Relation between L-glutamine supplementation and risk of schizophrenia There is the glutamate hypothesis of schizophrenia. Which tells you that excessive levels may increase the risk of obtaining schizophrenia.

L-glutamine turns into glutamate directly. Does this mean that L-glutamine supplementation, which is common among bodybuilders, increases the risk?
Glutamate availability in the brain is strictly dependent on de novo synthesis of glutamine in astrocytes. This process  requires the enzymes pyruvate carboxylase and glutamine synthetase to form glutamine, which is then converted into glutamate by deamidation via phosphate-activated glutaminase in a reaction that also yields ammonia (Schousboe et al., 2014). 

In other words, whatever you ingest in terms of glutamate or glutamine via your food doesn't reach the brain and won't play a role in psychosis. 

This is good news, as glutamate is an abundant, naturally occurring amino acid and is found in tomatoes, grapes, cheese, mushrooms and other foods. It is also widely used as a flavor enhancer with an umami taste that intensifies the meaty, savory flavor of food. It's commonly used in stock, soups, ramen, savoury snacks etc. (source: wikipedia).  

Reference
- Schousboe et al., Adv Neurobiol (2014); 11:13-30