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It sounds as if you have a

It sounds as if you have a fungus disease, powdery mildew. If the plants are too infected, you'll need to discard them. Don't plant peas in the same place next year. Next spring, plant peas early (in March even if there's snow as long as it's not soggy), Watch carefully for mildew (whitish color) and spray a mix of 9 parts water to 1 part powered milk to avoid this problem. Also,be sure to water peas early in the day and water at the soil line not overhead to avoiding wet leaves. Also, buy a  disease-resistant variety such as Sugar Ann.