scholarly journals On free massless (pseudo)scalar quantum field theory in 1+1-dimensional space-time

2002 ◽  
Vol 24 (4) ◽  
pp. 653-663 ◽  
Author(s):  
M. Faber ◽  
A.N. Ivanov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Space Time ◽  
Quantum Field ◽  
Scalar Quantum ◽  
Dimensional Space Time ◽  
Pseudo Scalar

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.

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.

QUANTUM FIELD THEORY ON NONCOMMUTATIVE SPACE–TIME: THE RELATION BETWEEN ULTRAVIOLET BEHAVIOUR, TOPOLOGY AND SYMMETRY

2001 ◽  
Vol 16 (04n06) ◽  
pp. 235-240
Author(s):  
M. CHAICHIAN ◽  
A. DEMICHEV ◽  
P. PREŠNAJDER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Star Product ◽  
Space Time ◽  
Time Variable ◽  
Noncommutative Space ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Interaction Terms ◽  
Scalar Quantum

We study properties of a scalar quantum field theory on two-dimensional noncommutative space–times. We show that ultraviolet behaviour of a field theory on noncommutative spaces is sensitive to the topology of the space–time, namely to its compactness. The compactness of space-like coordinates implies discreteness of the time variable which leads to appearance of unphysical modes and violation of unitarity even in the absence of a star-product in the interaction terms. Thus, this conclusion holds also for other quantum field theories with discrete time.

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