The Higgs Mechanism: How Symmetry-Breaking in Quantum Fields Gives Mass to Fundamental Particles

Mark Marrocco and Dr. Edward DeveneyDepartment of Physics, Bridgewater State University, Bridgewater MA 02325

Abstract

The fundamental particles of nature are most successfully modeled as excitations in quantum fields which permeate all of space-time. These particles, and their associated forces, are described in the Standard Model of particle physics with mathematical constructs known as Gauge Theories. Gauge theories have the property that their associated Lagrangian must be invariant with respect to local transformations. Some fundamental forces have a gauge theory which is symmetric and therefore implies that they should be associated with massless particles. However, observation shows that this is not the case for the weak force, as its associated gauge particles do in fact have mass. The Higgs field is another type of quantum field postulated as a mechanism to explain how these types of gauge fields could have their symmetries broken and thereby allow their associated particles to acquire mass. This mechanism was proposed by Peter Higgs et al in the 1960’s, but the Higgs boson was not observed until July 4th, 2012, when the LHC at CERN was finally able to operate at high enough energies to do so. Here, the Higgs mechanism is elaborated in the language of quantum field theory.

Works Cited1. Lancaster, Tom, and Stephen Blundell. Quantum Field

Theory for the Gifted Amateur. Oxford: Oxford UP, 2015. Print.

2. Griffiths, David J. Introduction To Quantum Mechanics. Upper Saddle River, NJ: Pearson Prentice Hall, 2005. Print.

Figure 1. The namesake of the theory, physicist Peter Higgs.

Figure 2. The Standard Model of particle physics and the sombrero-potential of the Higgs field.

A one-component field in a false vacuum ground state undergoes SBS into one of two final broken symmetry discrete ground state vacuums and two-component

field after SBS into a continuum of possible true ground state vacuums (wiki images)

2nd Quantization, Relativistic Quantum Field Theory (RQFT), is ‘Operator valued’ and solves the problems inherent in 1st Quantization:

RQFT is inherently a many-particle theory from the outset (particle creation and annihilation operators) and,

according to Feynman, Negative Energy states are interpreted as real particles moving backward in time which is equivalent to antiparticles moving forward in

time all of which can be depicted and quantified for calculations symbolically using Feynman Diagrams (wiki image).