Abstract
We show new applications of the notion of clothed particles in quantum field theory. Its realization by means of the clothing procedure put forward by Greenberg and Schweber allows one to express the total Hamiltonian H and other generators of the Poincare group for a given system of interacting fields through the creation (annihilation) operators for the so-called clothed particles with physical (observed) properties. Here such a clothed particle representation is used to calculate the matrix elements (shortly, form factors) of the corresponding Nother current operators sandwiched between the H eigenstates. Our calculations are performed with help of an iterative technique suggested by us earlier when constructing the NN → πNN transition operators. As an illustration, we outline some application of our approach in the spinor quantum electrodynamics.
Highlights
The method of unitary clothing transformations (UCTs) ([1]–[5]) allows us to develop an alternate approach for calculating the matrix elements Fμ(p, p) ≡ p ; out|Jμ(0)|p; in of the Nöther current density operator Jμ(0) sandwiched between the in(out) states of interacting fields
Since every UCT W(αc) = W(α) = exp R, R = −R† connects a primary set α of creation operators in the bare-particle representation (BPR) with new operators αc in the clothed-particle representation (CPR) via similarity transformation α = W(αc)αcW†(αc), we consider the expansion
E-mail: shebeko@kipt.kharkov.ua where ψ(0) is the electron-positron field ψ(x) at x = (0, 0). In both cases the matrix elements of interest between the one-fermion states |p; in = |p; out = b†c(p)|Ω with the 4-momentum p = (p0, p), p0 = p2 + m2 are expressed through the Dirac F1(q2) and Pauli F2(q2) form factors (FFs) that depend on the ’transferred’ 4-momentum q = p − p squared, viz., Fμ(p, p) = eu(p ){F1(q2)γμ + iσμνF2(q2)(p − p)ν}u(p)
Summary
The method of unitary clothing transformations (UCTs) ([1]–[5]) allows us to develop an alternate approach for calculating the matrix elements Fμ(p , p) ≡ p ; out|Jμ(0)|p; in of the Nöther current density operator Jμ(0) sandwiched between the in(out) states of interacting fields. Where ψ(0) is the electron-positron field ψ(x) at x = (0, 0) In both cases the matrix elements of interest between the one-fermion states |p; in = |p; out = b†c(p)|Ω with the 4-momentum p = (p0, p), p0 = p2 + m2 are expressed through the Dirac F1(q2) and Pauli F2(q2) form factors (FFs) that depend on the ’transferred’ 4-momentum q = p − p squared, viz., Fμ(p , p) = eu(p ){F1(q2)γμ + iσμνF2(q2)(p − p)ν}u(p).
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