Spontaneous symmetry breaking: A view from derived geometry

From Yukawa’s Pion to Spontaneous Symmetry Breaking

What we now call particle physics started first as nuclear physics in the 1930s, and I have once proposed to call Ernest Lawrence and Hideki Yukawa the two founders of particle physics: The first invented the cyclotron, the second ‘‘invented’’ the meson theory, which together opened the door to the exploration of ever higher energy phenomena and to the discovery of particles of ever increasing ...

Nonperturbative Spontaneous Symmetry Breaking

One of the most astonishing results of quantum field theory is spontaneous symmetry breaking. One can say that it is the situation when something arises from the quantization. This means that on the quantum level one has something that was not present on the classical level. Coleman and Weinberg [1] write : “ . . . higher-order effects may qualitatively change the character of a physical theory...

Spontaneous Symmetry Breaking

Symmetry breaking via internal geometry

Gauge theories commonly employ complex vector-valued fields to reduce symmetry groups through the Higgs mechanism of spontaneous symmetry breaking. The geometry of the internal space V is tacitly assumed to be the metric geometry of some static, nondynamical hermitian metric k. In this paper, we consider G-principal bundle gauge theories, where G is a subgroup of U(V ,k) (the unitary transforma...

Decoherence induced spontaneous symmetry breaking

We study time dependence of exchange symmetry properties of Bell states when two-qubits interact with local baths having identical parameters. In case of classical noise, we consider a decoherence Hamiltonian which is invariant under swapping the first and second qubits. We find that as the system evolves in time, two of the three symmetric Bell states preserve their qubit exchange symmetry wit...