scholarly journals SCALING ALGEBRAS AND SUPERSELECTION SECTORS: STUDY OF A CLASS OF MODELS

2006 ◽  
Vol 18 (05) ◽  
pp. 565-594 ◽  
Author(s):  
CLAUDIO D'ANTONI ◽  
GERARDO MORSELLA
Keyword(s):  
Field Theory ◽  
Short Distance ◽  
Scaling Limit ◽  
Sufficient Conditions ◽  
Irreducible Representations ◽  
Quantum Field ◽  
Compact Lie Group ◽  
General Study ◽  
Closed Normal Subgroup ◽  
Distance Properties

We analyze a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R. Verch). In particular, we show that for each pair (G, N), with G a compact Lie group and N a closed normal subgroup, there is a net of observable algebras which has (a subset of) DHR sectors in 1-1 correspondence with classes of irreducible representations of G, and such that only the sectors corresponding to representations of G/N are preserved in the scaling limit. In the way of achieving this result, we derive sufficient conditions under which the scaling limit of a tensor product theory coincides with the product of the scaling limit theories.

scholarly journals SHORT DISTANCE PROPERTIES FROM LARGE DISTANCE BEHAVIOR

1998 ◽  
Vol 13 (23) ◽  
pp. 4101-4122 ◽  
Author(s):  
PAUL MANSFIELD ◽  
MARCOS SAMPAIO ◽  
JIANNIS PACHOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Large Distance ◽  
Short Distance ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
Expansion Coefficients ◽  
Distance Behavior ◽  
Distance Properties

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficients can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counterterms. We also describe an approximate simplification that occurs for the sine–Gordon and sinh–Gordon vacuum functionals.

scholarly journals Scaling Algebras and Renormalization Group in Algebraic Quantum Field Theory.

1998 ◽  
Vol 10 (06) ◽  
pp. 775-800 ◽  
Author(s):  
D. Buchholz ◽  
R. Verch
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Short Distance ◽  
Relativistic Quantum ◽  
Free Field ◽  
Scaling Limit ◽  
Quantum Field ◽  
Algebraic Quantum ◽  
Spatial Dimensions ◽  
Local Observables

The concept of scaling algebra provides a novel framework for the general structural analysis and classification of the short distance properties of algebras of local observables in relativistic quantum field theory. In the present article this method is applied to the simple example of massive free field theory in s=1,2 and 3 spatial dimensions. Not quite unexpectedly, one obtains for s=2,3 in the scaling (short distance) limit the algebra of local observables in massless free field theory. The case s=1 offers, however, some surprises. There the algebra of observables acquires in the scaling limit a non-trivial center and describes charged physical states satisfying Gauss' law. The latter result is of relevance for the interpretation of the Schwinger model at short distances and illustrates the conceptual and computational virtues of the method.

Introduction to renormalization theory and renormalization group (RG)

2021 ◽  
pp. 185-219
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Short Distance ◽  
Large Scale ◽  
Relativistic Quantum ◽  
Power Counting ◽  
Fine Tuning ◽  
Quantum Field ◽  
Renormalizable Theory ◽  
Renormalization Theory

A straightforward construction of a local, relativistic quantum field theory (QFT) leads to ultraviolet (UV) divergences and a QFT has to be regularized by modifying its short-distance or large energy momentum structure (momentum regularization is often used in this work). Since such a modification is somewhat arbitrary, it is necessary to verify that the resulting large-scale predictions are, at least to a large extent, short-distance insensitive. Such a verification relies on the renormalization theory and the corresponding renormalization group (RG). In this chapter, the essential steps of a proof of the perturbative renormalizability of the scalar φ4 QFT in dimension 4 are described. All the basic difficulties of renormalization theory, based on power counting, are already present in this simple example. The elegant presentation of Callan is followed, which makes it possible to prove renormalizability and RG equations (in Callan–Symanzik's (CS) form) simultaneously. The background of the discussion is effective QFT and emergent renormalizable theory. The concept of fine tuning and the issue of triviality are emphasized.

scholarly journals QUANTUM NOETHER'S THEOREM AND CONFORMAL FIELD THEORY: A STUDY OF SOME MODELS

1999 ◽  
Vol 11 (05) ◽  
pp. 519-532 ◽  
Author(s):  
SEBASTIANO CARPI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Scaling Limit ◽  
Momentum Tensor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Time Dimension ◽  
Complex Scalar

We study the problem of recovering Wightman conserved currents from the canonical local implementations of symmetries which can be constructed in the algebraic framework of quantum field theory, in the limit in which the region of localization shrinks to a point. We show that, in a class of models of conformal quantum field theory in space-time dimension 1+1, which includes the free massless scalar field and the SU(N) chiral current algebras, the energy-momentum tensor can be recovered. Moreover we show that the scaling limit of the canonical local implementation of SO(2) in the free complex scalar field is zero, a manifestation of the fact that, in this last case, the associated Wightman current does not exist.

scholarly journals Double-scaling limit of a broken symmetry quantum field theory in dimensions D<2

2001 ◽  
Vol 42 (5) ◽  
pp. 1960 ◽  
Author(s):  
Carl M. Bender ◽  
Stefan Boettcher ◽  
H. F. Jones ◽  
Peter N. Meisinger
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scaling Limit ◽  
Broken Symmetry ◽  
Quantum Field ◽  
Double Scaling Limit

FINITE CASIMIR EFFECT IN QUANTUM FIELD THEORY

1994 ◽  
Vol 09 (10) ◽  
pp. 1677-1702 ◽  
Author(s):  
A. BLASI ◽  
R. COLLINA ◽  
J. SASSARINI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Short Distance ◽  
Casimir Effect ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Quantum Field ◽  
Complete Control ◽  
Soft Term ◽  
Distance Behavior

The computation of the Casimir effect is directly linked to the modification of the vacuum energy due to the presence of boundaries. In order to have complete control of the short distance behavior also near the boundary, the analysis is performed in the precise framework of a local, renormalizable quantum field theory which includes the boundary contributions. We show that the presence of soft terms at the boundary, needed to implement Robin's conditions, introduces a free parameter in the final, finite answer, a parameter which has no natural normalization condition within the scheme. We discuss in detail a free massless scalar field in R3 with plane and cylindric boundaries; in particular the second case, where the boundary soft term is essential to remove sub-leading short distance divergencies, suffers the mentioned indeterminacy, which might be removed by a phenomenological interpretation relating the soft term to a microscopic description of the boundary.

scholarly journals Hidden Degeneracy in the Brick Wall Model of Black Holes

2003 ◽  
Vol 18 (21) ◽  
pp. 1463-1471 ◽  
Author(s):  
Kumar S. Gupta ◽  
Siddhartha Sen
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Short Distance ◽  
Black Hole Entropy ◽  
Brick Wall ◽  
Quantum Field ◽  
Wall Model ◽  
Brick Wall Model ◽  
Distance Cutoff ◽  
Degenerate Modes

Quantum field theory in the near-horizon region of a black hole predicts the existence of an infinite number of degenerate modes. Such a degeneracy is regulated in the brick wall model by the introduction of a short distance cutoff. In this paper we show that states of the brick wall model with nonzero energy admit a further degeneracy for any given finite value of the cutoff. The black hole entropy is calculated within the brick wall model taking this degeneracy into account. Modes with complex frequencies however do not exhibit such a degeneracy.

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