Relativistic Invariance and Mass Renormalization in Quantum Field Theory
Starting from the instant form of relativistic quantum dynamics for a system of interacting fields, where only the Hamiltonian and the boost operators carry interactions among ten generators of the Poincar´e group, we propose a constructive way of ensuring the relativistic invariance (RI) in quantum field theory (QFT) with cutoffs in the momentum space. Our approach is based on an opportunity to separate a part in the primary Hamiltonian interaction, whose density in the Dirac (D) picture is the Lorentz scalar. In this work, we study the compatibility of the RI requirements as a whole, i.e., the fulfilment of the well-known commutations for these generators with the structure of mass counterterms in the total field Hamiltonian.
P.A.M. Dirac, Rev. Mod. Phys. 21, 392 (1949).
B.D. Keister and W.N. Polyzou, Adv. Nucl. Phys. 20, 225 (1991).
B.L.G. Bakker, in: Lectures Notes in Physics, edited by H. Latal and W. Schweiger (Springer, Berlin, 2001), p. 1.
A.V. Shebeko and P.A. Frolov, Few-Body Syst. 52, 125 (2012).
R. Machleidt, Adv. Nucl. Phys. 19, 189 (1989).
A.V. Shebeko and M.I. Shirokov, Progr. Part. Nucl. Phys. 44, 75 (2000).
A.V. Shebeko and M.I. Shirokov, Phys. Part. Nuclei 32, 31 (2001).
V.Yu. Korda, L. Canton, and A.V. Shebeko, Ann. Phys. 322, 736 (2007).
S. Weinberg, The Quantum Theory of Fields (Cambridge Univ. Press, Cambridge, 1995), Vol. 1.
H. Kita, Prog. Theor. Phys. 39, 1333 (1968).
C. Chandler, in: Proceed. of the 17-th Intern. IUPAP Conference on Few Body Physics (Durham, USA) and the private communication (2003).
K. Friedrichs, Perturbation of Spectra in Hilbert Space (Amer. Math. Soc., Providence, RI, 1965).