Do the equations on this piece of art have physical significance Someone I know owns a piece of art, which is shown in the figure. 
 
$$[\varphi_\alpha(x), \varphi_\beta(y)]= -i\Delta_{\alpha\beta}(x-y)$$ 
and 
$$U[\sigma,\sigma_0]= I-i\int_{\sigma_0}^\sigma\mathcal{H}'(x')U[\sigma',\sigma_0]\,\mathrm dx'\,. $$
I have some theories on what the physical significance (or lack there of) of the particular symbols are, but would like to see if meaning jumps out at anyone. 
(If this is completely out of place on the Stack Exchange, let me know, as this is meant to be a light-hearted question.)
 A: In quantum field theory bosonic fields $\varphi_\alpha\left(x\right)$ satisfy $\left[\varphi_\alpha\left(x\right),\,\varphi_\beta\left(y\right)\right]=0$, unless noncommutative geometry is incorporated in which case we achieve the moral general case in the first equation you've asked about. This is analogous to the fact that discrete quantum mechanics satisfies $\left[x_i,\,x_j\right]=0$ without noncommutative geometry, or $\left[x_i,\,x_j\right]=-i\Delta_{ij}$ with it. Note that each $\Delta$ is antisymmetric; the $-i$ is there so the entries of $\Delta$ will be real.
The second equation is equivalent to the conditions $$U\left[\sigma_0,\,\sigma_0\right]=I,\,\frac{\partial U\left[\sigma,\,\sigma_0\right]}{\partial \sigma}=-i\mathcal{H}\left[\sigma,\,\sigma_0\right]U\left[\sigma,\,\sigma_0\right],$$which characterise unitary transformations between states with parameters $\sigma_0,\,\sigma$ for some dimensionless function $\mathcal{H}$ along the path. A gradual increase in the state's parameter during a gradual unitary evolution is depicted in the diagram.
