4
votes
1answer
75 views

The correspondence between Grassmann number and 4-spinor

In canonical quantization, we view the Dirac field $\psi$ as a $4\times1$ matrix of complex number. While in path integral quantization, we view the Dirac field $\psi$ as a Grassmann number. For two ...
2
votes
0answers
93 views

Normal ordering and path integrals

What is the manifestation of normal ordering for creation/annihilation operators in the path-integral formalism?
6
votes
2answers
335 views

In what sense is the path integral an independent formulation of Quantum Mechanics/Field Theory?

We are all familiar with the version of Quantum Mechanics based on state space, operators, Schrodinger equation etc. This allows us to successfully compute relevant physical quantities such as ...
2
votes
0answers
73 views

Is time ordering defined for a single operator depending of two time variables?

The time ordering for the purpose of quantum mechanics is e.g. given by $${\mathcal T} \left[A(x) B(y)\right] := \begin{matrix} A(x) B(y) & \textrm{ if } & x_0 > y_0 \\ \pm B(y)A(x) & ...
7
votes
1answer
397 views

What is the value of a quantum field?

As far as I'm aware (please correct me if I'm wrong) quantum fields are simply operators, constructed from a linear combination of creation and annihilation operators, which are defined at every point ...