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

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.

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.

scholarly journals QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

1999 ◽  
Vol 11 (05) ◽  
pp. 519-532 ◽  
Author(s):  
SEBASTIANO CARPI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Scaling Limit ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Complex Scalar

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

scholarly journals Examining a covariant and renormalizable quantum field theory in de Sitter space by studying “black hole radiation”

2016 ◽  
Vol 31 (11) ◽  
pp. 1650052 ◽  
Author(s):  
Hamed Pejhan ◽  
Surena Rahbardehghan
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Hole ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
De Sitter ◽  
Black Hole Radiation

Respecting that any consistent quantum field theory in curved space–time must include black hole radiation, in this paper, we examine the Krein–Gupta–Bleuler (KGB) formalism as an inevitable quantization scheme in order to follow the guideline of the covariance of minimally coupled massless scalar field and linear gravity on de Sitter (dS) background in the sense of Wightman–Gärding approach, by investigating thermodynamical aspects of black holes. The formalism is interestingly free of pathological large distance behavior. In this construction, also, no infinite term appears in the calculation of expectation values of the energy–momentum tensor (we have an automatic and covariant renormalization) which results in the vacuum energy of the free field to vanish. However, the existence of an effective potential barrier, intrinsically created by black holes gravitational field, gives a Casimir-type contribution to the vacuum expectation value of the energy–momentum tensor. On this basis, by evaluating the Casimir energy–momentum tensor for a conformally coupled massless scalar field in the vicinity of a nonrotating black hole event horizon through the KGB quantization, in this work, we explicitly prove that the hole produces black-body radiation which its temperature exactly coincides with the result obtained by Hawking for black hole radiation.

FINITE CASIMIR EFFECT IN QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (10) ◽  
pp. 1677-1702 ◽  
Author(s):  
A. BLASI ◽  
R. COLLINA ◽  
J. SASSARINI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Short Distance ◽  
Casimir Effect ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Complete Control ◽  
Soft Term ◽  
Distance Behavior

The computation of the Casimir effect is directly linked to the modification of the vacuum energy due to the presence of boundaries. In order to have complete control of the short distance behavior also near the boundary, the analysis is performed in the precise framework of a local, renormalizable quantum field theory which includes the boundary contributions. We show that the presence of soft terms at the boundary, needed to implement Robin's conditions, introduces a free parameter in the final, finite answer, a parameter which has no natural normalization condition within the scheme. We discuss in detail a free massless scalar field in R3 with plane and cylindric boundaries; in particular the second case, where the boundary soft term is essential to remove sub-leading short distance divergencies, suffers the mentioned indeterminacy, which might be removed by a phenomenological interpretation relating the soft term to a microscopic description of the boundary.

A novel method for renormalization in quantum-field theory in curved spacetime

2018 ◽  
Vol 27 (11) ◽  
pp. 1843001 ◽  
Author(s):  
Gabriel Freitas ◽  
Marc Casals
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Kerr Black Hole ◽  
Field Operator ◽  
Massless Scalar ◽  
Energy Tensor ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Curved Spacetime ◽  
Renormalization Method

In quantum-field theory in curved spacetime, two important physical quantities are the expectation value of the stress-energy tensor [Formula: see text] and of the square of the field operator [Formula: see text]. These expectation values must be renormalized, which is usually performed via the so-called point-splitting prescription. However, the renormalization method that is usually implemented in the literature, in principle, only applies to static, spherically-symmetric spacetimes, and does not readily generalize to other types of spacetime. We present a novel implementation of the renormalization procedure which may be used in the future for more general spacetimes, such as Kerr black hole spacetime. As an example, we apply our method to the renormalization of [Formula: see text] for a massless scalar field in Bertotti–Robinson spacetime.

STABLE QUASIPARTICLE PICTURE IN THERMAL QUANTUM FIELD PHYSICS

1994 ◽  
Vol 09 (10) ◽  
pp. 1703-1729 ◽  
Author(s):  
H. CHU ◽  
H. UMEZAWA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Degrees Of Freedom ◽  
Fock Space ◽  
Quantum Field ◽  
Self Energy ◽  
Vector Algebra ◽  
Physical Particle ◽  
Usual Quantum ◽  
Definition Of

It is well known that physical particles are thermally dissipative at finite temperature. In this paper we reformulate both the equilibrium and nonequilibrium thermal field theories in terms of stable quasiparticles. We will redefine the thermal doublets, the double tilde conjugation rules and the thermal Bogoliubov transformations so that our theory can be consistent for most general situations. All operators, including the dissipative physical particle operators, are realized in a Fock space defined by the stable quasiparticles. The propagators of the physical particles are expressed in terms of the operators of such stable quasiparticles, which is a simple diagonal matrix with the diagonal elements being the temporal step functions, same as the propagators in the usual quantum field theory without thermal degrees of freedom. The proper self-energies are also expressed in terms of these stable quasiparticle propagators. This formalism inherits the definition of on-shell self-energy in the usual quantum field theory. With this definition, a self-consistent renormalization is formulated which leads to quantum Boltzmann equation and the entropy law. With the aid of a doublet vector algebra we have an extremely simple recipe for computing Feynman diagrams. We apply this recipe to several examples of equilibrium and nonequilibrium two-point functions, and to the kinetic equation for the particle numbers.

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