4
votes
2answers
130 views

Why Goldstone Bosons? (A Question about VEVs)

I understand how the mechanism of spontaneous symmetry breaking works, and why it produces Goldstone bosons (for global symmetries) and massive gauge bosons (for local ones). However, I'm confused as ...
2
votes
1answer
175 views

Symmetry Breaking and Vacuum Expectation Values

Consider a real scalar field $\phi$ in a theory with a Lagrangian $$ \mathcal{L}:=-\frac{1}{2}\partial _\mu \phi \partial ^\mu \phi -V(\phi ), $$ where $$ V(\phi ):= -\mu ^2\phi ...
1
vote
1answer
164 views

Multiple vacua vs. vev's in qft

Take a (possibly supersymmetric) relativistic quantum field theory: when we construct it, we suppose that there is a unique vacuum state $|0\rangle$ which is Lorentz invariant, vector of some Hilbert ...
5
votes
1answer
199 views

Spontaneous symmetry breaking: How can the vacuum be infinitly degenerate?

In classical field theories, it is with no difficulty to imagine a system to have a continuum of ground states, but how can this be in the quantum case? Suppose a continuous symmetry with charge $Q$ ...