TOPOLOGICAL STRUCTURE OF RENORMALIZATION CONSTANTS IN QUANTUM FIELD THEORY AT SHORT DISTANCE

1991 ◽  
Vol 11 (2) ◽  
pp. 221-224
Author(s):  
Shusong Zhao
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Topological Structure ◽  
Short Distance ◽  
Quantum Field ◽  
Renormalization Constants

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.

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 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.

Sign in / Sign up

Export Citation Format

Share Document