Three Exactly Soluble Quantum Field Theory Models in 2-,3- and 4-Dimensional Space Time and Some General Questions They Suggest

1992 ◽  
pp. 393-398 ◽  
Author(s):  
Arthur S. Wightman
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Space Time ◽  
Quantum Field ◽  
Dimensional Space Time

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.

scholarly journals ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

1998 ◽  
Vol 13 (16) ◽  
pp. 2857-2874
Author(s):  
IVER H. BREVIK ◽  
HERNÁN OCAMPO ◽  
SERGEI ODINTSOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Space Time ◽  
Quantum Field ◽  
Curved Space ◽  
Njl Model ◽  
Effective Lagrangian ◽  
Special Solutions ◽  
Curvature Approximation ◽  
Symmetric Phase

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

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