scholarly journals Tunneling in a quantum field theory on a compact one-dimensional space

2006 ◽  
Vol 745 (3) ◽  
pp. 142-164 ◽  
Author(s):  
Jürgen Baacke ◽  
Nina Kevlishvili
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Quantum Field ◽  
One Dimensional

THE PRINCIPLE OF MINIMAL SENSITIVITY APPLIED TO A NEW PERTURBATIVE SCHEME IN QUANTUM FIELD THEORY

1989 ◽  
Vol 04 (07) ◽  
pp. 1735-1746 ◽  
Author(s):  
H. F. JONES ◽  
M. MONOYIOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Exact Result ◽  
Field Theories ◽  
Quantum Field ◽  
One Dimensional ◽  
Perturbative Method ◽  
Improved Accuracy

A recently proposed perturbative method for solving a self-interacting scalar φ4 field theory consists of writing the interaction as gφ2(1+δ) and expanding in powers of δ. The method contains an ambiguity in so far as one could modify the interaction Lagrangian by a factor λ(1−δ). The truncated expansion depends on the unphysical parameter, whereas the exact result does not. We exploit this ambiguity by assigning to λ the value for which the truncated result is stationary, thus minimizing its sensitivity to λ. The technique is applied to field theories in zero-and one-dimensional space-times and gives improved accuracy as compared to fixed λ.

KOLMOGOROV SYSTEMS AND ANOSOV SYSTEMS IN QUANTUM THEORY

2001 ◽  
Vol 04 (01) ◽  
pp. 85-119 ◽  
Author(s):  
H. NARNHOFER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Theory ◽  
Quantum Field ◽  
Modular Systems ◽  
One Dimensional ◽  
Classical Systems ◽  
Anosov Systems

In analogy to classical systems, quantum K-systems and quantum Anosov systems are defined. Their relation especially for modular systems is discussed as well as the consequences on clustering properties. Examples for such systems in the framework of quantum field theory and one-dimensional theories are offered.

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.

SOLUTION OF A CLASS OF CONFORMAL QUANTUM FIELD THEORY MODELS IN D-DIMENSIONAL SPACE

1989 ◽  
Vol 04 (28) ◽  
pp. 2773-2790
Author(s):  
E.S. FRADKIN ◽  
M.Ya. PALCHIK
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Central Charge ◽  
Dimensional Space ◽  
Dimensional Euclidean Space ◽  
Constant Field ◽  
Quantum Field ◽  
Algebraic Equations ◽  
Field Equations ◽  
Parameter Symmetry

A method of solving a class of conformal quantum field theory models in D-dimensional Euclidean space-time is proposed. Some of the models are determined by regularized field equations. The method allows us to obtain closed differential equations for each Green function of fundamental and composite fields, and also algebraic equations for scale dimensions of fields. Each D>2-model involves an analogue of the central charge, i.e., a special scalar field P of dimension dP=D−2. When D=2, this becomes a constant field. We also obtain a new class of D=2 models with broken infinite parameter symmetry. Closed differential equation for Green functions of these models are found.

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.

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