Conventions

Displayed formulas in this passage

• Oai282-B@1#eq:W · line 301

  $$W(x-y)=⟨\Omega ,\varphi (x)\varphi (y)\Omega ⟩=\hslash {\int }_{C_{+}}{e}^{-\mathrm{i}p\cdot (x-y)}\mathrm{d}\mu (p).$$

• Oai282-B@1#eq:CCR · line 327

  $$[\varphi (x),\varphi (y)]=-\mathrm{i}\hslash E(x-y),[{\partial }_0\varphi (t,\mathbf{x}),\varphi (t,\mathbf{y})]=-\mathrm{i}\hslash {\delta }^{(3)}(\mathbf{x}-\mathbf{y}).$$

• unlabeled · line 264

  $$\eta =\mathrm{diag}(1,-1,-1,-1),\square ={{\partial }_0}^2-{\Delta }_{\mathbf{x}},\hslash >0.$$

• unlabeled · line 272

  $$C_{+}=\{p=(|\mathbf{p}|,\mathbf{p}):\mathbf{p}\in {\mathbb{R}}^3,\mathbf{p}\ne 0\},\mathrm{d}\mu (p)=\frac{{\mathrm{d}}^3\mathbf{p}}{(2\pi {)}^{3}2|\mathbf{p}|}.$$

• unlabeled · line 279

  $$\mathfrak{h}=L^2(C_{+},\mathrm{d}\mu ),\mathcal{H}={\Gamma }_s(\mathfrak{h}).$$

• unlabeled · line 288

  $$\varphi (x)=\sqrt{\hslash }{\int }_{C_{+}}(e^{-\mathrm{i}p\cdot x}a(p)+e^{\mathrm{i}p\cdot x}{a}^{\ast }(p))\mathrm{d}\mu (p).$$

• unlabeled · line 296

  $$\hat{f}(k)={\int }_M{e}^{\mathrm{i}k\cdot x}f(x){\mathrm{d}}^{4}x.$$

• unlabeled · line 310

  $$W(z)=\frac{\hslash }{4{\pi }^2}\underset{ϵ\downarrow 0}{\lim }\frac{1}{|\mathbf{z}{|}^2-(z^0-\mathrm{i}ϵ{)}^2}.$$

• unlabeled · line 319

  $$\square R={\delta }_0,\mathrm{supp}R\subseteq {\overline{V}}_{+},R(z)=\frac{1}{2\pi }\Theta (z^0)\delta (z^2).$$