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The deformation parameter $q$ is related to the metric components via $q_\\mu = \\sqrt{|g^{\\mu\\mu}|}$. By promoting $g^{\\mu\\mu}(x)$ to spacetime-dependent background fields, we define a deformed covariant derivative $D_\\mu^{(q)} = \\partial_\\mu + ieA_\\mu(x)/\\sqrt{|g^{\\mu\\mu}(x)|}$ (no sum over $\\mu$). 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The deformation parameter $q$ is related to the metric components via $q_\\mu = \\sqrt{|g^{\\mu\\mu}|}$. By promoting $g^{\\mu\\mu}(x)$ to spacetime-dependent background fields, we define a deformed covariant derivative $D_\\mu^{(q)} = \\partial_\\mu + ieA_\\mu(x)/\\sqrt{|g^{\\mu\\mu}(x)|}$ (no sum over $\\mu$). 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