Multiparticle Fields on the Subset of Simultaneity
We propose a model describing the scattering of hadrons as bound states of their constituent quarks. We build the dynamic equations for the multiparticle fields on the subset of simultaneity, using the Lagrange method, similarly to the case of “usual” single-particle fields. We then consider the gauge fields restoring the local internal symmetry on the subset of simultaneity. Since the multiparticle fields, which describe mesons as bound states of a quark and an antiquark, are two-index tensors relative to the local gauge group, it is possible to consider a model with two different gauge fields, each one associated with its own index. Such fields would be transformed by the same laws during a local gauge transformation and satisfy the same dynamic equations, but with different boundary conditions. The dynamic equations for the multiparticle gauge fields describe such phenomena as the confinement and the asymptotic freedom of colored objects under certain boundary conditions and the spontaneous symmetry breaking under another ones. With these dynamic equations, we are able to describe the quark confinement in hadrons within a single model and their interaction during the hadron scattering through the exchange of the bound states of gluons – the glueballs.
H. Yukawa. On the radius of the elementary particle. Phys. Rev. 76, 300 (1949). https://doi.org/10.1103/PhysRev.76.300.2
H. Yukawa. Quantum theory of non-local fields. Part I. Free fields. Phys. Rev. 77, 219 (1950). https://doi.org/10.1103/PhysRev.77.219
H. Yukawa. Quantum theory of non-local fields. Part II. Irreducible fields and their interaction. Phys. Rev. 80, 1047 (1950). https://doi.org/10.1103/PhysRev.80.1047
P. Dirac. Forms of relativistic dynamics. Rev. Mod. Phys. 21, 392 (1949). https://doi.org/10.1103/RevModPhys.21.392
T. Heinzl. Light cone quantization: Foundations and applications. Lect. Notes Phys. 572, 55 (2001). https://doi.org/10.1007/3-540-45114-5_2
A. Logunov, A. Tavkhelidze. Quasi-optical approach in quantum field theory. Il Nuovo Cim. Ser. 10 29, 380 (1963). https://doi.org/10.1007/BF02750359
A. Logunov, A. Tavkhelidze, I. Todorov, O. Khrustalev. Quasi-potential character of the scattering amplitude. Il Nuovo Cim. Ser. 10 30, 134 (1963). https://doi.org/10.1007/BF02750754
R. Faustov. Relativistic wavefunction and form factors of the bound system. Ann. Phys. 78, 176 (1973). https://doi.org/10.1016/0003-4916(73)90007-9
S. Tomonaga. On a relativistically invariant formulation of the quantum theory of wave fields. Prog. Theor. Phys. 1, 27 (1946). https://doi.org/10.1143/PTP.1.27
P. Dirac, W. Fock, B. Podolsky. On quantum electrodynamics. Phys. Zs. Sowjet. 2, 468 (1932).
S. Petrat, R. Tumulka. Multi-time wave functions for quantum field theory. Ann. Phys. 345, 17 (2014). https://doi.org/10.1016/j.aop.2014.03.004
N.O. Chudak, K.K. Merkotan, D.A. Ptashynskiy et al. Internal states of hadrons in relativistic reference systems. Ukr. Fiz. Zh. 61, 1039 (2016).
E. Marx. Generalized relativistic Fock space. Int. J. Theor. Phys. 6, 359 (1972). https://doi.org/10.1007/BF01258729
H. Sazdjian. Relativistic wave equations for the dynamics of two interacting particles. Phys. Rev. D 33, 3401 (1986). https://doi.org/10.1103/PhysRevD.33.3401
S. Petrat, R. Tumulka. Multi-time equations, classical and quantum. Proc. Royal Soc. of London A: Math., Phys. Eng. Sci. 470, 1364 (2014). https://doi.org/10.1098/rspa.2013.0632
D.A. Ptashynskiy, T.M. Zelentsova, N.O. Chudak et al. Multiparticle fields on the subset of simultaneity. arXiv:1905.07233 [physics.gen-ph].
N. Chudak, M. Deliyergiyev, K. Merkotan et al. Multiparticle quantum fields. Phys. J. 2, 181 (2016).