it from the back are not.

The hoop is its shape rather than a physical object. Gate creates a SET (Swirly Energy Thing) through which you can travel to other places. It is not a physical object you can move around, it's a tunnel between different planes of existence. Even if you could move it around, you run into this:

You may hold the gate open only for a brief time (no more than 1 round per caster level), and you must concentrate on doing so, or else the interplanar connection is severed.

So even if you could pick up and move around with it your options are limited. Concentrating on the Gate is a standard action, and while you can perform a move action while concentrating you'll have to make a Concentration roll as per the Concentration skill.

Answer 2

The gate spell's effect can't be moved after its creation

The gate spell's effect is a "a circular hoop or disk from 5 to 20 feet in diameter (caster’s choice)" that is "an interdimensional connection between your plane of existence and a plane you specify" (PH 234). The spell doesn't provide any indication that this "two-dimensional window" can be moved after its creation.

The Player's Handbook on Subjects, Effects, and Areas says that

If the spell creates an effect, the effect lasts for the duration. The effect might move (for example, a summoned monster might chase your enemies) or remain still. Such an effect can be destroyed prior to when its duration ends (for example, fog cloud can be dispersed by wind). (176)

No mention's made of how a creator can move the gate spell's effect, therefore—unless the DM rules otherwise—a gate spell's effect is stationary, like the effect of a fog cloud or wall of thorns spell. Compare gate's effect to a spell that creates an actual object like minor creation or to a spell with rules for moving its effect after the effect's created like arcane eye, flaming sphere and mage's (né Mordenkainen's) sword.