scholarly journals LARGE-N RENORMALIZATION GROUP ON FUZZY SPHERE

2013 ◽  
Vol 21 ◽  
pp. 151-152 ◽  
Author(s):  
SHOICHI KAWAMOTO ◽  
DAN TOMINO ◽  
TSUNEHIDE KUROKI
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Scalar Field ◽  
Fixed Points ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Fuzzy Sphere ◽  
Scalar Field Theory ◽  
Large N

We study the large-N renormalization group of scalar field theory on a fuzzy sphere. We carry out perturbative analysis and formulate the renormalization group equation. We then search for fixed points and investigate their properties.

scholarly journals FUNCTIONAL RENORMALIZATION OF NONCOMMUTATIVE SCALAR FIELD THEORY

2011 ◽  
Vol 26 (23) ◽  
pp. 4009-4051 ◽  
Author(s):  
ALESSANDRO SFONDRINI ◽  
TIM A. KOSLOWSKI
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
High Energy ◽  
Flow Equation ◽  
Renormalization Group Equation ◽  
Dual Model ◽  
Group Equation ◽  
Scalar Field Theory ◽  
Covariant Model ◽  
The Matrix

In this paper we apply the Functional Renormalization Group Equation (FRGE) to the noncommutative scalar field theory proposed by Grosse and Wulkenhaar. We derive the flow equation in the matrix representation and discuss the theory space for the self-dual model. The features introduced by the external dimensionful scale provided by the noncommutativity parameter, originally pointed out in R. Gurau and O. J. Rosten, J. High Energy Phys.0907, 064 (2009), are discussed in the FRGE context. Using a technical assumption, but without resorting to any truncation, it is then shown that the theory is asymptotically safe for suitably small values of the ϕ4coupling, recovering the result of M. Disertori et al., Phys. Lett. B649, 95 (2007). Finally, we show how the FRGE can be easily used to compute the one-loop beta-functions of the duality covariant model.

scholarly journals Commutative–non-commutative dualities

2020 ◽  
Vol 98 (2) ◽  
pp. 158-166
Author(s):  
F.G. Scholtz ◽  
P.H. Williams ◽  
J.N. Kriel
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Scalar Field ◽  
Lorentz Symmetry ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Dual Theory ◽  
Constructive Approach ◽  
Non Local ◽  
Exact Renormalization Group

We show that it is in principle possible to construct dualities between commutative and non-commutative theories in a systematic way. This construction exploits a generalization of the exact renormalization group equation (ERG). We apply this to the simple case of the Landau problem and then generalize it to the free and interacting non-canonical scalar field theory. This constructive approach offers the advantage of tracking the implementation of the Lorentz symmetry in the non-commutative dual theory. In principle, it allows for the construction of completely consistent non-commutative and non-local theories where the Lorentz symmetry and unitarity are still respected, but may be implemented in a highly non-trivial and non-local manner.

scholarly journals ASYMPTOTIC FREEDOM IN A SCALAR FIELD THEORY ON THE LATTICE

1998 ◽  
Vol 13 (31) ◽  
pp. 2495-2501 ◽  
Author(s):  
KURT LANGFELD ◽  
HUGO REINHARDT
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Scalar Particle ◽  
Higgs Sector ◽  
Asymptotic Freedom ◽  
Scalar Field Theory ◽  
Large N ◽  
The Standard Model ◽  
Conceptual Problems ◽  
The Continuum

A scalar field theory in four space–time dimensions is proposed, which embodies a scalar condensate, but is free of the conceptual problems of standard ϕ4-theory. We propose an N-component, O(N)-symmetric scalar field theory, which is originally defined on the lattice. The scalar lattice model is analytically solved in the large-N limit. The continuum limit is approached via an asymptotically free scaling. The renormalized theory evades triviality, and furthermore gives rise to a dynamically formed mass of the scalar particle. The model might serve as an alternative to the Higgs sector of the standard model, where the quantum level of the standard ϕ4-theory contradicts phenomenology due to triviality.

scholarly journals The KAM theorem and renormalization group

2009 ◽  
Vol 29 (2) ◽  
pp. 419-431 ◽  
Author(s):  
E. DE SIMONE ◽  
A. KUPIAINEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Elementary Proof ◽  
Renormalization Group Equation ◽  
Quadratic Nonlinearity ◽  
Picard Iteration ◽  
Group Equation ◽  
Quantum Field ◽  
Kam Theorem

AbstractWe give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a certain PDE with quadratic nonlinearity, the so-called Polchinski renormalization group equation studied in quantum field theory.

scholarly journals SOLUTIONS OF THE POLCHINSKI ERG EQUATION IN THE O(N) SCALAR MODEL

2002 ◽  
Vol 17 (32) ◽  
pp. 4871-4902 ◽  
Author(s):  
YU. A. KUBYSHIN ◽  
R. NEVES ◽  
R. POTTING
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Scalar Model ◽  
Regular Solutions ◽  
Exact Renormalization Group

Solutions of the Polchinski exact renormalization group equation in the scalar O(N) theory are studied. Families of regular solutions are found and their relation with fixed points of the theory is established. Special attention is devoted to the limit N = ∞, where many properties can be analyzed analytically.

scholarly journals WAVE FUNCTIONALS, HAMILTONIANS AND THE RENORMALIZATION GROUP

1996 ◽  
Vol 11 (15) ◽  
pp. 2749-2763 ◽  
Author(s):  
D. MINIC ◽  
V.P. NAIR
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Canonical Structure ◽  
Energy Eigenvalues

We analyze the renormalization of wave functionals and energy eigenvalues in field theory. A general discussion of the canonical structure of the renormalization group equation is also given.

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