Chapter 6/Asymptotic Behavior in Quantum Field Theory

1983 ◽  
pp. 135-181
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behavior ◽  
Quantum Field

QUANTUM FIELD THEORY RENORMALIZATION GROUP APPROACH TO SELF-ORGANIZED CRITICAL MODELS: THE CASE OF RANDOM BOUNDARIES

2002 ◽  
Vol 16 (08) ◽  
pp. 1171-1204 ◽  
Author(s):  
D. VOLCHENKOV ◽  
PH. BLANCHARD ◽  
B. CESSAC
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behavior ◽  
Renormalization Group ◽  
Coupling Constants ◽  
Threshold Condition ◽  
Dimensional Manifold ◽  
Quantum Field ◽  
Stochastic Problem ◽  
Self Organized

The long time and large scale asymptotic behavior for a stochastic problem related to self-organized critical (SOC) models is studied in the framework of advanced quantum field theory renormalization group (RG) method. The threshold condition and time scale separation between the slow dynamics of energy injection and the fast dynamics of avalanches (relaxation) are taken into account in the model. Herewith, the reciprocal correlation time at wavenumber k scales as tc(k) ∝ k-2+2η with some phenomenological parameter η > 0 corresponding to the anomalous diffusion coefficient z = 2(1 - η). The quantum field theory corresponding to the nonlinear stochastic problem is multiplicatively renormalizable and has an infinite number of coupling constants. The RG equations have a two-dimensional manifold of fixed points. Some of them relate to the stable asymptotic solutions and stipulate a general scaling with the critical dimensions of time Δ[t] = -2 + 2η and the energy field Δ[E] = d/2 - 3(1 - η). Possible corrections to the leading asymptotic behavior are discussed.

scholarly journals Reconstructing spacetime from the hologram, even in the classical limit, requires physics beyond the Planck scale

2016 ◽  
Vol 25 (12) ◽  
pp. 1644012 ◽  
Author(s):  
David Berenstein ◽  
Alexandra Miller
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behavior ◽  
Classical Limit ◽  
Additional Data ◽  
Planck Scale ◽  
Quantum Field ◽  
Counter Example ◽  
Classical Fields ◽  
Dual Quantum

In this paper, we argue that for classical configurations of gravity in the AdS/CFT setup, it is in general impossible to reconstruct the bulk geometry from the leading asymptotic behavior of the classical fields in gravity alone. This is possible sufficiently near the vacuum, but not more generally. We argue this by using a counter-example that utilizes the supersymmetric geometries constructed by Lin, Lunin, and Maldacena. In the dual quantum field theory, the additional data required to complete the geometry is encoded in modes that near the vacuum geometry lie beyond the Planck scale.

MULTIHADRON PRODUCTION AND A MODIFICATION OF POLYAKOV’S FORM

1992 ◽  
Vol 07 (19) ◽  
pp. 1749-1756 ◽  
Author(s):  
SAUL BARSHAY ◽  
PATRICK HEILIGER
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behavior ◽  
General Structure ◽  
Quantum Field ◽  
Similarity Hypothesis ◽  
Energy Formula ◽  
Multiplicity Distributions ◽  
Physical Impact

We compare a modification of the general structure of hadronic multiplicity distributions, derived by Polyakov from the dynamics of quantum field theory with a similarity hypothesis, to the multiplicity data at the present highest energy, [Formula: see text]. We emphasize the physical impact of Polyakov’s dynamics in the context of the possibility that limiting (asymptotic) behavior is nearly reached only at much higher energies ~1000 TeV.

scholarly journals HIGH ENERGY SCATTERING IN THE QUASIPOTENTIAL APPROACH

2012 ◽  
Vol 27 (01) ◽  
pp. 1250004 ◽  
Author(s):  
SUAN HAN NGUYEN ◽  
THI HAI YEN LE ◽  
NHU XUAN NGUYEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behavior ◽  
Scattering Amplitude ◽  
High Energy ◽  
Quantum Field ◽  
Quasipotential Approach ◽  
Scalar Particles ◽  
Systematic Scheme ◽  
High Energy Scattering

Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasipotential approach and the modified perturbation theory a systematic scheme of finding the leading eikonal scattering amplitudes and its corrections are developed and constructed. The connection between the solutions obtained by quasipotential and functional approaches is also discussed. The first correction to leading eikonal amplitude is found.

Asymptotic behavior of the Gell-Mann-Low function in quantum field theory

JETP Letters ◽  
2003 ◽  
Vol 77 (9) ◽  
pp. 453-457 ◽  
Author(s):  
D. I. Kazakov ◽  
V. S. Popov
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behavior ◽  
Quantum Field
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