Hand cramps are a result of hand muscles and nerve condition. A common cause of cramping is dehydration, heat exhaustion, fatigue, and injury or trauma of nerves. This is also common in people with Diabetes and to any condition that affects the nerves outside the brain and spinal cord.
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It could be an electrolyte imbalance, probably a potassium deficiency.
More likely that it could be related to carpal tunnel syndrome in which case some 100 mg of vitamin B6 could be helpful [or acupuncture]
If a problem with minerals then salt shortage [natrium] would be more likely [see the book of Donald Lepore.
Magnesium should also be considered and potassium is "unlikely" as it is the left arm.[Lepore]
Cramps in the fingers of the left hand could result from simple muscle fatigue. It could also be a deficiency in an electrolyte such as sodium or potassium.