Free Field Theory

see also:

• Gaussian Fixed Point
• Gaussian Free Field

A free field theory typically involves fields that do not interact with each other. In the context of statistical mechanics and quantum field theory (QFT), such a model might represent, for example, a scalar field (\phi) whose dynamics are governed by a quadratic Hamiltonian or Lagrangian, lacking any higher-order interaction terms. The simplest form of such a Hamiltonian in a d-dimensional space for a real scalar field (\phi) can be written as:

$\mathcal{H}=\int d^{d}x\left[\frac{1}{2}(\nabla \varphi {)}^2+\frac{1}{2}{m}^2{\varphi }^2\right]$

where ((\nabla \phi)^2) represents the spatial derivatives (kinetic term) and (m^2\phi^2) is a mass term, with (m) being the mass of the field quanta.