Revision as of 15:59, 6 November 2023 edit 160.179.204.214 (talk) →Integrals with an imaginary linear term in the argument of the exponent ← Previous edit		Revision as of 16:10, 16 February 2024 edit undo 163.118.90.10 (talk) →Integrals with a linear term in the argument of the exponent Next edit →
Line 38: Therefore: <math display="block">\begin{align} & \int_{-\infty}^\infty \exp\left( -{1 \over 2} a x^2 + Jx\right) \, dx \\ &= \exp\left( { J^2 \over 2a } \right ) \int_{-\infty}^\infty \exp \left [ -{1 \over 2} a \left ( x - { J \over a } \right )^2 \right ] \, dx \\[8pt] &= \exp\left( { J^2 \over 2a } \right )\int_{-\infty}^\infty \exp\left( -{1 \over 2} a w^2 \right) \, dw \\[8pt]

Common integrals in quantum field theory: Difference between revisions