Renormalization group equation for the vacuum energy of a scalar field in curved space-time

1983 ◽  
Vol 26 (8) ◽  
pp. 721-725 ◽  
Author(s):  
I. L. Bukhbinder ◽  
S. D. Odintsov
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Vacuum Energy ◽  
Renormalization Group Equation ◽  
Space Time ◽  
Group Equation ◽  
Curved Space

scholarly journals Renormalization group and diffusion equation

2020 ◽  
Author(s):  
Masami Matsumoto ◽  
Gota Tanaka ◽  
Asato Tsuchiya
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Diffusion Equation ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Initial Time ◽  
Group Equation ◽  
Cutoff Function ◽  
Exact Renormalization Group ◽  
And Diffusion

Abstract We study relationship between renormalization group and diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed action. As a generalization of the result obtained by Sonoda and Suzuki, we find that the correlation functions of diffused fields with respect to the bare action agree with those of bare fields with respect to the effective action, where the diffused field obeys a generalized diffusion equation determined by the cutoff function and the seed action and agrees with the bare field at the initial time.

scholarly journals THE EFFECTIVE POTENTIAL IN THE MASSIVE $\phi_4^4$ MODEL

2007 ◽  
Vol 22 (01) ◽  
pp. 1-9 ◽  
Author(s):  
F. BRANDT ◽  
F. CHISHTIE ◽  
D. G. C. MCKEON
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Effective Potential ◽  
Quantum Electrodynamics ◽  
Renormalization Group Equation ◽  
Massless Scalar ◽  
Group Equation ◽  
Scalar Quantum ◽  
Text Model

By applying the renormalization group equation, it has been shown that the effective potential V in the massless [Formula: see text] model and in massless scalar quantum electrodynamics is independent of the scalar field. This analysis is extended here to the massive [Formula: see text] model, showing that the effective potential is independent of ϕ here as well.

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.

APPROXIMATE CALCULATION OF THE N-LOOP EFFECTIVE POTENTIAL FOR LARGE FIELD VALUES THROUGH THE RENORMALIZATION GROUP EQUATION

1996 ◽  
Vol 11 (10) ◽  
pp. 805-813
Author(s):  
MURAT ÖZER
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Effective Potential ◽  
Approximate Calculation ◽  
Approximate Expression ◽  
Renormalization Group Equation ◽  
Large Field ◽  
Group Equation

The renormalization group equation is used to obtain an approximate expression for the N-loop effective potential VN(ϕ) for large values of an interacting scalar field ϕ. The expression thus obtained is valid when the leading logarithms are much larger than the nonleading ones.

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 Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation

2009 ◽  
Vol 324 (2) ◽  
pp. 414-469 ◽  
Author(s):  
Alessandro Codello ◽  
Roberto Percacci ◽  
Christoph Rahmede
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation

RENORMALIZATION GROUP EQUATION AND EFFECTIVE ACTION IN STRING THEORY

1989 ◽  
Vol 04 (10) ◽  
pp. 941-951 ◽  
Author(s):  
J. GAITE
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Generating Functional ◽  
S Matrix

The connection between the renormalization group for the σ-model effective action for the Polyakov string and the S-matrix generating functional for dual amplitudes is studied. A more general approach to the renormalization group equation for string theory is proposed.

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