Quantum field theory without Fock space

2012 ◽  
Author(s):  
Roman Sverdlov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fock Space ◽  
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

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.

scholarly journals From Quantum Field Theory to the Contemporary Quantum Mechanics

2019 ◽  
Vol 2 (4) ◽  
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Fock Space ◽  
Relativistic Quantum ◽  
Model Space ◽  
Physical Vacuum ◽  
Quantum Field ◽  
Scattering States ◽  
Exact Eigenvalue

In this talk we remind how the notion of the so-called clothed particles, put forward in relativistic quantum field theory by Greenberg and Schweber, can be used via the method of unitary clothing transformations (shortly, the UCT method) when finding the eigenstates of the total Hamiltonian H in case of interacting fields with the Yukawa - type couplings. In general, the UCT method is aimed at reduction of the exact eigenvalue problem in the primary Fock space to the model-space problems in the corresponding Hilbert spaces of the contemporary quantum mechanics. In this context we consider an approximate treatment of the physical vacuum, the observable one-particle and two-particle bound and scattering states.

scholarly journals PRIME NUMBERS, QUANTUM FIELD THEORY AND THE GOLDBACH CONJECTURE

2012 ◽  
Vol 27 (23) ◽  
pp. 1250136 ◽  
Author(s):  
MIGUEL-ANGEL SANCHIS-LOZANO ◽  
J. FERNANDO BARBERO G. ◽  
JOSÉ NAVARRO-SALAS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Fock Space ◽  
Dimensional Space ◽  
Canonical Quantization ◽  
Prime Numbers ◽  
Large Integer ◽  
Quantum Field ◽  
Dimensional Space Time ◽  
Prime Fields

Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space–time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators [Formula: see text] — labeled by prime numbers p — acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.

scholarly journals On the interacting Free Fock space and the deformed Wigner law

1997 ◽  
Vol 145 ◽  
pp. 1-28 ◽  
Author(s):  
Y. G. Lu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Hilbert Spaces ◽  
Fock Space ◽  
Basic Structure ◽  
Stochastic Calculus ◽  
Quantum Field ◽  
Complex Field ◽  
Quantum Stochastic Calculus ◽  
Direct Sum

The Fock space is a basic structure for the quantum field theory and quantum stochastic calculus. In all the cases, a Fock space can be described as a direct sum of a sequence of some Hilbert spaces, i.e. a Fock space has the form of , where, is the complex field and is a given Hilbert space.

scholarly journals A NOVEL VARIATIONAL APPROACH FOR QUANTUM FIELD THEORY: EXAMPLE OF STUDY OF THE GROUND STATE AND PHASE TRANSITION IN NONLINEAR SIGMA MODEL

2005 ◽  
Vol 20 (15) ◽  
pp. 3488-3494 ◽  
Author(s):  
YURIY MISHCHENKO ◽  
CHUENG-RYONG JI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Ground State ◽  
Variational Approach ◽  
Sigma Model ◽  
Fock Space ◽  
Nonlinear Sigma Model ◽  
Quantum Field ◽  
Expectation Values ◽  
Optimization Under Constraints

We discuss a novel form of the variational approach in Quantum Field Theory in which the trial quantum configuration is represented directly in terms of relevant expectation values rather than, e.g., increasingly complicated structure from Fock space. The quantum algebra imposes constraints on such expectation values so that the variational problem is formulated here as an optimization under constraints. As an example of application of such approach we consider the study of ground state and critical properties in a variant of nonlinear sigma model.

scholarly journals THERMAL FIELD THEORY IN NON-EQUILIBRIUM STATES

1996 ◽  
Vol 10 (13n14) ◽  
pp. 1599-1614 ◽  
Author(s):  
P.A. HENNING ◽  
K. NAKAMURA ◽  
Y. YAMANAKA
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Thermal Field ◽  
Transport Theory ◽  
Fock Space ◽  
Quantum Effect ◽  
Nonequilibrium Systems ◽  
Quantum Field ◽  
Degenerate Plasma ◽  
Nonequilibrium Effects

Conventional transport theory is not really applicable to nonequilibrium systems which exhibit strong quantum effects. We present two different approaches to overcome this problem. Firstly we point out how transport equations may be derived that incorporate a nontrivial spectral function as a typical quantum effect, and test this approach in a toy model of a strongly interacting degenerate plasma. Secondly we explore a path to include nonequilibrium effects into quantum field theory through momentum mixing transformations in Fock space. Although the two approaches are completely orthogonal, they lead to the same coherent conclusion.

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