Hamiltonian Formalism and the Canonical Commutation Relations in Quantum Field Theory

1960 ◽  
Vol 1 (6) ◽  
pp. 492-504 ◽  
Author(s):  
H. Araki
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hamiltonian Formalism ◽  
Quantum Field ◽  
Canonical Commutation Relations ◽  
Commutation Relations

Some quantum field theory aspects of the superspace quantization of general relativity

1976 ◽  
Vol 351 (1665) ◽  
pp. 209-232 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Perturbation Theory ◽  
Constraint Equation ◽  
Mathematical Structure ◽  
Quantum Field ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
The Status

An investigation is started into a possible mathematical structure of the Wheeler-DeWitt superspace quantization of general relativity. The emphasis is placed throughout on quantum field theory aspects of the problem and topics discussed include canonical commutation relations in a triad basis, the status of the constraint equation and the rôle played by perturbation theory.

On the Feynman principle

1955 ◽  
Vol 230 (1181) ◽  
pp. 272-276 ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Equations Of Motion ◽  
Canonical Formalism ◽  
Quantum Field ◽  
Usual Definition ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Feynman Amplitudes ◽  
Definition Of

The formulation of quantum field theory in terms of the Feynman principle is discussed. It is shown that the operators defined in terms of this principle satisfy the equations of motion. A definition of canonically conjugate momenta is given in terms of the principle and is shown to be equivalent to the usual definition. The canonical commutation relations are then deduced and the equivalence of this formulation and the canonical formalism is thereby established. The equations for Feynman amplitudes are also obtained. In conclusion some difficulties of the theory and some possible extensions are discussed.

Variational formulation of relativistic four-body systems in quantum field theory: scalar quadronium

2002 ◽  
Vol 80 (5) ◽  
pp. 605-612
Author(s):  
B Ding ◽  
J W Darewych
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fock Space ◽  
Hamiltonian Formalism ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Scalar Particles ◽  
Pairwise Interactions ◽  
Approximate Wave

We discuss a variational method for describing relativistic four-body systems within the Hamiltonian formalism of quantum field theory. The scalar Yukawa (or Wick–Cutkosky) model, in which scalar particles and antiparticles interact via a massive or massless scalar field, is used to illustrate the method. A Fock-space variational trial state is used to describe the stationary states of scalar quadronium (two particles and two antiparticles) interacting via one-quantum exchange and virtual annihilation pairwise interactions. Numerical results for the ground-state mass and approximate wave functions of quadronium are presented for various strengths of the coupling, for the massive and massless quantum exchange cases. PACS Nos.: 11.10Ef, 11.10St, 03.70+k, 03.65Pm

scholarly journals Interparticle potentials in a scalar quantum field theory with a Higgs-like mediating field

2013 ◽  
Vol 91 (4) ◽  
pp. 279-292 ◽  
Author(s):  
Alexander Chigodaev ◽  
Jurij W. Darewych
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Equations ◽  
Hamiltonian Formalism ◽  
Particle Systems ◽  
Stationary States ◽  
Quantum Field ◽  
Scalar Theory ◽  
Scalar Quantum ◽  
Interparticle Potentials

We study the interparticle potentials for few-particle systems in a scalar theory with a nonlinear mediating field of the Higgs type. We use the variational method, in a reformulated Hamiltonian formalism of quantum field theory, to derive relativistic three- and four-particle wave equations for stationary states of these systems. We show that the cubic and quartic nonlinear terms modify the attractive Yukawa potentials but do not change the attractive nature of the interaction if the mediating fields are massive.

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