Armie Hammer 's back out in the world after multiple years as persona non grata in Hollywood ... grabbing lunch with a woman and walking through a farmer's market after.

Hammer and this mystery woman were spotted in Westwood -- a neighborhood in West Los Angeles -- leaving a sushi joint Thursday afternoon. TMZ.com

The two dressed casually ... Hammer in a black t-shirt and matching jeans while his companion added a splash of color in a bright red jacket and blue jeans.

They took a look around at some of the stalls at the local market before making their exit ... unclear if they stopped for a closer look at any of the goods.

To be clear, there's no PDA between these two ... so, this could just be a friendly afternoon out. We've reached out to Hammer's rep for more details. Galler

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