Path integral for the Weyl quantized relativistic Hamiltonian (Q1079270)

The author gives a path integral representation of the solution of the Cauchy problem for the equation \[ \partial_ t\psi (t,x)=-(H-mc^ 2)\psi (t,x),\quad t>0,\quad x\in R^ d. \] Here c is the light velocity, H is the quantum Hamiltonian, i.e. the pseudo-differential operator whose symbol (in Weyl's sense) is a classical Hamiltonian \(h(p,x)=((cp-eA(x))^ 2+m^ 2c^ 4)^{1/2}+e\phi (x)\), \(p\in R^ d\), \(x\in R^ d\), of a relativistic spinless particle of mass \(m>0\) and charge e interacting with electromagnetic vector and scalar potentials A(x) and \(\phi\) (x).