# Search results

1. ### Higgs Field

In regard to the confusion about the exciting the Higgs, By definition, a particle is a quantum flluctuation about a vacuum, i.e pick a classical field configuration of minimal energy, that is the vev of your field, consider small fluctuations about it and quantize them (have them obey Bose or...
2. ### Higgs Field

Yes, it's an SU(2) doublet with two complex components, or equivalently 4 real components.
3. ### How to compute the energy of scalar wave equation

In case you haven't studied SR: $$\mathcal{L}=\int d^{3} x\frac{1}{2}\Big( (\dot u)^2 -(∇u)^{2})$$
4. ### How to compute the energy of scalar wave equation

Hi, First of all notice that this PDE is linear - that is, the unknown function u(x,t) appears in powers of one only. Therefore this a free (non-interacting, V(x)=0) scalar theory which can be easily solved (diagonalized) via a Fourier Transformation. An easy way to see that there is no...
5. ### Infinitesimal transformations and the Hamiltonian as generator

Hi, first of all, to clear things up, you should notice that what enters in the Poisson Brackets is functions (this is clear since the P.B involves differentiation). However, once also notices that the coordinates q and p enter the P.B. which "contradicts" the above statement. What I'm trying...
6. ### General questions on the formalism of QFT

You are absolutely right and I should've been more careful. What I really had in mind, when I quoted that statement, was the group of symplectomorphisms Sp which acts as automorhisms on the Heisenberg algebra (defined by the commutation of q and p). The group of translations is encoded in the...
7. ### General questions on the formalism of QFT

Hi, I'm a grad student and the past semmester I took a qft course which led me to the exact same questions. So here is my humble understanding on this topic. To understand what is really going on you need to understand what it means mathematically to canonically quantize your system. In...