gamma

The symbol $\gamma$ is highly context-dependent. In spin and magnetic-resonance settings it often denotes a gyromagnetic ratio; in relativistic kinematics $\gamma$ often denotes the Lorentz factor; in decay or open-system notation a gamma-like symbol can denote a rate.

Spin and Magnetic Moments

For a spin degree of freedom, a common convention writes the magnetic moment as proportional to angular momentum:

$$\boldsymbol\mu = \gamma\,\mathbf S, \qquad H_Z = -\boldsymbol\mu\cdot\mathbf B.$$

The sign and numerical value of $\gamma$ depend on the particle and on the convention used for charge, magnetic moment, and $g$ factor. This is why Zeeman formulas should state the magnetic moment convention rather than relying on the letter alone.

Relativistic Kinematics

In special relativity, the Lorentz factor is often written

$$\gamma_{\mathrm L} = \frac{1}{\sqrt{1-v^2/c^2}}.$$

The subscript is helpful on quantum-mechanics pages because $\gamma$ may already be used for magnetic coupling or a decay rate.

Rates and Linewidths

Lowercase $\gamma$ often denotes a damping rate, dephasing rate, or linewidth parameter. Uppercase $\Gamma$ is also common, especially for decay widths and transition rates. The units are then inverse time or energy, depending on whether the convention uses $\hbar\gamma$ as the width.

Common Collisions

• $\gamma$ as gyromagnetic ratio versus $\gamma_{\mathrm L}$ as Lorentz factor.
• $\gamma$ as a rate versus $\Gamma$ as a decay width or transition rate.
• $\gamma^\mu$ as a gamma matrix in relativistic wave equations and field theory.
• $\Gamma(z)$ as the Euler gamma function in special-function formulas.

Canonical Links

• What Spin Is
• Zeeman Effect
• Special Relativity Checklist
• Units and Constants

References

• J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, 3rd ed., Cambridge University Press, 2020.
• C. J. Foot, Atomic Physics, Oxford University Press, 2005.
• W. Rindler, Introduction to Special Relativity, 2nd ed., Oxford University Press, 1991.