scholarly journals Multimomentum hamiltonian formalism in quantum field theory

1994 ◽  
Vol 33 (12) ◽  
pp. 2365-2379 ◽  
Author(s):  
Gennadi A. Sardanashvily
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hamiltonian Formalism ◽  
Quantum Field

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.

Particle–antiparticle potential in scalar quantum field theory with a Higgs-like mediating field

2013 ◽  
Vol 91 (10) ◽  
pp. 764-769 ◽  
Author(s):  
Alexander Chigodaev ◽  
Jurij W. Darewych
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hamiltonian Formalism ◽  
Nonrelativistic Limit ◽  
Single Pair ◽  
Quantum Field ◽  
Short Range Potential ◽  
Interparticle Potential ◽  
Scalar Quantum ◽  
The One

We study the particle–antiparticle force in a model scalar quantum field theory (QFT) with a nonlinear Higgs-like mediating field. We use the variational method in a reformulated Hamiltonian formalism of the theory. The trial state consists of a superposition of single-pair and two-pair Fock states. Coupled relativistic integral equations for the one- and two-pair channel functions are derived and their nonrelativistic limit forms are obtained. Variational ansatz are used to derive the correction to the dominant Yukawa interparticle potential for the particle–antiparticle system. The correction is found to be an attractive short-range potential.

Relativistic three-particle bound states in scalar quantum field theory

1993 ◽  
Vol 71 (7-8) ◽  
pp. 365-379 ◽  
Author(s):  
Leo Di Leo ◽  
Jurij W. Darewych
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Bound States ◽  
Wave Equations ◽  
Hamiltonian Formalism ◽  
Relativistic Effects ◽  
Approximate Solutions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field

We derive relativistic three-particle wave equations for scalar particles [Formula: see text], [Formula: see text], and [Formula: see text], interacting via a massive or massless scalar field, χ. The variational method, within the Hamiltonian formalism of quantum field theory, is used to obtain the equations using a simple [Formula: see text] Ansatz. Approximate solutions of these equations are presented for various strengths of the coupling. The magnitude of the relativistic effects in the three-particle energies and wave functions is illustrated by comparison with nonrelativistic results.

scholarly journals The Entropic Dynamics of Quantum Scalar Fields Coupled to Gravity

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1324
Author(s):  
Selman Ipek ◽  
Ariel Caticha
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Relativistic Quantum ◽  
Superposition Principle ◽  
Hamiltonian Formalism ◽  
Scalar Fields ◽  
Space Time ◽  
Relativistic Quantum Mechanics ◽  
Quantum Field ◽  
Entropic Dynamics

Entropic dynamics (ED) are a general framework for constructing indeterministic dynamical models based on entropic methods. ED have been used to derive or reconstruct both non-relativistic quantum mechanics and quantum field theory in curved space-time. Here we propose a model for a quantum scalar field propagating in dynamical space-time. The approach rests on a few key ingredients: (1) Rather than modelling the dynamics of the fields, ED models the dynamics of their probabilities. (2) In accordance with the standard entropic methods of inference, the dynamics are dictated by information encoded in constraints. (3) The choice of the physically relevant constraints is dictated by principles of symmetry and invariance. The first of such principle imposes the preservation of a symplectic structure which leads to a Hamiltonian formalism with its attendant Poisson brackets and action principle. The second symmetry principle is foliation invariance, which, following earlier work by Hojman, Kuchař, and Teitelboim, is implemented as a requirement of path independence. The result is a hybrid ED model that approaches quantum field theory in one limit and classical general relativity in another, but is not fully described by either. A particularly significant prediction of this ED model is that the coupling of quantum fields to gravity implies violations of the quantum superposition principle.

Bound and resonant relativistic two-particle states in scalar quantum field theory

1992 ◽  
Vol 70 (6) ◽  
pp. 412-426 ◽  
Author(s):  
Leo Di Leo ◽  
Jurij W. Darewych
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Wave Equations ◽  
Decay Channel ◽  
Hamiltonian Formalism ◽  
Bound State ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Scalar Quantum

We derive relativistic particle–antiparticle wave equations for scalar particles, [Formula: see text] and [Formula: see text], interacting via a massive or massless scalar field, χ (the Wick–Cutkosky model). The variational method, within the Hamiltonian formalism of quantum field theory is used to derive equations with and without coupling of this quasi-bound [Formula: see text] system to the χχ decay channel. Bound-state energies in the massless case are compared with the ladder Bethe–Salpeter and light-cone results. In the case of coupling to the decay channel, the quasi-bound [Formula: see text] states are seen to arise as resonances in the χχ scattering cross section. Numerical results are presented for the massive and massless χ case.

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