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Spontaneous symmetry breaking in the Higgs mechanism

van Dam, Suzanne Spontaneous symmetry breaking in the Higgs mechanism. .


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The Higgs mechanism is very powerful: it furnishes a description of the electroweak theory in the Standard Model which has a convincing experimental verification. But although the Higgs mechanism had been applied successfully, the conceptual background is not clear. The Higgs mechanism is often presented as spontaneous breaking of a local gauge symmetry. But a local gauge symmetry is rooted in redundancy of description: gauge transformations connect states that cannot be physically distinguished. A gauge symmetry is therefore not a symmetry of nature, but of our description of nature. The spontaneous breaking of such a symmetry cannot be expected to have physical effects since asymmetries are not reflected in the physics. If spontaneous gauge symmetry breaking cannot have physical effects, this causes conceptual problems for the Higgs mechanism, if taken to be described as spontaneous gauge symmetry breaking.

In a gauge invariant theory, gauge fixing is necessary to retrieve the physics from the theory. This means that also in a theory with spontaneous gauge symmetry breaking, a gauge should be fixed. But gauge fixing itself breaks the gauge symmetry, and thereby obscures the spontaneous breaking of the symmetry. It suggests that spontaneous gauge symmetry breaking is not part of the physics, but an unphysical artifact of the redundancy in description.

However, the Higgs mechanism can be formulated in a gauge independent way, without spontaneous symmetry breaking. The same outcome as in the account with spontaneous symmetry breaking is obtained. It is concluded that even though spontaneous gauge symmetry breaking cannot have physical consequences, the Higgs mechanism is not in conceptual danger. The mechanism relies on the non-zero ground state value of the Higgs field, rather than on spontaneous symmetry breaking.

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Item Type: Other
van Dam,
Additional Information: This essay was submitted as part of the Master's course "Part III of the Mathematical Tripos" at the University of Cambridge.
Keywords: spontaneous symmetry breaking, Higgs mechanism, gauge symmetry
Subjects: Specific Sciences > Physics > Fields and Particles
Specific Sciences > Physics > Quantum Field Theory
Specific Sciences > Physics > Symmetries/Invariances
Depositing User: Ms. Suzanne van Dam
Date Deposited: 02 Sep 2012 13:06
Last Modified: 10 Jun 2014 20:41
Item ID: 9295

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