The Meaning of Life, the Universe, and Everything.
Minecarts do not have an Invisible field (nor a NoGravity field). As far as I know there aren't any really reliable way of making them invisible. You can make them ignore gravity, but if you need them to be invisible I guess that won't help you.
The standard way of making something rideable and invisible is to use invisible horses.
There is a way to make really good seats in bedrock where you teleport a minecart where you want the player to sit and have a rail under the seat and the minecarts hitbox(and where the player sits) will be where you teleported the minecart it but the minecart's actual visuals will be on the rail. There might be something like that for java(never tryed)