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 Scenario for the renormalization in the 4D Yang–Mills theory

2016 ◽  
Vol 31 (01) ◽  
pp. 1630001 ◽  
Author(s):  
L. D. Faddeev
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Background Field ◽  
Space Time ◽  
Quantum Field ◽  
Yang Mills ◽  
Dimensional Space Time ◽  
Field Formalism

The renormalizability of the Yang–Mills quantum field theory in four-dimensional space–time is discussed in the background field formalism.

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.

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