Stochastic Quantization of the Maxwell Field: Some Comments on the Paper of Guerra and Loffredo.
S. C. Lb
Recently GUER~A and LOFF~]~D0 (:) have constructed a stochastice elctromagnetic field by applying the stochastic quantization method of Nelson (2) to the classical electromagnetic field. According to their results the (( space part ~) of the Euclidean electromagnetic field F~j (with i, ] = 1, 2, 3) can be regarded as the ground-state stochastic electromagnetic field defined in the real physical time, in complete analogy with the case of the scalar massive boson field (3). In this note we shall comment on a basic assumption contained in the paper of Guerra and Loffredo. The main feature in their construction is that the magnetic field B(~, t) is assumed to be promoted to a random ~iarkov process by the stochastic quantization procedure. The electric field E(~, t) is then split into a couple of functions /~( ~, t) expressible in terms of B(~, t). By considering the classical Maxwell field in terms of normal canonical co-ordinates and employing the stochastic differential equation of Ito type, they obtained the ground-state stochastic magnetic field with zero mean and covarianee given by
•Jan 1, 1981•0 citations