Broken Symmetry and the Mass of Gauge Vector Mesons

Summary

This paper, published in 1960, proposes that the masses of gauge vector mesons—particles that mediate fundamental forces—arise from a broken symmetry in the vacuum state, not from explicit mass terms in the Lagrangian. Nambu argues that a vacuum with a non-zero expectation value for a scalar field can spontaneously break a continuous symmetry, generating mass for the gauge bosons via a mechanism analogous to the Meissner effect in superconductivity. The key idea is that the gauge symmetry remains exact in the equations of motion but is hidden by the vacuum, leading to massive vector mesons without violating gauge invariance.

The paper introduces the concept of "spontaneous symmetry breaking" as a dynamical process, where the ground state of a system does not share the full symmetry of the underlying laws. Nambu shows that this mechanism yields a mass for the gauge boson proportional to the vacuum expectation value of the scalar field, and that the resulting theory remains renormalizable. A reader takes away a concrete understanding of how particle masses can emerge from vacuum structure, a foundational insight later formalized in the Higgs mechanism.

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Key concepts

• Spontaneous symmetry breaking — A process where the ground state of a system does not exhibit the full symmetry of the underlying equations, leading to mass generation for gauge bosons.
• Gauge vector mesons — Particles that mediate fundamental forces, such as the photon for electromagnetism, whose masses are explained by this mechanism.
• Vacuum expectation value — The non-zero average value of a scalar field in the vacuum state, which breaks the symmetry and gives mass to gauge bosons.
• Meissner effect analogy — The expulsion of magnetic fields from a superconductor, used by Nambu to illustrate how a broken symmetry in the vacuum can generate mass for gauge fields.
• Renormalizability — The property of a quantum field theory that allows finite predictions despite infinities, preserved in Nambu’s mechanism.