Hiroshi Enatsu

Enatsu has found[1] that the commutation relation[2]

${\displaystyle [\psi (x,\tau ),\psi ^{*}(x',\tau )]=\delta (x-x')}$

in a relativistic Hamiltonian formalism is equivalent to that in the conventional non-relativistic Hamiltonian formalism of quantum field theory, where ${\displaystyle [\psi ,\phi ]=\psi \phi -\phi \psi }$ is the commutator, ${\displaystyle x}$ is space-time coordinates, ${\displaystyle \tau }$ is proper time, ${\displaystyle \psi ^{*}}$ is Hermitian adjoint of ${\displaystyle \psi }$, and ${\displaystyle \delta (x)}$ is the Dirac delta function, with the aid of the relation

${\displaystyle \epsilon (x-x')\epsilon (\tau -\tau ')=1}$.

Here, a step function ${\displaystyle \epsilon (x)}$ follows ${\displaystyle \epsilon (x)=1}$ for ${\displaystyle 0<x}$, and ${\displaystyle \epsilon (x)=-1}$ for ${\displaystyle x<0}$.

• On the Photodisintegration of the Deuteron (Pseudoscalar Meson Theory.), December 1949
• On the Nuclear Forces, February 1950
• On the Interaction of Mesons and Nucleons, September 1950
• On the Mass of Cohesive Meson and the Mass Difference Of Nucleon, April 1951
• On the Mass of Cohesive Meson and the Mass Difference of Nucleons, II, June 1951
• On the Mass Difference of Nucleons and the Cohesive Mesons, October 1951
• On the Self-energies of Mesons, October 1951
• On the Self-Energies of Nucleons, October 1951
• Self-Energies of Nucleons and the Mass Spectra of Heavy Particles, February 1952
• Mass Spectrum of Elementary Particles I: Eigenvalue Problem in Space-time, February 1954
• Mass Spectrum of Elementary Particles, II, September 1954
• Theory of Unstable Heavy Particles, July 1954
• Relativistic quantum mechanics and mass-quantization, 1956
• Relativistic Hamiltonian Formalism in Quantum Field Theory and Micro-Noncausality, August 1963
• Covariant Hamiltonian Formalism for Particles of any Spin and Nonzero Mass, 1968
• Micro-noncausal theory of the hydrogen atom 1971
• Covariant Hamiltonian formalism for quantized fields and the hydrogen mass levels, 1975
• On the hyperfine structure splittings of hydrogen, 1975
• Proton-proton scattering problem in a covariant Hamiltonian formalism, 1976
• Four-dimensional tensor forces and electric quadrupole moments in the bound-states of the deuteron, 1976
• Micrononcausal euclidean wave functions for hadrons, February 1978
• Hyperfine structure splittings of the hydrogen atom in a covariant Hamiltonian formalism, 1983
• Bethe-Salpeter type equations for a covariant Hamiltonian formalism in quantum field theory, 1984
• Quantization of masses of elementary particles with micrononcausal structures, October 1986
• Quantization of masses of elementary particles with micrononcausal structures 1987
• Quantization of the mass of the W-boson in the Weinberg-Salam theory, 1988

• Levere Hostler, "Quantum field theory of particles of indefinite mass. II. An electromagnetic model", 1981
• John R. Fanchi & Weldon J. Wilson, "Relativistic many-body systems: Evolution-parameter formalism", 1983
• Matej Pavsic, "PseudoEuclidean signature harmonic oscillator, quantum field theory and vanishing cosmological constant", 1998
• Juan P. Aparcio, Fabian H. Gaioli, and Edgardo T. Garcia Alvarez, "Proper Time Derivatives in Quantum Mechanics", 1998
• Edgardo T. Garcia Alvarez & Fabian H. Gaioli, "Covariant Hamiltonian Formalisms for Particles and Antiparticles", 1999
• (Eds.) Rosolino Buccheri, Metod Saniga & William Mark Stuckey, "The Nature of Time: Geometry, Physics and Perception", pp. 173-pp. 174, 2003 (Springer).
• Ed Seidewitz, "Foundations of a Spacetime Path Formalism for Relativistic Quantum Mechanics", November 2006